Macroeconomics Lecture Note - instruct.uwo.cainstruct.uwo.ca/economics/220a-570/JD Han - Notes for I… · Web viewMacroeconomics36 Chapter II Appendix. Macroeconomics. 13. Chapter

MACROECONOMICS

© J.D. Han*

King’s University CollegeAt the University of Western Ontario

Acknowledgement

"Of course, no reasonable man ought to insist that the facts are exactly as I have described them. But that either this or something like it is a true account ...... This, I think, is both a reasonable contention and a belief worth risking, for risk is a noble one......" (Plato, Phaedo, II 4 d.)

I wish to acknowledge that this lecture note owes greatly to the macroeconomics I have learned from Professor Jack Carr at the University of Toronto.

When I was leaving for my first teaching post at Carleton University in Ottawa, Professor Carr was so kind as to give his handwritten lecture notes. Professor Carr took macroeconomics from Professor Milton Friedman at the University of Chicago, and his notes contained many class examples taken by Professor Friedman.

I simply typed his manuscript and started teaching based on the manuscript. Just like I had done so in Professor Carr’s macroeconomics class, the students in my class positively responded to the simplicity of exposition, the depth of theories, and the relevance of examples. It encouraged me to expand the manuscript into a book length.

There are two reasons why I have decided to pursue a publication of my manuscript into a textbook format: First, most textbooks are too voluminous and too verbose with irrelevant examples and explanations. Second, they are expensive. The two issues are probably intertwined, and the second reason, which is an economic one, seems to dictate the first: There is a certain threshold price for a textbook in today’s marketing system, and a fair volume may be necessary to justify the price. A major problem, with which most instructors are faced, is that due to external constraint of time and voluntary choice to skip verbosity they end up using only a part of the textbooks. Students get disgruntled, feeling that a partial use of the textbook does not justify the price they pay. This book has come from our conviction that we can slim-down macroeconomics textbooks for both a better understanding of essential models, and a better satisfaction of our customer students.

I have been extremely fortunate to have talented and hard-working teaching and research assistants over the last 10 years. Robert Faissal, Lui Leo, Lisa Mo, Leo Wang, Karen Xuan, Herbert Zhang, Bochao Fan, and Kevin Chen have all worked on this manuscript at one point of time. They all have taken my macroeconomics course based on this book, and many of them have become a colleague economist. The copyright of this book is protected. No part of this material shall be reproduced without the author’s consent.

Macroeconomics 1 Chapter I. Introduction

Chapter I. Introduction

1. Key Issues in Macroeconomics: What are our interests and goals in Macroeconomics?

Economics is devoted to the betterment of human material welfare. The material welfare is measured best, at the practical level, by the per capita national income, which is equal to the GDP divided by the size of population.

In terms of per capita national income, the optimal situations can be described as follows: (1) The per capita national income should be high at the maximum potential level at any point in time; (2) the per capita national income should grow rapidly with minimum inflation, and (3) the national income should be stable over time.

We may also want a lowest possible rate of inflation and a stable price level as well.

(1) Maximum Potential Income: Full Employment - Short-term Goal

It is ideal if the actual national income approaches its maximum potential. How would we know whether or not the maximum potential is being realized now? One obvious indicator is the rate of unemployment. There is a one-to-one relationship between the unemployment rate and the level of national income: The higher the rate of unemployment, the lower the level of the national income.

The maximum potential national income can be called the ‘Full Employment National Income’ (Yf for its notation). The full employment national income or Yf does not correspond to the zero rate of unemployment, but to a certain positive figure of unemployment rates. That positive figure of unemployment rate is only ‘Natural’ and the best that we can achieve in terms of employment. Thus it is also called ‘Natural Rate of Unemployment’. In other words, the Full Employment means a positive figure of the Natural Rate of Unemployment or NRU in a short form (its notation is UN).

How do we know when the actual national income is below the maximum potential level? One sign is the existence of unemployment of production factors above and beyond the ‘natural level’. When capital and labour available are ùnder-employed', the aggregate income created from the employment of the factor does fall short of the maximum potential income, that is, the Full Employment (National) Income or the Natural Rate (of Unemployment National) Income.

Under-employment indicates the situation where the actual rate of unemployment (U) exceeds the natural rate of unemployment (UN): U>UN. The difference between the two unemployment rates is called `Cyclical Unemployment', which points to under-employment. The natural rate of unemployment is some positive rate of unemployment perfectly compatible with full employment, and consists of frictional and structural employment.

Questions arise as to a) the cause of, b) the duration of and c) the remedy for the under-employment situation where the actual national income is smaller than the full employment


income: What prevents an economy from enjoying the maximum potential income? How long would the undesirable situation of the under-employment last? In other words, is the under-employment transient meaning `will be gone', or of equilibrium, meaning `being stuck'? What can be done about the under-employment?

(2) Strong Economic Growth with Minimum Inflation - Long-term Ideal

The performance of per capita national income over time determines the future path of an economy in the long-run. In Canada, the national income evaluated at the current market prices or the market prices of each year grew at an average 10% annum during the ten year period of 1976-1986, 7% of which could be attributed to the simple increases in the prices and the rest to the actual growth of the amount of goods and services. In other words, the rate of the growth of national income in real terms is 3% per annum. This is a strong growth in the light of the size of the Canadian economy and its advanced stage of economic growth.

(3) Stabilization of National Income - Medium-term Ideal We would like to have a stable national income over time, having the least fluctuations and deviations from the Long-run Growth Trend. These ups and downs of the national income over time are called, in their entirety, ‘business cycles’. Minimizing business cycles, if possible, is welfare-increasing.

When the government is trying to stabilize the national income, it may use fiscal and monetary policies. The policies are called ‘income stabilization policies’ or ‘activist policies’. Whether the government can eliminate/reduce the amplitude and the duration of business cycles or not is an open question. Keynesians do believe that it is possible, and Classical economists think otherwise.

(4) Stable Price Level: A Low Inflation

Inflation is not just a nuisance. It leads to misallocation of resources, diverting valuable resources from their best uses. This may not decrease the accounting value of national income. However, it certainly decreases economic welfares.

The costs of inflation are represented with Menu Cost, and Shoe-Leather Cost, for instance. However, innocuous they may sound, they may seriously harm efficient allocation of resources.

Surprice inflation has an additional cost for the society: it helps employers at the expense of employees, and debtors at the expense of creditors.

(5) Trade Off Between Two Goals: Income versus Inflation.

Some economists argue that the above the goal of high income cannot be obtained by a low


inflation: The two goals cannot be achieved at the same time, and there is an inevitable trade-off between the two.

The level of national income is inversely related to unemployment rates. Therefore, the above argument means that a low unemployment rate (meaning a high level of national income) can only be achieved with a relatively high rate of inflation. As we will see later, this is the idea behind Phillips Curve.

Other economists do not agree with this. They argue that depending on the inflation expectations, a low rate of inflation and a low rate of unemployment can be achieved at the same time. This will be reviewed in terms of “Expectations Augmented Phillips Curve”.

2. Divided House of Macroeconomics Thoughts In contrast to microeconomics (Price Theory) where there is a general consensus, the macroeconomics has many irreconcilable divisions within its house: There are multiple schools of macroeconomic thoughts, which have quite different, and competing frames of references. Sometimes they are completely opposite. They tend to disagree on what the most important issues are, let alone what the solutions should be. We are going to review the Keynesian School, the Classical School, the Neo-Classical Synthesis, the New Classical School or the Rational Expectations Theory Model, and the New Keynesian School.

For instance, as to the key issues raised above, each school of macroeconomics thought has different views. Suppose that an economy is not achieving its maximum potential national income, or that the actual rate of unemployment is higher than the natural rate of unemployment.

(1) The Keynesian School of Macroeconomics Thoughts

The Keynesian school of macroeconomics was initiated by John Maynard Keynes through his publication of The General Theory of Employment, Interest, and Money in 1936.According to the

Inflation

Unemployment


Keynesian school, it is the lack of the economy’s aggregate demand that prevents the economy from achieving the maximum potential national income. The ‘cyclical’ component of unemployment rates will not easily go away: Some equilibrating or ‘anchoring’ forces hold the economy down at a level of under-employment. The remedy should be an injection of demand.

Given the bleak prospect of business, which presumably has caused the current recession, it is unlikely that any private economic agents, such as households or firms, will bring an additional demand for the economy: They are all concerned with, and thus constrained by the financial bottom line.

It should be the government that has to bring more demand to the economy. In fact, according to the Keynesian view, the government is able to do so, as it is not constrained by the budget constraint: The government is the only economic agent that can spend more than earn for a prolonged period of times due to its prerogative or sovereign privileges of printing paper monies and issuing bonds.

How about an increase in the aggregate supply? It would not resolve the recession: The recession was caused by ‘too little demand amid too much supply’. An increase in supply will be just added to inventories, which will put more downward pressures on production processes at the corporate level.

Can we reduce the unemployment with wage cuts? In fact, all the economists in the 1930swere believed that wage cuts were classical. They believed that workers could not get a job or were unemployed when they demanded too high wages. Thus, they thought that the only solution to the Great Depression was a wage cut: If wages are cut, and thus the cost of hiring workers is reduced, in the very short run there occur incentives for employers to hire more workers.

However, Keynes disagreed. The above solution is unsustainable. If wage rates are cut, some may get new jobs. More outputs may be produced. However, there will be a reduction in the wages of the previously employed labor forces. The total aggregate wage bills may decrease. If so, there will be less consumption, and thus the newly produced outputs will not be sold. The production should scale down, and the national income falls.

Keynesian Arithmetics: Why wage cuts worsen a recession?A major component of the aggregate demand is consumption: AE = C (+ I + G + X-M).The consumption of the workers’ households depend on the component of their income, which is the total wage bills: C = f(Y), and Y = W (+ R + Int. + Profits).The total wage bill for the economy = nominal wage rates (Wage rate) x number of employed workers (#): When Wage rates go down and # goes up, the product of the two may go up or down, depending on the relative magnitude of a changes in W and a change in #. If Wage rate (a decrease in the wage rate) exceeds #, then the total wage bill rises. Thus the consumption goes up and so does the aggregate demand.If Wage rate (an increase in the wage rate) falls short of #, then the total wage bill falls. Thus the consumption goes down and so does the aggregate demand.

(2) The Classical School of Macroeconomic Thoughts


On the other hand, according to the economists of the Classical school, as long as there is a well-functioning labor market system without undesirable impediments, a prolonged recession is impossible while certain degrees of short-run fluctuations might be inevitable.

Under-employment of a production factor (such as labor) situation comes from the temporary failure of the alignment of supply and demand of the factor (labor) market. Most commonly, unemployment occurs when some workers are demanding too high a wage rate and thus are not hired by any willing employers. In the absence of any stubborn stupidity of individuals (such as money illusion) and any structural rigidity of the economic system (such as unions), in the long-run as the workers `come to their senses' out of hardship and lower their wage rate to a reasonable level, the unemployment will vanish. Therefore, as long as the functioning of market forces is not hindered, eventually (in the long-run) the national income gravitates to the level corresponding to the full level of employment. The full employment (national) income is the very equilibrium income at least in the long-run.

Money Illusion

How many workers are going to work for how many hours (a week) depends on the workers’ motivation. The motivation in turn depends on the reward for work that workers perceive to receive. Note that it does not have to be the actual reward, but the ‘perception of rewards’. If workers somehow do not feel rewarded enough for their work efforts, they would not supply labor forces and would rather go for leisure or unemployment.

The rewards for a worker should be measured by ‘how much commodities or outputs can he purchase with the money wage’: In other words, the labor supply should be an increasing function of real wages.

However, some workers may have some hang-up on a particular value of nominal values for their wages. While they really should pay attention to real wages or real values of their wages, they are erroneously sticking to a certain nominal or money value of wages. This is called ‘money illusion’. The word ‘money’ is the opposite of ‘real (value)’.

In the Keynesian school of macroeconomics, money illusion is an important element in the derivation of its aggregate supply curve.

In the classical school of macroeconomics, ultimately in the long-run, money illusion does not exist.

The short-run fluctuations or business cycles are inevitable. In fact, recessions give a good lesson to undisciplined workers and correct them. They are the periods of consolidation and adjustment for the better. What we can do best to the economy in the short-run is to inform the worker correct and to remove any structural rigidity because both hinder the smooth functioning of the market forces.


Is there any way of increasing the full employment income in the classical model? Yes, in the long-run, there is. The level of full employment income is constrained by the amount of production factors. Even the national income might be at the full employment level, but the actual value is small because the level of the full employment income is low. For instance, suppose that there is a large population yet a small amount of capital in an economy. The scarcity of capital imposes a bottleneck in the production: The low capital-labor ratio means a scarcely equipped worker having a low productivity of labor. The national income is stuck low at the ‘low’ full employment of the existing capital and labor. It is not too difficult to imagine an economy where workers are fully employed, tinkering all day long with poor equipment, for a pittance. The situation is a kind of ‘low level equilibrium.’

According to the classical school of macroeconomics, the level of the full employment income can be raised with a breakthrough in the availability of production factors. If the amount of capital increases or there occurs an innovation of capital-saving technology, the workers’ productivity will rise to bring larger wages. The level of the full employment national income will rise.

3) Differences between Classical and Keynesian Schools

This disagreement between the two schools is highly politicized in the realm of policy issues. They do have fundamentally different views on the role of government in the economy: Except for some monetarists (to whom the author belong), it is generally accepted that a government's expansionary monetary or fiscal policy will increase aggregate demand. However, the rightward shift of the aggregate demand curve may bring different impacts on the price level and the national income depending on the shape and configuration of the aggregate supply curve.

In other words, Keynesian and Classical schools do operate on different assumptions of the aggregate supply conditions. In the Keynesian School, there is a positive economic role for government: Expansionary fiscal and monetary policies which shift the aggregate demand to the right will bring about and increase in real national income without any increase in the price level. In the Classical school in its alliance with fiscal and monetary conservatives, it is argued that the lasting impact of the increased AD due to an expansionary monetary or fiscal policy is only inflationary.

This difference in political implications comes from the different assumptions of the supply conditions. Keynesians assume that the Aggregate Supply curve is horizontal or relatively flat. What does the horizontal supply curve mean? It means that the (aggregate) supply (of all the goods and services) increases greatly in response to a very small stimulus of an increase in the price level. In other words, the aggregate supply is infinitely elastic with respect to the change in the price level.


Recall that in microeconomics the price elasticity of supply measures the increase of supply in response to a unit price rise.

For a given increase in price, the responsive increase in supply is relatively small in Case I: the supply is inelastic with respect to price. For the same increase in price, the resultant increase in supply is relatively large in Case II: the supply is elastic with respect to price. The first case is close to the assumption of the Classical school and, the latter to the Keynesian aggregate supply curve.

Why is the aggregate supply assumed to be elastic in the case of the Keynesian school? The Keynesian economics came out during the Great Depression when there was a lot of unemployed workers and idle capacities. In the face of a rising price of output, entrepreneurs could easily increase production and supply of output without substantially raising the costs of hiring production factors. This means that the supply could be so easily expanded, and was very responsive and elastic with respect to a rise in output prices: the supply curve was in fact almost horizontal.


With this configuration of the supply and demand curves, only the shift of the aggregate Demand curve will bring about an increase in the equilibrium national income. Put differently, when a government is engaged in expansionary monetary policy (by increasing money supply [MS]) or/and fiscal policy (by increasing government expenditures [G] or cutting taxes [T]), the resultant increase in the aggregate demand shifts the aggregate demand curve. It will bring about only benevolent impacts on the economy: the national income rises while the price level remains unchanged. The rigidity of the general price level is the cornerstone of the Keynesian theory.

The Classical school consists of many branches, but they all basically assume a vertical aggregate supply curve for the economy. For instance, the Monetarists belong to a branch of classical school largely attributed to Milton Friedman. They argue that there are two kinds of the aggregate supply curve. The long-run Aggregate Supply curve is vertical while the short-run Aggregate Supply curve may be positively sloped. In the long-run, as all production factors are more or less fully utilized in the economy in its own way. An increase in the price of outputs does not lead to any increase in production. The aggregate supply curve is vertical at the full employment level. The vertical AS curve implies that it is impossible to increase the equilibrium national income only by increasing the AD.

With the given configuration of the aggregate supply and demand curves, expansionary monetary policy (increasing money supply [MS]) or/and fiscal policy (increasing government expenditures [G] or cutting taxes [T]) increases aggregate demand [AD] and shifts the AD curve. It will bring about only a rise in the price level.

In this situation, only a (rightward) shift of the aggregate supply curve can bring about an increase in the equilibrium national income. In this case, the equilibrium national income is also the full employment income. It may be timely to be reminded of what the major production factors are: capital, labor, and technology. Therefore, only an increase in the stock of capital, an increase in labour force, and technological innovations can lead to an increase in national income. If the government is going to increase the national income, it has to focus on the breakthrough in the supply side. Its economics focuses on the Supply Side. It has to be the “Supply Side of Economics”.


4) Neo-Classical Synthesis

The Neo-Classical School is a synthesis of the Keynesian and Classical ideas. It adopts the Keynesian aggregate supply (horizontal) curve for the short-run and the Classical aggregate supply (vertical) curve for the long-run. Thus the Neo-classical AS curve has upward sloping and vertical segments. Therefore, an increase in the AD leads to an increase in the national income in the first range, a simultaneous increase in the national income and the price level in the second range, and an increase in the price level in the last range.

5) New Classical School of Macroeconomics: “Rational Expectations Theory”

As we might have noted, there is no obvious presentation of the short-run fluctuations of income in the classical model. The New Classical Macroeconomics or Rational Expectations Theory is the most recent offspring of the Classical school. It has come up with exposition of short-term fluctuations in terms of expectations failures. In short, it states that only unanticipated changes in the Aggregate Demand (AD) leads to short-run fluctuations of the national income.


The theory adds Expectations Augmented Aggregate Supply Curve (EAS hereafter) to the classical model. This EAS curve moves around as the public's expectations as to the price level which in turn depends on the aggregate demand:

When shifts of the AD are anticipated/expected (to bring about changes in the price level), the EAS shifts up simultaneously to nullify any impact on the equilibrium national income. The path of motion is given along the vertical AS curve in the first panel below. For instance, as long as it is fully expected, any government policy which results in an increase in the AD will not have any impacts on real variables such as real wages, level of employment, and real national income: When a rise in the price level is expected, the workers and entrepreneurs will revise their expectations about the price level and rewrite the wage contract to reflect the increase in the money wages. Proportional increases in the price level and the money wages lead to the constancy of real wages and all other real economic variables.

This is called the “Policy Invariance Theorem” or “Policy Ineffectiveness Theorem”: Any anticipated (monetary) policy does not have any impacts on real variables such as real national income. This is the major criticism of so-called “Activist Monetary Policy”, which advocates the use of monetary policy to stabilize the national income. The Policy Invariance Theorem suggests that as long as they are fully announced, monetary policies do not achieve the intended goal.

Only unanticipated shifts of the AD curve will not be accompanied with shifts of the AS curve. Wrong expectations can happen in the short-run: over-expected, under-expected or unanticipated events may occur. In this case, the AD shifts without the offsetting shifts of the short-run AS curve. This leads to temporary deviations of national income from the full employment level. However, in the long-run when expectations catch up with the reality, -unless another unexpected events involving the AD happen- in any case the EAS will eventually shift by the same amount and in the same direction of the AD curve to nullify the short-term deviation. The path of motion is given as 1 to 2, and to 3 in the second panel below.

Anticipated Changes in AD : Unanticipated Changes in AD:No changes in Y* Changes in Y* in the Short-run;

In the Long-run Y* = Yf


6) New Keynesian School of Macroeconomics

The New Keynesian school tries to explain fluctuations of national income in terms of structural rigidifies such as long-term non-indexed labor contracts. Most wage contracts cover a multiple number of periods and do not have the clause of escalating the money wages along with inflation.

In this model the wage contracts are signed on the basis of ex-ante expectations as to the future price level. Once the contracts are signed, nothing can be done about the wage in response to changes in the AD situations and the price level. Unexpected changes in the price level result in changes in real wages, employment, and real national income.

7) A Pendulum of the History of Macroeconomic Thoughts

The above investigation suggests that the Keynesian school focuses on the demand; and that the Classical school focuses on the supply.

Let’s put these macroeconomic theories in historical perspectives: The historical progression of economics theories mirrors changes in an actual economy, with a time-lag. The most pressing economic concern of the time called for a new frame of reference which suggests a new solution for the problem. Each theory, to a large extent, is the child of times. And as the times change, the theories change. In the pre-industrial age, the greatest economic concern was the bottleneck in production, or the shortage of the supply of goods and services. It was best epitomized in the famous `Malthusian Apocalypse': the growth of production (of food) would never catch up with the increasing demand (for food) propelled by a growing population. Therefore, excess demand or general famine seemed inevitable. Naturally, the focus of economics was on how to make a breakthrough in production or supply. For instance, Adam Smith extolled the benefit of the division of labour, specialization, and scales of economy in production.


The bottleneck on the supply side was removed by the Industrial Revolution which accelerated innovation and technology in production. The demand also grew: the territorial expansion of imperial powers brought markets that created an increased demand for production. In the early twentieth century, however, market expansion reached its limit. There occurred signs of general glut, or of supply exceeding demand.

On October 24, 1929 the precipitous crash of the New York Stock Market triggered the Great Depression. Unsold goods piled up. Physical capital, equipment and human capital was the problem. The second part of the problem is called ùnemployment'. Unemployment was the key social issue. It was regarded by the classical school as a necessary adjustment period of `cooling down' after a century of dashing expansion and growth on the supply side. However, Keynes regarded the depression as a rising from the lack of purchasing power, or effective demand. As there were idle capacities, the supply curve was not a problem: the production could increase very easily with just a small stimulus. The larger the demand, the higher the equilibrium national income level becomes. For instance, in order to increase in national income, consumption and spending should be encouraged. Thrift, which leads to a smaller consumption and thus a smaller demand, should be discouraged as a vice. This contrasts with the fact that thrift is a virtue and a way of achieving prosperity at the level of individuals. What is true of individuals is not necessarily true of the society as a whole. Keynes pointed out the fallacy of composition in savings or thrift, and called it the `Paradox of Thrift.'

In addition, in order to ensure the stability of income, Keynes came up with the so called Àggregate Demand Management Policy'; He argued that the investment demand is the major source of fluctuations of the equilibrium national income and thus too volatile to be trusted with the private sector. So semi-autonomous institutions not based on profit principle should be created to be in charge of the aggregate demand management.

The Keynesian economics was transplanted in the experimental farm of the American New-Deal policy. It became a sort of hybrid by being merged with some classical economics into so-called `Neoclassical Synthesis'. Behind this marriage was the social atmosphere of the time: the original policy recommendations by Keynes were modified to be acceptable by the Americans. For instance, the Àggregate Demand Management Policy' by a semi-autonomous institution was too suggestive, of a planned economy or a George Orwellian authoritarian society, for the Americans to swallow. So the new eclectic policy recommendation was made that government should intervene in an economy only when there is overheating or over cooling of economic activity, or in other words, when there occurs a deviation of the economy from the long-run trend. That is called `Counter-cyclical Policy' or `(Income) Stabilization Policy'. Subsequently, it gained a wide acceptance particularly in the post-war United States and the world.

Up until the 1970s, on the basis of the Keynesian principle the government was freely engaged in the `fine-tuning' of the economy. The end result was increased spending which led to the development of an inflationary trend. The policies designed to counter inflation then smothered the private production sector.The resultant combination of high inflation and high unemployment, or stagflation, could not be resolved within the Keynesian frame of reference.


Here came the Monetarists represented by Milton Friedman who reemphasized the basic tenet of the classical school: “There is no such a thing as a free lunch.” The aggregate demand management policy ultimately cannot increase the national income in the long-run. The real national income cannot be increased at no real cost through gimmick policies: Increases in production factors, such as capital stock (K), labour inputs (L), and better Technology (T) should shift the AS curve in order to have a lager equilibrium national income. Capital stock can increase only when the citizens save by practising thrift and the increased savings are channelled into a larger amount of investment. ‘Toil and labour’ is required to increase the labour input. ‘Ingenuity’ should be encouraged to facilitate technological innovations. The government has no direct control over these variables of the supply side.

He goes one step further to suggest that government policies can possibly do more harm than good. The time-lag of policies severely limits the economic role of government. For instance, there should be a ‘rule’ as opposed to discretion in money supply, so that the government cannot arbitrarily resort to the increase in the money supply to finance its deficit.

New Classical economics or the rational expectations theory emerged in the 1970s. They shared policy views with the Monetarists. The market consists of rationally forecasting and behaving individual economic agents, and works best if being left alone. The basic tenet is the ‘Policy Ineffectiveness Theorem’ that anticipated government policies are ineffective without any impact on real macroeconomic variables such as real national income or investment: anticipating economic agents.

Macroeconomics 14 Chapter II. National Income Accounting

Chapter II. National Income Accounting

Now this is the time for some tedious, yet important, number crunching. Our macroeconomic goals have been expressed in terms of national income. How to calculate the national income? What determines the level of national income as we have?

1. The Theoretical Part of the National Income Accounting System

1) Supply Sides of National Income

(1) Income Approach

There are two aspects of national income: How it is created, and how it is disposed of.

i) Creation of National Income

The National Income with its notation of Y is the sum of the incomes of all the households/individuals. The categories of income are a) labor income such as wages and salaries (W), b) investment income such as rents (R) and interest payment (Int.), c) profits (P) claimed by entrepreneurs. They are the payments for the production factors (Factor Payment) engaged in production, which are not explicitly shown but implied in the above table:

National Income or Y = W + R + Int. + P = Factor Payments ........(1)

The source of the Factor Payments/Costs and Profit is the Value-Added, which is equal to Total Revenues minus Material Costs. At the aggregate level, VA is the sum of the net increase in values over material inputs in all industries:

Value Added = Total Revenues – Material Costs ........(2)

Total Revenues from the sales of final goods are equal to Total Production Costs plus Profit: TR = TC + P.

The Total Production Costs can be broken down roughly into the Costs of Materials (MC) and the Costs of hired Factors(FC: Factor Payment minus Profit):

TR = MC + FC + P = MC + Factor Payment ........(3).

Therefore, from (1) and (3.b), we get Y = W + R + Int. + P = VA = Factor Payments.

Note that not all incomes at a personal level are to be included in the national income. The only personal income, which is the factor payment or the reward for participation of production process, is qualified to be included in the national income. For instance, pension income has no counterpart of production, and is not to be included in the national income.


National Income versus Personal Income

The National Income is not simply a sum of incomes of all individual residents of the economy. Personal income consists of two parts; one is earned income, and the other is given or transferred from others' earned income. The first is a part of national income, and the second not. For instance, out of the Gross National Income (= W + R + I + P), some portion will not come to individuals: Depreciation does not go for consumption by individuals. Part of Corporate Profits will remain undistributed in the firms to become UDCP (Undistributed Corporate Profits). Corporate Profits taxes (CPT) will go to government. In addition, there are some personal income items which are not earned -so they are not part of National Income, but are simply given to individuals: Transfer payment (TR) and Interest payment on bonds (IB).

(Aggregate) PI = GDI - D - UDCP - CPT + TR + IB.

Personal Disposable Income is after-tax income for individuals:PDI = PI - Direct Taxes.

ii) Disposal of National Income

With income, first you pay taxes, and then you spend on goods and services. The latter is Consumption Expenditures. Then, any left over will be saved: Savings.

Y = C + S + T

(2) Output Approach

Another way of measuring the national income is getting the total value of the goods and services produced as the result of the above production process.

Frequently, we use GDP or GNP to measure this aspect of national income.

The GNP or Gross National Product is defined as(a) the total market value (b) of final (excluding intermediate) goods and services(c) produced (not only sold but also added to inventory) (d) by the citizens of an economy (e) for a year (within a current year).

The GDP or Gross Domestic Product is defined as the total market value of final goods and services produced in a country for a year.

First, let’s explain why only final goods and services are included :For the above economy, in calculating the GNP, we count only $ 25, not $ 55. Here the principle is to count the value of every good but once. The problem of double-accounting is counting the


value of some outputs twice or more. The values of the material inputs or intermediate goods should not be counted separately once the values of final goods which use them as ingredients are counted. When we take account of final goods, we are taking the value of intermediate goods, which make up the final goods, into account. Counting the value of intermediate goods separately in addition to final goods leads to double counting.

Double Counting in the National Income Accounting System:

Problem of double counting is the most serious with government sector. According to the Output approach, the value of final goods and services produced by the government should be included.

Since there are no markets where government goods and services are bought (or evaluated), the value of goods and services produced by government or `public goods' are evaluated at their production costs. Subsequently, the value on the basis of cost is included in the national income.

Whenever government makes expenditures to produce some goods and services, the national income accounting system simply assumes that there occurs an increase in national income by the amount of government expenditures; all government expenditure is assumed to be on final goods. The very problem blurs the distinction between final and intermediate goods in the government sector.

Second, what does it mean by “by the citizens of an economy”:If all the goods and services produced by the citizens or the nationals are summed up, the result is Gross National Product.

If all the goods and services are produced by the residents, national or non-national, the result is Gross Domestic Product.

GDP versus GNP

The difference is created by the foreign and overseas investment.Some countries have many citizens as well as their capital (money) working overseas. In this case, GNP is larger than GDP. Japan and Holland are good examples. Kuwait is another example where a lot of her citizens doing business and residing in foreign countries.

The countries, which take a lot of foreign investment, should have GDP larger than GNP; not all of what is produced in the countries is necessarily produced by the national. Canada belongs to this group.

The difference between GDP and GNP is the net factor payments to foreign residents, who have contributed production factors, such as capital, labor, and management skills to the domestic production.


Third, the only goods and services produced within the current year are included:

Last, but not least, what if there are no market prices? Certain goods and services do no go through the market and thus they do not carry any prices.

The goods and services produced by the government or public goods should be included in the National Product. There arises a question of how to come up with the market value of public goods? How to include the value of the Gibbon's park service on Sunday? How about an hour of lecture delivered by a professor? How about national defence by the military forces?

There is no market or market price for any of these public goods. So the National Income Account calculates the value on a cost basis: The operating costs for the park service are its value. The total costs incurred in creating an hour of a university lecture are the value of the educational session that enters the national income accounting. Therefore the value of public goods is equal to their cost of production.

In this method, we are measuring the National Product(NP) or the Aggregate Output (YS) while Method I focuses on the National Income (NI or Y as a shorter abbreviation). It is found that in this simple economy, without government or foreign sector, the National Income, obtained in Method I, is equal to the National Product in Method II at all times:

National Income = National Product;Domestic Income = Domestic Product;Aggregate Income = Aggregate Product, or Y = YS at all times.

If a $ 1,000 billion or $1 trillion of national income is created in the economy, then aggregate outputs of the same amount must be produced newly in all industry in a year.

In sum, the supply side of the national income is

W + R + Int. + P = Y = C + S + T (Creation) (Disposal)


Can you express Y = YS graphically?

Put Y on the horizontal axis;Put YS on the vertical axis;Draw the line with an angle of 45 degrees – Remember a 45 degree line has the slope equal to one.

Macroeconomics 19 Chapter II Appendix

2) Demand Side = Expenditure Approach

Method III: Expenditure Approach)

We have so far focused on the supply side in the circular flow of goods and services in an economy. The value of supply of final goods and services is equal to their value of demand. In a general economic model, who demands goods and services?Consumers, firms, government, and foreigners.

The value of demand for an entire economy or is the sum of expenditure or Aggregate Expenditures (AE) on all the domestically or nationally produced goods and services. They consist of the following demands: First the expenditures by the consumers is called ‘Consumption Expenditure’ with the notation of C; the demand by the firms is called ‘Investment’ with the notation of I; the demand by the government is called ‘Government Expenditures’ with the notation of G; and the demand by the foreigners is called “Exports’ with the notation of X.The sum of these expenditures is the Aggregate Expenditures: AE = C + I + G + X.Two important points should be made:

Why C + I + G + X – M?

First, for the accounting simplicity, in reality the statistical data of C, I and G include the components of foreign goods and services. For instance, you must know how much the total amount of your annual consumption is. However, can you break the total amount into the expenditures on the domestically produced goods –made in Canada- and the foreign made goods? Probably, we cannot do that at the individual level. So, C, reported or collected, must contain the expenditures on the domestic as well as the foreign (made) goods and services.

As the Aggregate Expenditures are on the domestically made or the nationally made goods and services, the foreign components should be subtracted. Although we do not know our individual expenditures on foreign goods and services, the total expenditures on the foreign goods and services, which are made by all the civilian households, firms and government agencies, can be captured by the customs office in its aggregate data of Imports (with the notation of M).

Therefore the aggregate expenditures on the purely domestically produced goods and services are equal to C + I + G + X – M.

The difference between the Ex-ante and Ex-post Aggregate Expenditures

Second, there are the ex-ante aggregate expenditures and the ex-post aggregate expenditures.There are two different kinds of demands or expenditures depending on whether or not the expenditure or demand is planned ahead of time.

The difference between the ex-ante and the ex-aggregate expenditures is Inventories. Inventories are goods which are not demanded now and thus carried over the next period. In a sense, as the firms would not throw these inventories away, the inventories are regarded as ‘being demanded by the firms themselves’. Obviously, this part of demand or expenditures was not planned at all


by the firms, but in fact is made after the unfolding of the unfortunate result of planned expenditures falling short of supply. In this sense, it is ex-post (after the event) demand. This part of expenditures on inventories by the firms is regarded as ‘ part of Investment for the future sales’, and thus is to be included in I.

In sum, ex-ante I + Inventories = ex-post I, or

AE ex-ante = C + planned I only + G + X – M: only sold part of aggregate products is included.AE ex-post = C + planned I + unplanned I or Inventories + G + X: all part of aggregate product is included.

What about the Depreciation of Capital?

Investment is the sum of net investment and depreciation (allowance). Depreciation is capital consumption or wears and tears of capital stock. Allowances are needed to maintain the constant level of production capacities. Capital Consumption Allowances and depreciations are different names for the same thing:

Net Investment = Gross Investment - Depreciation

This depreciation makes difference between the Net and Gross concepts of National Income or Product:

Net National Product = Gross National Product - Depreciation;

NDP (Net Domestic Product) = GDP (Gross Domestic Product) – Depreciation

Elusive concept of Deprecation and Capital

In reality, however, we do not see any international comparison of national income done with NDP (Net Domestic Product), NNP(Net National Product) or any Net concept of national income or product.

The reason for this lies in the difficulties in measuring the wears and tears of capital. More fundamentally, the main problem is defining capital in the first place; what is capital? It involves a fair amount of ambiguity to draw a line between durable and non-durable goods. Usually, all goods that have a life longer than certain duration will be treated on a capital basis, their wears and tears are regarded as capital consumption. On the other hand, the goods that have a life span shorter than this duration will be treated on an inventory basis and their using up is treated as a cost of production. The dividing line is intrinsically arbitrary.

Each country could have different tax regulations concerning the allowances for capital consumption. The `magic number' happens to be 3 years in Canada now. This amount of depreciation (capital consumption) depends crucially on the above rule of defining what constitutes capital. The Net Domestic Product is an economically more meaningful concept than GDP, but because of the difficulty in measuring depreciation GDP is used.


These Net concepts of national income or national product may measure the total amount of outputs available for consumption and investment above the maintenance of the present economic level. Thus they give us an idea of what is available for consumption. Deprecation Allowances of the National Income should not be consumed away. Therefore, if we are interested in a national income as a measure of the standard of living or, we must look at the Net concept of National Income or Product.

3) Equilibrium National Income: Circular Flow of National Income

It is established that Y YS = AE ex-post in reality at all times. The equalities are of identity: they are trivially equal to each other at all time, i.e., at the equilibrium as well as at the disequilibrium.

However, Y = YS = AE ex-ante only at the equilibrium. Of course, Y = YS = AE ex-post.

And at the disequilibrium, (Y = YS) AE ex-ante. Still Y = YS = AE ex-post.

Let’s have some numerical examples which illustrate the difference between the ex-ante and the ex-post Aggregate Expenditures:

Suppose that there is only one demander, and there is one supplier in the economy. They meet each other only once a year on the market day.

Prior to the market day, the demander will come up with how much he would like to purchase on the market day. The amount, say $100 billion, is the planned or ex-ante demand or expenditure.

On the other hand, the supplier guesses how much the demander will purchase, and produces outputs. Suppose that the total amount of the outputs is $120 billions.

On the market day, the supplier and the demander reveal each other’s figure at the market. Obviously, it turns out that the demand falls short of the supply by $ 20 billions. There will be $ 20 billion worth of products left over at the end of the day. They are not going to be left on the market. They will be taken back by the supplier for future sales. Who demands these inventories? The producer. Under what category? Investment on inventories, but they are unplanned or ex-post (after the market day) demand.

YS = Y = 120, and ex-ante AE = 100.

Thus,YS > AE ex-ante.

This is a disequilibrium.

SD = AE


How much will be the production level for the next year, assuming that the AE level will remain constant? The producer will produce only $ 80 billions so that the supply will be equal to the demand at $ 100 billions. That is how much income is going to be created: for the next year, Y = YS = $ 80 billions. You note that Y will decrease as S > D or YS > AE.

In this case, the total ex-post demand is the sum of the ex-ante demand of $100 billions, which has been planned, and the unplanned demand or inventory accumulation of $ 20 billions. Thus, the total ex-post AE = 100 + 20 = 120, which is equal to the supply. The unplanned AE will always fill the gap between the ex-ante AE (Demand) and the supply.

Now we are not going into specific mathematical equations for the aggregate expenditures. We will cover them in the next section. However, in general what kind of AE curve are we looking for the equilibrium?

Recall that the supply side of national income gives the curve Y = YS which is a 45 degree line. The equilibrium means the intersection of Supply and Demand curve. The demand side curve or AE curve should be sloped less than at 45 degrees, and should have some positive vertical intercept.

What kind of individual components of expenditures would lead to this Aggregate Expenditure curve? We will examine them in the next section.

Let's sum up:

-National Income: W + R + Int. + P = Y = C + S+ T

-Aggregate Output or National Product: YS = Pmarket x Qfinal

-Supply Side: Y = YS at all times.

-Demand Side: ex-ante AE = C + I + G + X –M ex-post AE = C + I + Inventories + G + X – M

-Equilibrium: Y = ex-ante AE in equilibrium.

C + S + T = C + I + G + X –MS + T + M = I + G + X

↓ ↓ Leakage Injection


This equality can be well illustrated with the following Circular Flow Chart:

Note: The following Leakages (S and T) and Injections (I + G) should be explicitly written on the above corresponding arrows:

For Financial Intermediaries = Banks, the leakage is S(saving) to the right of the above graph, and the injection is I(investment funds provided by banks) to the left of the above graph.

For Government: In this case, the leakage is T(tax) to the right of the above graph, and the injection is G(government expenditures) to the left of the above graph.

4) Applications of the Equilibrium Condition for National Income

(1) Principle

Ex-ante (meaning that we exclude Inventories from the Aggregate Expenditures)As we can see in the above chart, the injection combined together (I + G + X) is not necessarily equal to the leakage put together (S + T + M). The investment here is the planned one. Only when they are equal to each other, there is an equilibrium, where the current level of flow of the national income persists.

When the injection is larger than the leakage (I + G + X > S + T + M), the flow levels up and the national income rises.

Ex-post (meaning that we include Inventories in the Aggregate Expenditures)I + Inv + G +X = S + T + M at all times, at both equilibrium and disequilibrium. The total


investment is the planned investment I plus the unplanned investment, i.e., inventory accumulation.

(2) What we do actually see is the ex-post aggregate expenditure.

The statistical book of the National Income Accounting reports Investment as the sum of the planned I and inventory accumulation: The investment reported in the NIA is the ex-post aggregate expenditure. Thus, the Y=YS = ex-post AE: The three aspects of the national income are equal to each other.

Thus, in the statistical book, the supply is equal to the demand. However, the demand is the ex-post one. Thus, the equality of the supply and the demand does not mean that the economy is at the equilibrium and the national income will persist at the present level.

(2) Applications:

i) “Twin Deficits”

The condition for the equilibrium national income is ex-ante I + G + X = S + T + M.

In economics, we assume that the economy gravitates to this equilibrium condition: related economic variables do change in the way to bring about the equilibrium.

We can re-arrange the equilibrium condition for national income as

I - S + G - T = M –X.

I – S is the investment in excess of savings; G- T is government expenditures in excess of tax revenues, or in a word, government budget deficit; and M-X is exports in excess of imports and thus international trade deficit.

If the part of I-S is held constant, an increase in the other left-hand side variable, G-T or government budget deficit, leads to an increase in the right-hand side variable, M-X or international trade deficit. One cause of international trade deficits is government budget deficit.In many cases, we observe the two deficits rising at the same time. Thus, government budget deficit and international trade deficit are just like “Twins”. They are called “Twin Deficits”.

ii) “Trade deficit is an indicator of a good prospect of the economy”

We can look at another cause of international trade deficit: In the above equation of the equilibrium condition for national income, if G-T is held constant, an increase in M-X or international trade deficit goes hand-in-hand with an increase in the term I-S or investment in excess of savings.

When investment exceeds savings, domestic savings falls short of the total investment. The


difference comes from the foreign country. In other words, the difference between investment and savings is the foreign investment. If a country has a bad prospect, no foreigner would bring any investment to the country. The strong investment from foreign countries is an indicator of a good prospect of the economy.

At this time, we can reflect on the U.S. trade deficits. Many argue that the U.S. trade deficits are caused mainly by some countries’ unfair trade practices: The Japanese government might be blocking the imports of the U.S. goods. However, the above applications of the equilibrium condition for national income provide us with quite different perspectives: First, the U.S. trade deficit may be caused by the government budget deficit. In fact, it can be supported with historical data. Second, the U.S. trade deficit may be also caused by the strong investment demand, which goes beyond the savings by the American people and thus is supplemented by the foreigners bringing investment funds to the U.S. This is something to welcome.

2. Technical Part of the National Income Account (Review from the first year economics class)

1) How to measure the National Income and the Price Level?

(1) Nominal versus Real National Income

We have obtained the National Income by evaluating the aggregate output of the current period, say year t, at the current market prices. Let's call it the Nominal National Income (its notation is Yt):

Yt = Pt Qt .........(1)

The nominal GDP was $190 billion in 1976 and $672 billion in 1989. Not all of what appears to be the growth of GDP is the indication of a raised standard of living. Why? Because part of the increase in the GDP is simply the result of an increase in the price level or inflation. Only the increase in the real quantity of goods and services or the aggregate output helps raise the standard of living. The change in the GDP consists of an increase in the price level and the growth of aggregate output.

How can we measure a change in the aggregate output alone, separately from the changes in the price level? We can do it by controlling the price level or by using the same price level for the two time points. First of all, we choose a certain time-point(year) for a benchmark, and call it the base period(year). There are two time points: the base period and the current period. In the base year the price level is P0, and the aggregate output Q0 includes various final goods and services. In the current period the price level is Pt and the aggregate output Qt.

The National Income of the base period is

y0 = P0 Q0 ........ (2)


Note: There is no difference between the Nominal and Real National Income for the base period as P0= Pt for the base period.

The aggregate output of the current period Qt evaluated at base period's prices give the Real National Income (its notation is yt):

yt = P0 Qt ....... (3)

The ratio of the real national income of the current period (3) to that of the base year (2) gives an indicator of the increase in the real national income. As the price level is being held constant here, the index measures how much the aggregate output has increased between the base and current year. It is called the Real National Income Index:

real income index =∑ P0 Qt

∑ P0Q0

× 100=P0

h Qth+P0

s Qts . . ..

P0h Q0

h+P0s Q0

s . . .. . × 100

(2) General Price Level

How can we measure a change in the price level itself? We have to control or fix the aggregate output this time. We can get the ratio of the current period's price level P t to the base period's price level P0. There are two different indexes depending on how to assign weights to individual prices. The first is to get the ratio of the price levels with fixed weights of the base period's output basket Q0. In this case, we also confine the outputs in this bundle to consumer goods. In Canada, the basket includes about 490 items of consumer goods. This price index is called the Consumer Price Index:

consumer price index =∑ PtQ0

∑ P0 Q0× 100=

Pth q0

h + Pts q0

s .. . .

P0h q0

h + P0s q0

s .. . ..× 100

Alternatively, we can get the price index by getting the ratio of P t to P0 with fixed weights of the current period's aggregate output Qt. The resultant price index is called the GDP Deflator:

GDP deflator =∑ PtQt

∑ P0 Qt× 100=

Pth Qt

h + Pts Qt

s .. ..

P0h Qt

h + P0s Qt

s .. .. .× 100

Note that the GDP deflator of the current period is equal to the ratio of the nominal to the real national income: (1)/(3). Therefore, if the price level P represents the price index, then the Nominal National Income is the Price Level times the Real National Income:

P = Y / y, or Y = P y.


(3) Numerical Examples

Refer to questions in Review Questions #1.

2) Various National Income Accounting System Equations (Review from Eco 100 or Eco 20).

GDP = GDI + IT = (W + I + R + P + D) + IT,where IT denotes indirect taxes; GDP denotes Gross Domestic Product; and GDI denotes Gross Domestic Income.

NDP = GDP – D, where D denotes depreciation or capital consumption; and NDP denotes Net Domestic Product. NNI = NNP – IT,Where NNI denotes Net National Income and NNP denotes Net National Product.

GDE = C + I + G + X-M NDE = GDE - D

= C + Net I + G + X-M

GDI = GDP - ITNDI = GDI - D

GNP = GDP - Net Investment Income Paid to Non-residents.NNP = NDP - Net Investment Income Paid to Non-residents.

3) Issues and Problems of the Current National Income Accounting.

(1) Conceptual Problems:

Income may be considered to be the maximum that could be consumed in a given period consistent with the maintenance of wealth or of income potential. Alternatively and essentially equivalent it may be considered the sum of the amount that is consumed in a given period and that amount that is added to wealth. It is taken for granted that income has a direct bearing on material welfare, which may not be always true. For instance, the average income level of the Canadian native people fares well in national and international comparison. However, their longevity and level of satisfaction seem to be very low. There has a move to come up with a better and more comprehensive indicator of the well-being of people than the current National Income Account. The new indicator should encompass income, longevity (health), and satisfaction.


(2) Missing Components of the National Income

We have already seen that the definition of GDP correctly excludes

a) Intermediate goods: They are counted in the value of final goods which are made of intermediate goods. If the values of intermediate goods are included, in addition to the value of final goods, they are counted twice.

b) Transfer income or Capital Gains: These items do not result from any productive services. They do not represent any production.

c) Capital Gains and Losses: Changes in the valuation of assets/wealth are clearly income at the personal level. However, they are usually not included in the National Income Account unless they represent new (current) production of goods or services. Sales of old houses, stocks, or antique may bring income to individuals, but do not increase any current production. They were included in the national income back at the time of new production. However, commission income of realtors is included in the current national income as the services rendered by them are new. The same is true of an antique dealer's value-added. Capital gains mostly arise from speculative activities. As speculation is usually a non-productive economic activity, gains from speculation are normally excluded from the calculation of national income.

(i) However, some capital gains do arise from what is a productive speculation. What is the productive speculation? Speculation that transferred goods from consumption at a time when they are plentiful and cheap to consumption at a time when they are scarce and expensive is productive. An example is the speculation on seasonal products such as fish: Without speculation the price of fish would show a larger degree of seasonal fluctuations and much of fish would be wasted. In season, fish is so cheap that workers may not care too much about wastes in the processing procedure. Out of season, the price of fish is too high for some people to have enough of. As a speculator buys fish in season when fish is cheap, and releases it out of season when it is expensive, the price shows smaller seasonal fluctuations. The price of fish is now higher in season, so there will be less waste and more fish to be stored. This means a larger supply of fish than otherwise. Out of season, fish price is lower, and there will be a larger demand for fish. This means more expenditure on fish. The speculator's capital gains represent a larger supply and demand or an increase in the national income.

(ii) Consumers-goods elements of job: Restaurant meals on an expense account are not included in the National Income. Expense account items of business representatives are goods and services which are clearly the consumption of goods and services on any reasonable interpretation, but they are classified as productive and therefore written off from the measured incomes of the person enjoying them. In Canada reform of tax regulations is under way to rectify this issue, which reduces the amount to be claimed in this way.

(iii) Household Production: Over the past twenty years the rate of participation of women in the work force has risen at an average rate of 2.2 % per year from 37.1 % of the Canadian labour


force in 1968 to 57.4 % in 1988. The rapid rates of increases are also reflected in employment growth over the same period, a compound annual rate of growth for women of 3.9 % compared to 1.5 % for men. There are no markets or prices at which all of household production activities, such as laundry, home-cooking, baby-sitting, cleaning and etc. can be evaluated. So they are not taken into account of national income. As the women participate in the work force, they would now rely on the market for those goods which they used to produce at home. The formerly non-market activities, such as child-care and home-cooking give way to paid baby-sitters and meals in restaurants. They will pay for the baby sitter. The family may eat out more frequently instead of eating home-cooked meals. They may even pay for the cleaning ladies. These are counted as a net addition to output. Part of the growth in GDP simply reflects the substitution of market activities for non-market home production.

But growth will be more or less overstated depending on what happened to the non-market activity previously undertaking by these new entrants to labour force. If some of the previous non-market activity is forgone entirely, as a result of women entering the labour market, then measured GDP growth should be reduced by an equivalent amount. If, on the other hand, the housework is not foregone, and the women or other members of household somehow take up the slack, then measured GDP should not be adjusted.

The difficulty, of course, is to estimate the value of household work and the degree of substitution or replacement. In Canada, estimates have been prepared for 1971 and 1981 using data from Census Information and time use studies for a range of household activities. Valuing these activities at counterpart rates (prices: for instance, home-cooking is evaluated with the price of restaurant foods) in the market produced totals equivalent to 39.5 % of GDP in 1971 and 34.0% in 1981. (30% in 1990, unofficially) This unpaid work is estimated to account for 30 % of GDP in Canada. The decline in the relative importance no doubt reflected other factors as well as the movement of women into the market economy, but the overall effect was considerable. Including the measured value of household work reduced the average rate of overall economic growth by 0.5 % per year. Alternatively put, Statistics Canada estimates that on average 0.5 percentage point of annual growth has come from the replacement of unpaid work with the market since 1971. In other words, even if the sum of home and market production does not increase at all, a mere substitution of market production for home production would make the GDP look as if it were growing at 5% per annum in Canada.


(iv) Underground Economy

Read the article entitled "Gross Deceptive Product" (GDP).

(3) False Components of the National Income

(i) Expenses of an Intermediate good nature

The current National Income Accounting System does not make any distinction between a leisurely driving and commutation for work. Expenses on commuting back and forth between home and work places are included in the national income. In fact they are costs for a further round of production, and should be excluded from the national income.

(ii) Systematic Exaggeration of the Government Role in a GDP Creation.

The following excellent example illustrates the seriousness of double-counting caused by the government: In the following two cases the real resources available for consumption, measured in the number of pairs of shoes, are identical, but the apparent National Income measured according to the present national income accounting system will be quite different.

Case 1. A ramp from a shoe factory to a highway is owned privately by a factory. Annually it costs a $1000 to maintain the ramp. The factory produces $100,000 worth of shoes. The costs and expenses of the ramp services are regarded as intermediate goods, and are already included in the values of the final goods or the shoes manufactured. Thus the ramp maintenance cost of $1000 is included in addition to the values of the shoes. The measure national income is $ 100,000 (= Y = C).

Case 2. Now government nationalizes the ramp and maintains it. The firm is required to pay annual tax of $1000 to government. Nothing has changed for the firm and the real economy: The firm is under the identical set of circumstances as in the original situation. The government makes expenditures in hiring workers and resources to upkeep the ramp. As the current National Income Accounting System values public goods provided by government on a cost basis, these government expenditures will be taken as increasing the national income. Now the measured income is the sum of private (shoes) and public goods (ramp services): Y = C + G = 100,000 + 1000 = 101,000. However, in fact, the cost of road services is already embodied in the value of the final goods or shoes. It is counted


twice; once in the shoes and secondly in government expenditure (G).

How serious is this double counting in the public sector? For Canada, according to Reich (1986) intermediate goods account for 22.9 % of government expenditure or public goods. Therefore, the correct and true national income accounting identity, which includes various expenditures on final goods only, should be

Y = C + I + 0.77 G + X - M in Canada.


Appendix: How the Circular Flow Chart is obtained:

Some of you have noticed that I have jumped from the model with only consumers to the model with consumer, firms, government and foreign sector. This appendix is for the mind which requires some convincing as regards the transition from the simplest model with consumers only to the complex model with consumers, firms, government, and foreign sector.

1. Economy with Consumption Only.

We have already view the simplest economy with consumers only: AE = C only. If there is only C on the aggregate expenditure side, the equilibrium condition for the national income is Y = C.Example I: Let's suppose that the following table shows an annual production of all industries evaluated at the current market prices in a simplest economy. What is the current national income?

Industry Sales Revenues = P x Q

Material Costs for Intermediate Goods

Factor Costs (Value Added)

Wheat $ 5 $ 0 $ 5

Flour $ 8 $ 5 $ 3

Bread $ 17 $ 8 $ 9

Deli-Bread $ 25 $ 17 $ 8

In the table, the sum of Value-Added of all industries is $ 5 + $3 + $9 + $8 = $25. Thus the current National Income is $25.

2. Economy with Consumption and Investment: No government or Foreign Sectors

Now let’s add Firms’ demand for goods and services produced in the economy: Now AE will turn to C + I in the following example.


Example II:

Let's also add a machine-making industry, which produces final goods for investment.

Industry Sales Revenues = P x Q

Material Costs for Intermediate Goods

Factor Costs (Value Added)

Wheat $ 5 $ 0 $ 5

Flour $ 8 $ 5 $ 3

Bread $ 17 $ 8 $ 9

Deli-Bread $ 25 $ 17 $ 8

Machine $ 50 $ 0 $ 50

The supply side has Y = YS:

Y = VA's = $5 + 3 + 9 + 8 + 50 = $75

YS= Pmarket x Qfinal = 25 + 50= $75

We have so far assumed that households spend all their income: the entire Y is disposed of as C. Let's now introduce savings: Households dispose of their income either in consumption spending or in savings. By the amount of the savings, which is a leakage from the circular flow, the national income does not go back to the flow of demand for goods: Y = C + S.

The demand is for deli-bread for consumption and for machines for investment: AE = C + I:

AE = C + I = 25 (Deli-Bread) + 50 (Machine) = $75

Note 1) Machines may be used in the production process. That does not make the machines an intermediate goods. Intermediate goods are materials, which are to be embodied in their outputs. Machines may wear and tear, but will not be made into outputs. Machine are a capital good which endures many cycles of production.


The Circular Flow Chart for this economy is modified as follows:

Note: Savings of households may be channelled by financial intermediaries, such as banks, to firms as investment. However, there is no guarantee that investment and savings are equal to each other as they are carried out by different economic agents: the first by households and the second by firms. For instance, when business outlook is break, households may cash their investment and hold their assets in deposits. Now savings become larger but investment smaller.

If they happen to be equal to each other, the circular flow will be maintained at the current level as the leakage(savings) is the same as the injection(investment). This is the equilibrium situation, meaning that the current state will persist in the absence of any disturbing forces.

Keynes noted that when savings exceeds investment, as leakage from the circular flow exceeds injection into it, the circular flow or the national income flow will diminish over time. He pointed out this problem as the cause of recession.

Example III: Inventory) The National Income should include all the factor payments(=VA) for goods produced of all the industries regardless of whether they are sold or unsold later in the economy. Income is created through the process of producing these aggregate outputs.

The existence of inventory compounds the output approach to the National Income. We should note that the value of inventories of final and intermediate goods should be included in the computation of the value of aggregate output. Sold intermediate goods get their value embodied in the value of final goods. The values of unsold intermediate goods are not reflected elsewhere and should be taken into account. Therefore, the Total Value of Output = Sold Final Goods + Unsold Final Goods + Unsold Intermediate Goods:

YS = P x Qfinalsold + P x Qfinal

unsold + P x Qintermediateunsold.

In the expenditure approach of getting the AE, the changes in inventories or Inventory Accumulation of final and intermediate goods are regarded as Investment on inventories:

AE = C + I.


Numerical example: Refer to Assignment #1.

2) An Economy with Government

What complications does the introduction of government bring to the national income accounting system?

i) The income approach national income Y (= W + R + I + P) should now include W, R, I, P paid by the government. They are all before-income-tax figures. The disposal of income should include direct taxes: Y = C + S + T. Consumers cannot spend taxes on final goods, and thus tax constitutes another leakage from the circular flow of the national income.

ii) In the output approach, the value of goods and services produced by the government or public goods should be included in the National Product. There arises a question of how to come up with the market value of public goods? How to include the value of the Gibbon's park service on Sunday? There is no market or market price for it. So the National Income Account calculates the value on a cost basis: The operating costs for the park service are its value. Therefore the value of public goods is equal to their production cost/expenditure.

Note: Problem of double counting is the most serious with government sector. According to the Output approach, the value of final goods and services produced by the government should be included. Since there are no markets where government goods and services are bought (or evaluated). The value of goods and services produced by government or `public goods' are evaluated at their production costs. Whenever government makes expenditures to produce some goods and services, the national income accounting system simply assumes that there occurs an increase in national income by the amount of government expenditures; all government expenditure is assumed to be on final goods. The very problem blurs the distinction between final and intermediate goods in the government sector.

iii) Indirect taxes or sales taxes will create inequality between the National Income, which is measured at the production stage(factory), and the National Product, which measured by the marketing stage(market). The value of output in the market is the sum of the factory value and sales taxes:

NI + Indirect Tax = NP.

iv) The government expenditure should be added to the Aggregate Expenditure as another injection to the system of circular flow:Government activity involves current expenditures or G (jet fighters, judges, policemen, civil services, etc.) and taxation. Government expenditures, which adds to the Aggregate Expenditures, are either on consumption-nature goods and services (Gc) or investment goods (GI). The latter is put together with Investment of the private sector to become the Total Investment of the economy. Therefore,

AE = C + Iprivate + G = C + I + Gc + GI = C + (I + GI) + Gc = C + I + G.

Note: Government Current Expenditure or Gc or G in the National Income Account could be a very misleading indicator of the size of government activities; Some items of government spending are not included in `G' of the national income account, and they are substantial in Canada; old age pensions, social welfare expenditures which are transfer payments from government to the private sector, and there are also interest payments on government bond


(IB). The government expenditure on currently produced goods and services accounts for only 44 % of the total government spending in Canada. The interest payment accounts for 22% of the total government spending and the transfer payment which does not bring about any production of goods and services in reciprocation of payment accounts for 34% of the total government spending. Therefore, Government Spending > Government Expenditures or G.

Summing up, we can write

Y = C + S + T ; YS ; AE = C + I + G.

The modified Circular Flow Chart is as follows:

3) A Complete Economy with Consumers, Firms, Government, and International Sector

How does an introduction of the foreign sector compound the National Income Account?

i) There are final goods and services which are produced in a country but will not be claimed by its nationals.

The difference between the National and Domestic concepts of the National Product or Income is that the first is produced/ created by the nationals (citizens) and the latter is produced/created in the country: The first focuses who produces outputs, and the second where output are produced. In a country where there are many foreign workers (L) and foreign capital (K), the Domestic Product (Income) is larger than the National Product (Income). Parts of the domestically produced outputs are claimed by non-nationals who contribute production factors to the country:

Domestic Income (Product) = National Income + Income paid for Foreign Labor/ Investment.

Think about which is the larger of the two in Canada, Japan, Kuwait, and other countries.

ii) The AE should include the expenditures on goods and services by foreigners, or the value of


exports(X). For an expedience in data collection and accounting, the Canadian purchase of foreign goods or the value of imports (M) are included in C + I + G. The value of imports (M) should be subtracted from GDE. The expenditures on the domestic outputs are C + I + G - M.

AE = C + I + G + X - M.Summing up, we can write

Y = C + S + T; YS; AE = C + I + G + X - M

The complete Circular Flow Chart is as follows: Exports are a new injection to the system and imports a new leakage. By the amount of imports national income does not become AE for domestic final goods.

Macroeconomics 38 Chapter III. Keynesian Cross Diagram

III. Keynesian Cross Diagram 1. IntroductionWhat determines GDP in an economy? Keynes says that the actual or equilibrium national income is not necessarily equal to the maximum potential output (full employment income). The question is what prevents us from enjoying the full employment income?

This is a simple Keynesian Model of Income Determination. It is ‘simple’ in the sense that it does not have the money market, and all the consequent implications and complications: For instance, there is no Crowding Out of government expenditure policy. We will introduce the money market in the next chapter.

Within this chapter, depending on the specifications of components of aggregate expenditures, there are three different cases; Case 1 has just lump-sum taxes; Case 2 has proportional as well as lump-sum taxes; Case 3 has imports and exports as well as proportional taxes.

2. Basic Principle (Strategy for Solving for Y*)

Always go through the following steps to solve for Y*:

Step 1. Spell out the Aggregate Supply side income;

YS (=W+R+I+P+D) = Y (=C+S+T).

Step 2. Spell out Aggregate Expenditure side income;

AE = C + I + G + X-M.

And, then Substitute the functional specifications given by the question for the variables C,I,G, X-M, and rewrite it in the form of AE = A + B Y, where A and B are specific (constant) numbers.

Step 3. At the equilibrium, we know S=D and that here YS = AE.

Y = C + I + G + X-M, or Y = A + B Y.

Therefore

(1−B )Y ¿=A

Y ¿=A1−B

where B is the slope of Aggregate Expenditure curve, and A is a set of Autonomous Aggregate Expenditures.


Note that B has the terms that are associated with Y and A has a set of variables independent of Y.Step 4. From the above equation, get the first derivatives of various components of A;

3. Case 1: T = T0

1) Basic Assumptions

i) No money market; No inflation (price level is fixed): ;ii) All taxes are lump-sum or of a fixed amount: ;iii) There are no exports or imports (closed economy): .

P (the price level) is assumed to be fixed because

a) we are dealing with short-run, where prices are inflexible;

b) we have unemployment situation. So an increase in demand would lead to the increase in production/output, not inflation;

Producers would not have any difficulties in increasing output fairly quickly without raising the costs or prices; there are idle capacities of capital and equipment. It is almost costless to bring them into production. And unemployed labour forces are standing by and are willing to be hired for pittance.

c) Y (= y) adjusts rather than P with the change of Demand.

d) All variables, such as consumption, investment, and government expenditure, are expressed in real terms. There is no distinction between real and nominal magnitude as the price level is fixed. The interest rate here is the real interest rate.

multipliertaxsumlumTY

multiplierendituregovernmentGY

multiplierenditureinvestmentIY

multiplierenditrenconsumptioCY

__;*

_exp_;*

_exp_;*

_exp_;*

0

0

0

0

PTT

0 XM


2) Supply Side

YS (=W+R+I+P+D) = Y(=C+S+T)

(Interpretation) The value of supply of final goods and services (=YS) will be paid out to households (in the forms of W, R, I, P, D) to become national income (=Y). It will be disposed of by the households either in consumption, savings, or taxes.

Graphically, in a quadrangle with YS on the vertical axis and Y on the horizontal axis, the 45 degree line from the origin represents the supply side of national income.

The horizontal distance from the origin to point A is equal to the vertical distance from the origin to point B on the 45 % line. It has a degree of 1. YS = Y. The line can be nothing but a 45 degree one as the firms pay out to households all of what they earn from production.

3) Demand Side: Aggregate Expenditure

(1) Consumption Function

Keynesian Consumption function:

C = C0 + c1 Yd, where Yd is disposable income, or Yd = Y-T.

For simplicity, let us assume that T = T0 independent of income level, or that all taxes are lump-sum.


What is the constraint on the value for C0 and c1 respectively?

C0 is an autonomous, exogenous, and independent consumption regardless of income level;

c1 is the Marginal Propensity to Consume.0< c1<1;

MPC measures how much of an increase in income will be consumed. The consumption increases as income increases (>0), but is not increasing as fast as income is (<1).

Let's quote Keynes' explanation of MPC;

"The fundamental psychological law is that men are disposed, as a rule and on average, to increase their consumption as their income increases but not by as much as the increase in income."

Graphically, c1 or MPC is the slope of the consumption curve drawn with C on the vertical axis and Y on the horizontal axis;

C = C0 + c1 (Y-T)

= {C0 – c1T} + c1 Y

Average and Marginal Propensity to Consume;

(Definitions)

MPC=ΔCΔY

APC=CY

APC1 > APC2


(Questions)

What is MPC at y1 and y2 respectively? (MPC is constant over y1 and y2)What is APC at y1 and y2 respectively? (APC decreases as Y)

Graphically, the MPC is the slope of the consumption curve, and is constant everywhere on the straight line of the consumption curve regardless of the level of income.

The APC is the slope of the line linking the origin and the point of interest on the consumption curve (= tangent of the angle Theta). APC at y1 is given by the slope of a hypothetical line linking the origin and point A. APC at y2 is equal to the slope of the imaginary line liking the origin and point B. The flatter is a curve, the smaller its slope will be. So APC at y 2 is smaller than APC at y1; the APC decreases as the national income level increases.

Also, naturally APC > MPC holds at all income level.

(2) Investment

Demand for addition to fixed capital formation and a voluntary addition to inventory.

I is for now assumed to be exogenous, such as

I = I0;

What it means is that we are assuming that investment is geared to long run; entrepreneurs make investment decision based on expected future income which is independent of current income. Even if the current income is very low, when there is a prospect that the demand for their goods will increase in the future, they will be engaged in the expansion of production facilities.

Naturally, the dependence of investment on expectations makes investment very volatile. What will be the impact on the output or income? As the expectations or business outlook changes, investment decision will vary. The expectations and business outlook are very much affected by rumours, fear, etc aroused by unexpected events. Would such variations in investment lead to smaller or larger changes in output than the changes in investment itself?

M P C = S lo p e( if s tr a ig h t l in e )


(3) Government Expenditures

G = G0.

Numerical Example: G= 150

(4) Foreign Sector

Let us assume that X-M = 0 for simplicity.

(5) Aggregate Expenditures

AE = C + I + G + (X-M);

Suppose that specifications of each variable are given as follows;

C = C0 + c1 (Y-T)

= C0 - c1 T + c1 Y;

I = I;

Investment is a major source of fluctuations of Y

TCC 21 II GG

GICAE AE

Y


G = G;

X-M = 0 for simplicity.

Substituting the above specifications for the variables in the equation, we get

AE = C + I + G + X-M

Note that I,G,C in the first equation are variables, and I,G in the second ones are numbers or specific values

AE = C0 – c1 T0 + I0 + G0 + c1 Y intercept slope

AE consists of two parts; one is independent of Y or national income, and the other dependent on Y. The first is called Àutonomous Aggregate Expenditures, and the latter Ìnduced Aggregate Expenditure.'

AE = Autonomous AE + induced AE

= A + B Y,

where A = C0 – c1 T0 + I0 + G0, and B = c1.

Note that the slope of the Aggregate Expenditure curve is equal to that of the consumption curve and the MPC = c1.


3) Equilibrium Y*

(1) Graphic Solution

(2) Algebraic Solution

Step 1: YS = Y; Supply side.

Step 2: AE = C+I+G+X-M; Demand side.

By substituting the functional forms, given by the question, for C,I,G,X-M, and rewriting it, we get

AE = {C0 – c1 T0 + I0 + G0} + c1 Y, or (X – M = 0) = A + B Y,

where A and B are numbers.

Step 3: YS = AE at equilibrium, so

Y* = {C0 – c1 T0+ I0 + G0} + c1 Y*

Solving for Y*, we get

E


The above is the equilibrium national income equation. If we know the values for C0, c1, T0, I0, and G0, we can get the numerical value for Ye.

(3) The Equilibrium Condition

YS = Y = C + T + S

AE = C + I + G + X-M

Equilibrium Condition S + T = I + G + X-M ; .Without government and foreign sector, S = I.

S = I + (G-T) + X-M suggests that the private sector has three ways of disposing its savings; by lending to the business sector which uses the funds for investment. By lending to the government which uses the funds for financing the government deficits. By lending to foreigners who would buy more goods and services from us than we are buying from them.

4) Comparative Statics

No change in the supply side or YS can alter the equilibrium national income.

Only change in the demand side or AE can do so. (Keynesian Idea)

AE = C0 – c1 T0 + I0 + G0 + c1Y = A+BY = Autonomous AE + Induced AE

Alternatively, when we draw the above AE curve with Y on the horizontal axis, we get

c=B ,G+I+TcC=A where,B1

A=Y call

}.G+I+Tc-C{c-1

1 = Y

.G+I+Tc-C = Y )c-(1

*

*

*

100010

000101

000101

Re


(1) Increases in Autonomous AE; changes in the intercept of the AE curve.

The vertical shift of the AE curve brings about the horizontal changes in Y*. The ratio of the (horizontal) change in Y* to the (vertical) change in the AE is given by a `(generic) multiplier', and is equal to one over one minus the slope of the AE curve. The slope of the AE curve is equal to that of the consumption curve in this particular case;

If all taxes are lump-sum, the slope of the consumption curve is equal to MPC or c1. So the multiplier is 1/(1-c1).

If there is a tax proportional to income, then the slope of the consumption curve is equal to c1 (1-t1) where t denotes the tax rate. The multiplier is equal to 1/{1-c1(1-t1)}.

ΔY ¿

Δ AE = increase in Y ¿ on horizontal axis

increase in AE on vertical axis

¿11 - c1

when T=T 0 :Case 1

¿11-c1(1-t1 )

when T = T 0+ t 1 Y :Case 2 .

Slope (B) : c1

Intercept (A): C0 – c1 T0 + I0 + G0;

.c-1

1 = AEY So,

.Y)c-(1 = Yc - Y =AE

AE.Y =Y c Then,

.Y

AEY=AC = c

*

***

**

e

*

1

11

1

1

AE AEAEAEEA

YYs

AE

sYAE //

*Y Y

*YAEY

AEYC

CYAEYrunriseC

YAEY

*1

1**

1*

*

)1(


(2) Individual Multipliers

What constitutes the intercept? - The components of the intercept {C0 – c1T0 + I0 + G0 + X0-M0}, that is, C0, T0, I0, G0, and X0-M0, are the components of Àutonomous Aggregate Expenditures'. Changes in autonomous expenditures are illustrated by changes in the intercept of the AE curve. These changes in the intercept shift up or down the AE curve in a parallel way. Then there will be resultant changes in Y* (given by the intersection of AE and YS=Y curves. The resultant changes in Y* is usually larger than the initial changes in AE. Therefore any change in the intercept will bring about the multiplier effect on national income.


C0: determined by consumers. I0: determined by firms.

G0 and T0: determined by government. A set of rules determining the level and changes in G0

or T0 is called fiscal policy.

X-M: determined by foreign sector.

The multiplier for each component can be obtained by differentiating the equilibrium national income equation with respect to the variable of Autonomous Aggregate Expenditure: A multiplier of a variable should be equal to the coefficient of the variable in the equilibrium national income equation.

Note that all multipliers but the tax multiplier one is equal to 1/1-c1.

a) Changes in C0, I0, and/or X0-M0 can cause a change in national income. C0 varies over time; I0 is even more volatile. These changes are beyond control by government; they constitute shocks to aggregate expenditures. Changes in I0 are magnified into larger changes in Y through the multiplier. If the changes are cyclical, there occurs a business cycle.

Government may try to counter the changes in the AE due to changes in C0, I0 or X0-M0 by adjusting T 0and G0 in the opposite direction by the same amount. If the changes in AE are successfully ironed out in this manner, there would not be any change in Y*; when I is decreasing, government increases G and thus AE is held constant and so is the national income.

c-1c=

dTdY

c-11=

dGdY

c-11=

dIdY

c-11=

dCdY

Therefore,

.Gc-1

1+Ic-1

1+Tc-1

c-Cc-1

1 = Y

}. G+I+Tc-C { c-1

1 = Y

e

e

e

e

*

*

1

1

0

10

10

10

01

01

01

10

1

000101

*YY e


This kind of government policy is called `Counter-Cyclical Fiscal Policy.' Can government actually fine-tune the economy in this fashion? The answer is rather negative mainly because of Time-lags.

b) An increase in G0 ( Δ G 0):

ΔY* = 1/(1-c1) ΔG0

ΔG0= k ΔY* = 1/(1-c1) ΔY*

Example) c1 = 0.75, and all taxes are lump-sum. Government is increasing its expenditure on final goods and services by $ 5 billion. What is the resultant increase in the national income?

The government expenditure multiplier is 1 over 1 minus 0.75, that is, 4. So ΔG will be multiplied into ΔY* by the factor of 4; k = 4. Therefore, ΔY* = 4 ΔG= 4 times $ 5 billion = $ 20 billion.

c) An increase in T ( Δ T 0) leads to a decrease in Y *. ΔT = k ΔY* = - c1/(1-c1) ΔY*


An increase in T will lead to a decrease in Disposable Income by ΔT 0 (note it does not increase Y for now); in Yd = Y - T, 0 ΔT 0= - ΔYd. The decrease in disposable income by dT will decrease consumption only by c2 ΔT0 (a MPC fraction of changes in disposable income = changes in consumption). This is shown as shift up of the intercept of the consumption curve and thus AE curve;

ΔT0 -ΔYd = -ΔT0 -ΔC = c1 x (-ΔYd) = -c1 ΔT0 =ΔAE (< -ΔT0)

This change should be classified as Autonomous, so there is multiplier effect to this increase in consumption;

ΔY* = k ΔAE= (1/(1-c1)) (-c1 ΔT0) = -c1/(1-c1) ΔT0.

Note that when taxation is increased by say, $1, the AE curve does come down vertically by less than $1; In other words, one dollars increase in taxes will bring about a less-than-one-dollar -decrease in consumption or AE.

d) Balanced Budget Multiplier;

Suppose government increases G by 1 billion dollars and at the same time taxes by 1 billion dollars. What happens to the National Income?

From (1) and (2), in this case, there are two forces working in opposite directions; ΔG brings about an increase in income and ΔT a decrease in income. However, the first is larger in its impact on Y* than the second, and thus there is a net positive increase in income. The increase in Y* is equal to the magnitude of operation, that is, the increase in government expenditure or taxation. In other words, if government expenditure is increased by ΔG and at the same time taxes are increase by ΔT where ΔT = ΔG, then ΔY= 1 ΔG= 1 ΔT. Balanced budget multiplier is 1 regardless of what the MPC is.

Proof 1 of Balanced Budget Multiplier being equal to one

-C1


Government increases G and T at the same time by the same amount, say, $1. We can think of the government operation as a sequence of two separate actions.

First, government increases its expenditure by $1. This pushes the AE curve upward by $1.

Second, government increases taxation by $1. This pushes the AE curve down by less than $1; people are taxed $1 more, and their disposable income decreases by $1. But the decrease in consumption will be less than $1; it will be a fraction of $1. They spend $ c 1 (<$1) less than before. So the decrease in AE is $ c1.

Combining the first and second changes in AE, there occurs a positive net increase in AE by 1-c1. We know that a $1 increase in AE will lead to an increase in the equilibrium national income by the factor of a multiplier k = ΔY* /ΔAE= 1/(1-c1); the net increase in AE by 1-c2 will lead to an increase in Y* by k time 1-c1 = 1/(1-c1) x 1-c1 = 1. The increase in G accompanied with an equal amount of increase in T will lead to an equal amount of increase in Y *. If G and T are increased by say, $50 billion, then Y* will increase by $50 billion.

Proof 2 of BBM =1 in Case 1 In this case, government increases G and T at the same time and by the same amount. Therefore, the resultant Balanced Budget Multiplier is a combination of the government expenditure and tax multipliers:

ΔY/ΔG= 1/(1-c1) = government expenditure multiplier;

An increase in G by 1 billion increases income by 1/1-c1.

ΔY/ΔT = -c1/(1-c1) = tax multiplier;An increase in T by 1 billion decreases income by c1/1-c1.

Combined Effect on income = 1/(1-c1) – c1/(1-c1) = 1.

ii) Change in the slope of the AE curve, which is equal to the slope of the consumption curve and MPC.

The larger MPC, the larger Y* and the larger K will be:

AS the MPC increases not only the income level but also the multiplier will increase.

i) As c1increases, Y * increases and the multiplier increases .


The larger MPC leads to a steeper AE curve and a larger Y*.

ii) the larger MPC is, the larger the multiplier will be.

4. Generalization of Keynesian Cross-Diagram of Income Determination

Recall Case 1: We have so far examined the case where all taxes are lump-sum; T= T0

W h e n M P C ; K ; Y *

)G + I + T c - C(c - 1

1 = Y ooo101

*


Case 2: Now there are two kinds of taxes. The one is fixed or lump-sum, and the other is proportional to the income level; T= T0 + t1 Y.

Step 1: Supply Side: YS = Y

YS = (W + R + I + P) = Y ( = C + S + T) ; Supply Side

Step 2: Demand Side: AE = C + I + G

= C0 + c1 Yd + I 0 + G 0 ; Yd is disposable income

= C0 + c1 (Y - T) + I0 + G0 ; Yd = Y - T

= C0 + c1 {Y - (T0 + t1 Y)} + I0 + G0 ; recall T = T0 + t1 Y

= Co + c1 Y - c1 T0 - c1 t1 Y + I0 + G0 ; expand the bracket

= C0 - c1 T0 + I 0 + G0 + c1 Y - c1 t1 Y ; separate Y terms

= C0 - c1 T0 + I0 + G0 + (c1 - c1 t1) Y ; factor Y out

= C0 - c1 T0 + I 0 + G0 + c1 (1 - t1) Y ; factor c out

The slope of the consumption curve is smaller in this case with proportional taxes than the case without them; c2 (1-t) < c2. The consumption curve is flatter.

We know that the slope of the AE curve is the same as the consumption curve. Thus, we can predict that the multiplier will be smaller in this case than in the case without proportional tax.

Step 3. At equilibrium, Y = AE and thus

Y* = C0 - c1 T0 + I0 + G0 + c1 (1 - t1 ) Y*

{1 - c1(1 - t1 )} Y* = C0 - c1T0 + I0 + G0 ; transpose Y to the left

Step 3: Equation


Step 4: Multipliers

The multiplier of a particular variable is obtained by differentiating the above equilibrium national income equation with respect to that variable.

What are the multipliers for the autonomous consumption and the autonomous investment?

t c+c - 11 =

IY

)t - (1 c - 1

1 = CY

111

11

0

0

*

*

What are the multipliers for government expenditures and lump-sum taxes? (Fiscal Policy)

t c+c - 1c =

TY

)t - (1 c - 1

1 =

GY

111

11

1

0

0

*

*

What is the multipliers for a balanced budget multiplier for the case where an increase in government expenditures is financed by an increase in lump=sum taxes?

)1(11*

11

11

00 tcc

t c+c - 1c

)t - (1 c - 1

1 =TG

Y

11111

Is this equal to one?

}{)1(1

100010

11

* GITcCtc

Y


What if the government does not increase T0 not by the full amount of ∆G0 in the first round but makes the overall increase in T equal to ∆G0?

Eventually the proportional tax revenues for the government will rise as the new equilibrium national income rise over time: In T = T0 + t1 Y, overall T increases as Y rises.

Thus in this case, the increases in proportional taxes resulting from increases in Y supplement the initial increase in lump-sum taxes. BBM is equal to one in this case. The result is the same as the previous Keynesian balanced budget multiplier as long as the change in the tax revenue is made by lump-sum taxes.

Proof:

Suppose that G0 = T = 1. We know that T = t1 Y; T t1 Y = 1 t1 Y

ΔY= 11 - c1(1 - t1)

ΔG0+ −c1

1 - c1+c1 t1ΔT 0

= 11 - c1 (1 - t 1)

1+ −c1

1 - c1+c1 t1(1−t t ΔY )

¿1

Remarks: Here again, we may note that the government expenditure multiplier is smaller with

proportional taxes than otherwise; For a given vertical shift-up of the AE curve (due to an increase in G), the resultant ∆Y* will be smaller with a flatter AE curve than a steeper AE curve. When the income tax rate increases, the national income will be smaller, and the impact of an increase in G will be smaller, too.

c - 11

)t - (1 c - 11

111

I0 and C0 exhibit cyclical movement over time, depending on, for instance, investors’ assessment of business outlook and consumer confidence. They are not directly controllable by the policy-makers. Their multipliers are the factor by which cyclical changes in basic consumption C0 and autonomous investment I0 are magnified into larger fluctuations in the equilibrium national income. Therefore, the multipliers associated with the above two variables have something to do with business cycles.

We also have noted that these multipliers are smaller for the case with proportional taxes than for the cases without proportional taxes (thus with only lump-sum taxes). With the presence of proportional taxes such as income taxes, the impact of cyclical changes in C0 and I0 on national


income will be smaller than in the case with only lump-sum taxes. Therefore the proportional tax system is called an ‘Automatic or Built-In Stabilizer’.

When national income increases in a booming stage, the proportional taxes increases too. This will in turn decrease the disposable income and the aggregate expenditures to a certain extent. And thus the overall increase in national income will be moderated. When income decreases in recession, the proportional taxes will also decrease. Thus there will be a boost to disposable income and consumption. It will offset the initial decrease in Y*. The overall decrease in national income will be moderated. All in all, business cycles will be smaller with the proportional taxes.

Case 3: There are imports proportional to national income:

Case 3 is built upon Case 2. There are two kinds of taxes. The one is fixed or lump-sum, and the other is proportional to the income level; T = T0 + t1 Y

T =T0 + t1 Y; and

AE = C + I + G + X – M.

The Aggregate Expenditures will have one additional element such as

NX = X – M;Net exports = Exports – Imports.

X = X0 …………(1)Exports are the demand for our domestic products by foreign countries. The exports are given and thus exogenous from the viewpoint of our economy: The domestic country has no control over the exports. The national income of the foreign countries is the major determinant of our exports to them.

M = M0 + m1 Y, …………(2)where M0 is the basic import, and m1 is the Marginal Propensity to Import (MPI).

he import demand for foreign goods is the function of the entire national income, not just the disposable income portion of it. This contrasts with the consumption function where the consumption is a function of the disposable income. In the case of imports, there are two agents of imports: The one is the private sector whose imports are based on the disposable income. The other is the government whose imports are based on tax revenues. Thus, the total imports are a function of disposable income plus taxes, the sum of which is the national income itself.

Solution for Y*:


Step 1. YS = (W + R + I + P) = Y ( = C + S + T)

Step 2. AE = C + I + G + X - M

= C0 + c1 {Y - (T0 + t1 Y)} + I0 + G0 + X0 - (M0 + m1 Y)

= C0 + c1 Y - c1 T0 - c1 t1 Y + I0 + G0 + X0 - M0 - m1 Y

= C0 - c1 T0 + I0 + G0 + X0 - M0 + c1 Y - c1 t1 Y - m1 Y

= C0 - c1 T0 + I0 + G0 + X0 - M0 + (c1 - c1 t1 - m1) Y

= C0 - c1 T0 + I0 + G0 + X0 - M0 + {c1 (1 - t1) - m1} Y

Step 3. At equilibrium, Y = AE and thus

Y* = C0 – c1 T0 + I0 + G0 + X0 - M0 + {c1 (1 - t1) - m1} Y*

{1 - c1 (1- t1) + m1} Y* = C0 - c1 T 0+ I0 + G0 + X0 - M0

Step 4. Multipliers – Comparative Static

The multipliers for autonomous expenditures can be obtained by differentiating the above equation with respect to C0, T0, I0, G0, X0, and M0 respectively.

Remarks:

The multipliers are still smaller in this case than in all the previous cases; the existence of m1 further reduces the magnitude of the multiplier. The open economy (with international trade) has a smaller multiplier than the closed economy. The more open the economy, the smaller the multiplier.

The smaller magnitude of the multipliers are "mixed blessings", being good and bad.

A small open economy has a larger value for m1 than a large country or a closed economy.

)M X +G + I + T c - C( m + t c - c - 1

1 =

)M X + G + I + T c - C( m + )t - (1 c - 1

1 = Y

00101111

0010111

*

00

000


Show the impact of a $1 increase in government expenditures on the equilibrium national income and on the import, when (1) c1 = 0.8; t1 = 0.5; m1=0.3, which may be the case for a small open economy, and when (2) c1 = 0.8; t1 = 0.5; m1=0.1, which may be the case for a large and less-open country, respectively. Prove numerically that in a small open economy, compared to a large less-open economy, an increase in government expenditures has smaller impact on the national income but a larger impact on the import thus on the trade balance.

We also know that the balanced budget multiplier is the sum of the government expenditure multiplier and the tax multiplier. Specifically, what will be the balanced budget multiplier if initially an increase in government expenditures is financed only by an increase in lump-sum taxes or ∆ T0

, if ↑ => total value of ↓, if m = 0, => very large multiplier => larger business cycle.

In this case, BBM ≠ 1; BBM < 1.

11

1

1111

1

mtcc

c

1m 1111

1

11

mtccc

Macroeconomics 60 Chapter III. Apendix

Appendix for Chapter III.

1. Numerical Examples:

A question will specify the functional forms for consumption, investment, government expenditure, and net exports.

What you should do is

Step 1: Write down YS [=(W+R+I+P+D)+IT] = YStep 2: Write down AE = C + I + G + X-MStep 3: Invoke the equilibrium condition,YS = AE or Y = C + I + G + X-M

Step 4: Substitute the given functional forms for the variables C,I,G, and X-M in the above equilibrium equation.

Step 5: Solve for Y* by rearranging and rewriting the equation.

(Question 1) In a simple economy without government or foreign sector, the consumption and investment functions are given as follows. Get the equilibrium national income.

C = 40 + 0.8 YI = 60

(Solution)As there are no government or foreign sector, there is no G, T, or X-M.

Step 1: YS = YStep 2: AE = C + I Step 3: At Equilibrium, Y = C + I (Note there is no G or X-M)Step 4: Substitute C = 40 + 0.8 Y (Note that YD = Y as T = 0), and I = 60 for C and I in the equilibrium equation, and thus get Y = 40 + 0.8 Y + 60

Step 5: Sending all the terms involving Y to the left hand side of the equality, we get

Y - 0.8 Y = 40 + 60 0.2 Y = 100Therefore, Y = 100/0.2 = 500.


(Question 2) Now in a little more complex economy with government and foreign sector, the consumption, investment, government expenditure, taxation, and net exports function are given as follows. Get the equilibrium national income.

C = 50 + 0.75 Yd; Yd = Y - TI = 70G = 120T = 100; all taxes are lump-sum.X-M = 0

Step 1: YS = YStep 2: AE = C + I +G + X-MStep 3: At Equilibrium, Y = C + I + G + X-MStep 4: Substitute C = 50 + 0.75 (Y-T) = 50 + 0.75 (Y-100),I = 70, G = 120, and X-M = 0 for C, I , G , X-M in the above equation, and get

Y = 50 + 0.75 (Y-100) + 70 + 120

Step 5: Sending all the terms involving Y to the left hand side of the equality, we getY - 0.75 Y = 50 - 75 + 70 + 120 0.25 Y = 165Therefore, Y = 165/0.25 = 660//.

(Question 3) If taxes are proportional to income and thus T = 0.6 Y instead of T = 100, and all other things are identical to the above economy, what is the equilibrium national income?

Step 1: YS = YStep 2: AE = C + I +G + X-MStep 3: At Equilibrium, Y = C + I + G + X-MStep 4: Substitute C = 50 + 0.75 (Y-T) = 50 + 0.75 (Y-0.6Y) = 50 + 0.75 (1-0.6) Y, I = 70, G = 120, and X-M = 0 for C, I , G , X-M in the above equation, and get

Y = 50 + 0.75 x 0.4 Y + 70 + 120

Step 5: Sending all the terms involving Y to the left hand side of the equality, we getY - 0.75 x 0.4 Y = 50 = 70 + 120 0.7 Y = 240Therefore,Y = 240/0.7 = approx. 343//.

(Question 4)

C = C0 + C1 (PDI) = 50 + 2/3 PDI


I = 70G = 120T = 100

(1) What is the equilibrium level of national income (Y*)?(2) What is the consumption at the equilibrium?(3) What is the Saving at the equilibrium?(4) What is the APC ?

(Solution)

First, it is important to figure out what to invoke to get the equilibrium, which is not given in the question.

Step 1. YS = Y = C + S + T

Step 2. AE = C + I + G= C0 + c1 (Yd) + I + G= (C0 + c1 Y - T) + I + G= 50 + 2/3 (Y - 100) + 70 + 120

Step 3. At equilibrium YS = AE, thereforeY* = 50 + 2/3 (Y*- 100) + 70 + 120 (Y becomes Y* now)

Putting all the terms involving Y on the left-hand side of the equation, we getY* - 2/3 Y* = 50 - 2/3 x 100 + 70 + 120.1/3 Y* = -2/3 x 100 + 240Y* = $ 520 billion.

C = 50 + 2/3 (Y - T) = 50 + 2/3 (520 - 100)= 330.

APC = C/PDI = 330/(520-100) = 33/42

S = Y - T - C = 520 - 100 - 330 = 90.

We can double-check the equilibrium; At equilibrium, S + T = I + G; the left hand side in this case is 90 + 100 =190, and the right hand side in this case is 70 + 120 = 190. Here the left hand side = the right hand side. So we can be reassured that this is an equilibrium.

(5) What will happen to Y* when the government simultaneously increases government expenditure and tax by an equal amount, 60 billion dollars? Now T = 160, and G = 180 billion dollars.


Solution:

YS = YAE= C + I + G

At the equilibrium, Y* = C + I + G;

We substitute the above given functions of C, I, and G for the variables of C, I, and G.

Y* = 50 + 2/3 (Y* - 160) + 70 + 180

Y* = 580 (billion dollars)

Alternatively, we can answer the above question as follows;this is a case for the balanced budget multiplier where the increase in government expenditure (G) is accompanied by the equal amount of increase in tax (T), and thus the balance of the government budget does not change; ΔG= ΔT. The balanced budget multiplier dictates that an increase in G accompanied by an equal amount of increase in T will add itself, nothing more or nothing less, to national income. In other words, the balanced budget multiplier is one. So ΔY= 1 x ΔG. With a $1 billion of increase in G accompanied by an $1 billion of increase in T will lead to an $ 1 billion of increase in Y*. ΔG= $ 60 billion, so Y* will increase by $ 60 billion from $ 520 billion to $ 580 billion.

2. Criticism against Balanced Budget Multiplier (A Monetarists' view of government fiscal policy)

1) Nonsensical Implication of the Keynesian Balanced Budget multiplier.

When government takes away $100 billion from the private sector in the form of taxation and puts it back to the economy through its expenditure, there should be an increase in income by $100 billion.

Ow! Thus it seems that you are pulling yourself up by your own bootstraps; you are increasing Y by 1 at no real cost by simply shifting resources from consumer to government.

In a hidden way, the MPC associated with government expenditure is regarded as 1, while the MPC associated with consumption expenditure is regarded as less than one. It is related to the way G is evaluated, i.e. on the cost (expenditure) basis; whenever there is an increase in G, it will be counted in national income to the full (all of government expenditure is regarded as the production of final goods).


2) Basic Tenet:"There is no such a thing as free lunch."

It seems strange that an increase in G should have a multiplier effect on income.

Contention: To the extent that government expenditures are on intermediate goods, the balanced budget multiplier is less than one.

Indeed, in a special case, the Balanced Budget Multiplier may be zero.

3) Review of Multipliers

(we have already seen the illustration, which is also in the textbook in a great detail)

Remember the illustration of multiplier.Increase in Autonomous Expenditure/Aggregate Demand______________________________________________________Period Increase in Increase in Increase in Demand Production Income______________________________________________________1 ΔAE ΔAE ΔAE

2 c1 ΔAE = c1 ΔAE = c1 ΔAE

3 c12 ΔAE c1

2 ΔAE c12ΔAE

4 c13 ΔAE c1

3 ΔAE c13 ΔAE

___________________________________________________. .. .

. . . .

The cumulative sum of the increases in income is

ΔY = ΔAE+ c1ΔAE+ c12 ΔAE+ c1

3 ΔAE.........

= ΔAE (1 + c1 + c12 + c1

3 ...........)

= 1 ---- ΔAE 1-c1

= multiplier x ΔAE


Note: If there is no net increase in AE in the first round (ΔAE= 0), there would not be anything which can bring about the multiplier effect; ΔY= k x 0 = 0.

Balanced Budget Financing Re-examined;

Government increases government expenditure (G) and at the same time increases tax (T) by an equal amount; ΔG = ΔT > 0.

If there is $ 1 billion of increases in G (Δ G = $ 1 billion), now it is assumed that there is $ 1 billion of increases in aggregate expenditures in the first round. On the other hand $ 1 billion increase in tax leads to a decrease in consumption by "c1 (MPC)" fraction of $ 1 billion because $ 1 billion increase in tax decreases personal disposable income by $ 1 billion, and the resultant consumption would decrease by c2 x $ 1 billion. In the equation of AE for the first round, in AE + Δ AE = C + ΔC + I + G + ΔG, ΔG= $ 1 billion, and Δ C = c1 x $1 billion, and thus net change in ΔAE = $ (1 – c1) billion. This is a net increase in AE, the parallel shift-up (an increase in the intercept) of aggregate expenditure curve. This parallel shift-up of $(1-c1) billion brings with it the multiplier effect (by k times ΔAE) as going through the second, third...... rounds. The resulting total cumulative increase in national income will be ΔY* = ΔAE x k = (1-c1) x 1/(1-c1) = 1.

4) A Correct National Income Accounting Identity without Double Counting

We should note the present inappropriate Definition of National Income;In the conventional national income accounting system,

AE = C + I + G + X-M;

However, erroneously, we regard all government expenditure as increasing aggregate expenditure or national income. But parts of government expenditures are on intermediate goods (eg. J. Carr's example of a shoe factory's road).

But only part of ΔG, the portion of government expenditure on final goods should be included in the 'correct' national income; In Canada 77% of ΔG are on final goods.

The correct national income account should be

AE = C + I + 0.77 G in Canada.

5) A Correct Balanced Budget Multiplier

When government increases its expenditure and taxation by the equal amount; ΔG= ΔT. Then, on the one hand, ΔG increases AE on final goods and services by 0.77 ΔG. On the other hand, ΔT decreases the disposable income by ΔT (ΔYd = -ΔT) and consumption by MPC times the decrease in the disposable income or -ΔT; ΔAE = -c1 ΔT;

AE = C + I + 0.77 G + X-M, and thus


AE + ΔAE= C - ΔC + I + G + 0.77 (ΔG);

ΔG ΔAE= 0.77 ΔG

ΔT ΔAE= -ΔC = MPC x – ΔYd = -c1 ΔT......(2)

The net change in AE is (1) + (2);Net ΔAE= 0.77 ΔG- ΔC = 0.77 ΔG- c1 ΔT.

As ΔT = ΔG with balanced budget fiscal policy, Net ΔAE= (0.77 – c1) ΔG.

The resultant change in the equilibrium national income is

ΔY= k (multiplier) x ΔAE= (0.77-c1)/(1-c1) ΔG.

The Balanced Budget Multiplier is (0.77-c1)/(1-c1) and smaller than the conventional Balanced Budget Multiplier which is equal to 1 = (1-c1)/(1-c1).

In a very special case where MPC happens to be 0.77, then the BBM = 0.

Balanced Budget Multiplier works through redistribution of income;

Income is redistributed from people whose MPC <1 to government whose MPC is assumed to be 1.

But real MPC of the government on final goods is not one.

You can have a non-zero balanced budget multiplier where expenditures by government are not a take over of private services (i.e., not an intermediate goods, eg. military expenditure)The above case, the only case you can get something for nothing is in the world of rigid prices and unemployed resources.

If national income were to be Y = C + I + G - T, the balanced budget multiplier would be equal to zero. Here all taxes would be regarded as taxes on intermediate goods, thus C > C + cY.

3. Criticism against a Naive View of the role of government

It seems strange that an increase in G should have a multiplier effect on income.

Why can't government expenditure simply be consolidated into the rest of the economy?

-i.e. we cannot view government as a giant corporation which produces goods and services and sells (or gives) them to consumers and is owned by the citizens as shareholders of the country. The corporation (is assumed to) acts in the interests of its shareholders.


It is true and to some extent it is recognized by people making consumption decisions that government expenditures of a consumption nature are of value only the extent that they have a consumption value to individual households and that under full employment the making of either type of expenditure (C or I) reduces the total real resources currently available to households for private consumption and addition to wealth.

If these facts were recognized and given exactly accurate weight by households in every relevant respect, then the government can, without error, be consolidated into the private sector.

From the standpoint of economic analysis there would be no more reason for treating government as an entity separate from the private sector than there would be for treating a company as an entity separate from its shareholders, where the stockholders were in full and knowledgeable control of its own affairs.

The point has generally been overlooked, the government having, habitually, and without justification, been cast in a separate role in effect as if households placed no value whatsoever on the goods and services supplied by government.

The truth may be somewhere between these two extremes.

If households do, after all, value government expenditures as income, as they would (meals supplied without charge at their jobs or other such income in kind) and similarly count in their consumption the consumption component of government expenditures then the consumption function will be

C + Gc = C0 + c1 (Y - T + Gc) = C0 + c1 Y if G = T (balanced budget).


i.e. government expenditure is income in kind. So consumption depends in total income. If people decide to spend money on recreation collectively (i.e. Gc up - parks built) they will spend less in recreation privately. You don't have to go up North for vacation if government builds national park besides you.

Here the changes in (balanced change) Gc have no effect (zero multiplier); balanced budget multiplier = 0 because the decrease in private consumption in C is equal to the increase in Gc. The result for consumption happens because an increase in government consumption(expenditure) will be matched by an equal decrease in private consumption, leaving no net increase in aggregate expenditure. These are same results which would be obtained if government were consolidated in private sector.

A zero multiplier for Gc, though it may appear paradoxical, is not because it simply shifts the composition of total consumption at any given level of income.

We can view the private offset to the consumption supplied by the government as having two components.

(1) those who are taxed to finance reduce their consumption by c2 of the taxes

(2) those who are recipients reduce private consumption by the fraction 1-c2 of their consumption (= regular fraction saved out of any income).

(3) the sum of (1) and (2) is one, giving total re-caution in private consumption = increase in Gc.

To the extent that the above is correct, balanced budget multiplier and the effect of G and T on NI given originally must be modified. We can also extend the above logic to Gc financed by bonds.

Macroeconomics 69 IV. IS-LM Model

Chapter IV. The IS-LM Curve Model

We are starting a new paradigm, IS-LM analysis.

The IS-LM curve model gives the equilibrium level of national income (Y*) in a larger setting. We have obtained Y* from the Keynesian Cross Diagram. The equilibrium condition of the goods market will be condensed into a curve of IS. We will introduce the money market; the equilibrium condition of the money market will give a one-line curve of LM. The IS and LM curves are delineated with two explicit variables of national income and interest rates.

In the IS-LM Curve Model, the interactions between the goods (output) market and the financial market gives the equilibrium Y* and the equilibrium interest rate i*.

As this new Y* satisfies the equilibrium condition in the goods market as well as the money market, it is an equilibrium of a broader scope and a higher order.

We still maintain the assumption about the fixed price level: The price level P is assumed to be fixed in the IS-LM model unless it is specified otherwise. This could be reasonable assumption when the actual equilibrium national income Y* is below the full employment national income level Yf. If there is such a buffer, an increase in demand would not push up the price level in any significant way.

1. Introduction

First, we will establish an inverse relationship between interest rates and investment in the goods market. This eventually leads us to the IS curve or the various combinations of i and Y, which satisfy the equilibrium condition in the goods market or make the demand equal to the supply in the goods market.

Second, we will establish an inverse relationship between interest rates and (real) money demand in the money market. This leads us to the LM curve or the various combinations of i and Y, which satisfy the money market equilibrium or make the demand equal to the supply in the money market.

Third, we will solve for the national income Y* and the interest rates i*, which satisfy the goods and money market equilibrium conditions at the same time. Basically, they are obtained from the intersection of the IS and LM curves.

Fourth, we will examine the Crowding-Out effect. An increase in aggregate expenditures will in general be accompanied by an increase in interest rates in the money market. This in turn will have a negative spill-over or feedback to the goods market as an increase in interest rates shaves off investment to an extent. Particularly when ∆G causes an increase in i and a decrease in I, it is called ‘Crowding-Out Effect’ of government expenditures


2. Modification of Investment Function

So far the investment function has been regarded as exogenous: It is determined or given from the outside.

Now let us endogenize the investment by making it a mathematical function of interest rates. The following re-specification of the investment function leads to a new paradigm.How can I establish the inverse relationship between investment I and interest rates i?

1) Marginal Efficiency of Capital Method

Investment is the demand for resources to be used for specific physical additions to the capital stock. An increase in capital stock or investment is expected to yield ‘a stream of net income’ over time. We can find the rate of return, which equates the present price tag of investment project on the left side of the equality and the stream of the expected returns. This rate of return is called ‘Marginal Efficiency of Capital’. As we start investing in the most lucrative project and move onto less profitable projects, the Marginal Efficiency of Capital declines as the amount of capital input increases.

The cost of the fund is the cost associated with the borrowing the fund. This is the ‘Marginal Cost of Fund’. It is generally equal to the interest rate paid on the interest bearing security, such as government bonds. In other words, the marginal cost of fund is fixed, and thus can be delineated by a horizontal line in the graph.

The entrepreneurs then weigh the benefit and the cost associated with the potential investment project. They will invest up to the point where the benefit is equal to the cost at the marginal level.

Marginal Cost of Fund = Interest Rate

When the interest rate goes up, the amount of capital input or investment declines. Simply, think of the project which is exactly making both ends, revenues and costs, meet in right now. If the interest rate and borrowing costs go up, the project has loss and will be knocked off. The investment volume decreases by the amount of investment.

2) Intuitively Speaking

How does a high real interest rate dampen economic activities? Actually it works in two ways; first it reduces the investment, and thus the AE, eventually reducing Y*. It also reduces the real money demand. At this moment ignore the second impact.

The (real) interest rate constitutes a cost of obtaining (financial) capital for additions to capital stock or investment. A higher interest rate means a higher cost, a lower profitability and the lower rate of return on investment projects.


Some investment projects which used to be marginally profitable or managed to make both ends meet are no longer profitable. So the desired investment will decrease as the interest rate increases.

3) Functional Form of Investment

I = I0 – b i,I0 is the autonomous investment and b is the elasticity of investment with respect to interest rates. b > 0. Here b measures the responsiveness to changes in investment to changes in the interest rate.

The larger the value of b, the more responsive the investment with respect to changes in interest rates. In other word, the larger the value of b, the more interest-rate elastic the investment will be.

A numerical example would be I = 100 – 5i: One percentage increase in interest rates will bring about a 5% decrease in investment.


(w.r.t. = with respect to)

3. IS Curve: Goods Market Equilibrium

The IS curve shows various combinations of national income and interest rates which bring out the equilibrium, or the equality between demand and supply, in the goods market.

Let’s plug the aforementioned modified investment function into the aggregate expenditure function, and solve for Y* and i*.

1) Algebraic Derivation

Recall there are three different cases of AE.

Case 1. All taxes are lump-sum or autonomous. T = T0. (Assume NX = X- M = 0 for simplicity for now)

Suppose that we are dealing with the aggregate expenditures with only lump-sum taxes and no exports or imports (This is Case 1 in the last chapter of the Keynesian Cross Diagram).

The AE will be

AE = C0 + c1 (Y – T0) + I0 – bi + G0

= c1 Y + (C0 - c1 T0 + I0 + G0 – bi0 )

At equilibrium, YS = AE

Y = c1 Y + (C0 – c1 T0 + I0 + G0 – bi)

Y – c1 Y = C0 – c1 T0 + I0 + G0 – bi

Solve for Y* and i*: We can rewrite this equation as a functional relationship between Y* and the interest rate i.

Y b

c - 1 - )G + I + T c - C( b1 = i

)G + i b - I + T c - C( c - 1

1 =Y

100010

000101

*

This is the algebraic expression of the relation between (i, Y) which represents equilibrium in the final goods market.


Note that the slope has a negative sign and thus the IS curve is downward sloping. This means that in equilibrium, of the goods market, the interest rate and income move in the opposite direction; if interest rate increases for some reason, in order to stay at the same equilibrium in the goods market, national income should decrease.

Also, we can draw the IS curve by putting i on the vertical axis and Y on the horizontal axis.

2) Intuitive Explanation of the IS curve.

We can also give the following intuitive explanation about the negative slope of the IS curve;

Let us start from one equilibrium: Y = YS = AE = C + I + G. Here let us change the interest rate and examine the responsive changes in Y. If i and Y turn out to be moving in the same direction, the slope of the IS curve will be positive, and vice versa.

Let us suppose that the interest rate decreases from i0 to i1. If investment is inversely related to the interest rate, there will be an increase in investment and thus an increase in the AE. This means that there will be an excess aggregate demand (now Y < AE’). How can we re-establish the equality between AE and Y? The answer is by increasing Y. In the equality of AE and YS, or the equilibrium of the goods market, when interest rates goes down and national income goes up. The interest rate and national income should move in the opposite direction.

We can express the above relationship with a curve in a graph with Y* on the horizontal axis, and the interest rate i* on the vertical axis. This curve is called the IS curve because, at equilibrium, AE = Y, which means C + I + G + X – M = C + S + T. As C in both side cancels out, the equilibrium condition of the goods market can be expressed as I + G +X = S + T + M. The first letter of each side of the equality read ‘I’ and ‘S’. So along the IS curve, I + G + X = S + T + M. So that is how the name, ‘IS curve’, came about.


3) Graphic Derivation of the IS curve.

Start with the Keynesian Cross- Diagram with which you are very familiar. Redefine the Investment function in the AE curve as being inversely related to the interest rate

Suppose that the initial interest rate is i0, it gives a certain investment level in AE, which in turn gives Y*. (see the initial equilibrium point at A in the graphs below)

Now change the interest rate up to i1. See the corresponding new Y*’ AE decreases: the new equilibrium point at B;

Also, change the interest rate down to i2, See the corresponding new Y*’’. AE increases, the new equilibrium at C.

These combinations of i and Y* will give an IS curve.


4) Comparative Statics of the IS Curve

What can cause a change in the IS curve?

(1) The slope of the IS curve

In summary, the following factors determine the slope of the IS curve:

i) The larger the marginal propensity to consume (c1), the flatter the IS curve.ii) The larger the elasticity of investment demand with respect to interest rate (b),

the flatter the IS.iii) The lower the income tax rate (t1), the flatter the IS.

Let us examine the second point: The more elastic the investment demand with respect to interest rate, the flatter the IS curve. The more sensitive the investment demand is towards the interest rate, the flatter the IS curve will be. Here the magnitude of b, or the elasticity of investment with respect to the interest rate, determines the slope of the IS curve.

Numerical Examples: Suppose that we have the following two different investment functions, which have different elasticity of investment with respect to the interest rate.

Case 1: Interest-rate Inelastic Investment eg) I = I 0 – 0.5 i

Here, the investment demand is inelastic with respect to interest rate: A 1% increase in the interest rate i will bring about a 0.5% decrease in the investment demand (Δ I0). Therefore, for a given increase in the interest rate, there occurs a relatively small decrease in AE = C + I + G , which will bring about a magnified but still small decrease in Y through a multiplier effect in the cross diagram.

Case 2: Interest-rate elastic Investment eg) I = I 0 – 10.0i

A 1% increase in interest rate will bring about a 10% decrease in investment (Δ I 0). Therefore there occurs a relatively large decrease in AE = C + I + G (Δ AE), which will bring about a correspondingly large decrease in Y through a multiplier (Δ Y) in the cross diagram.


We can see that the first example of IS curve is much steeper than the second example of the IS curve.

2) Changes in the intercept of IS curve.

Changes in the intercept of the IS curve will bring about Parallel Shifts of the IS curve. Changes in C0, I0, T0, G0 which constitute the intercept of the IS curve, will lead to the parallel shift of the IS curve.

i) Δ G0, Δ C0, and Δ I0 shift the IS curve to the right by the actor of their (simple) multiplier 1/(1-c1) (times the changes in those variables).

For instance, Δ G0 will bring about a horizontal shift of the IS curve. The distance of the horizontal shift is given by Δ G0 times 1/(1-c1).

Y *1 Y *0

Y = Ys Y = Ys

Y *1 Y *0


ii) Δ T0 will shift the IS Cure to the left by the amount of its multiplier c1/(1-c1) times Δ T0.

4. LM Curve and Money Market Equilibrium

LM curve shows the combinations of the interest rate and the income (i, Y) which satisfies the equilibrium in the money market.

1) ‘Nominal’ versus ‘Real’ Money Supply/Demand

We should make distinction between Nominal Supply or Demand and Real Supply or Demand. The first one is in monetary terms, and the second in quantity terms.

In microeconomic analysis of equilibrium, we define the demand and supply in real terms, not in monetary or nominal terms. For instance, if we say that $20,000 worth of hamburgers are demanded (or supplied), the statement is not clear enough. This $20,000 is nominal demand in monetary terms. What about the real demand or quantity? If the price is $1 per hamburger, in real terms, 20,000 units of hamburgers are demanded. If the price is $10, in real terms 2,000 hamburgers are demanded.


In the same vein, for the analysis of the money market equilibrium, the quantity of money should be also defined in real terms, not in nominal or monetary terms. The nominal quantity of money is the face value of the money, and the real quantity of money is the face value divide by the price level;

Real quantity of money = Nominal quantity of money/Price level.

m = M/ P

The real quantity of money supply m is the nominal money supply divided by the price level. For instance, nominal money supply is $2,000,000,00 dollars or $ 2 billion. The price level is measured by a price index. Suppose that the price index is 100 (or 1.00) right now. The real money supply m = 20,000,000,000/100 or 20/1.0 (units do not matter as long as there is a consistency).

2) Money Supply

The nominal quantity of the money supply is determined by the monetary authority, which usually is the central bank.

MS = M

Money supply varies depending on the scopes of money: it may include only cashes (in circulation) in a narrow scope, and may include cashes and all deposits in a broad scope such as M2. The different scopes of money supply will be discussed in full in the separate chapter.

For instance, M = $20,000,000,000 or $20 billion.

The monetary authority does not have to determine the nominal money supply on the basis of any variables in any given manner over time. Thus, we regard the nominal money supply as an exogenous variable, and regard it as arbitrarily determined by the monetary authority.

Mathematically, this means that the nominal money supply curve is vertical, being independent of interest rates. As the money supply is independent of the interest rate, when drawn in the interest rate and real quantity dimension, the money supply curve is vertical, being the same regardless of the level of the interest rate.


At one point of time it is fixed. However, of course, over time it can be changed by the monetary authority. In fact, the monetary authority sets the nominal money supply in each period.

For instance, depending on circumstances, the monetary authority may increase or decrease the nominal money supply when there is an increase in the national income. If the monetary authority wants to accommodate the booming or growing economy, it would increase the nominal money supply in the face of a rising national income. The logic is that a larger economy has a larger volume of economic transactions and needs a larger amount of medium of exchanges, i.e., money. On the other hand, if the monetary authority judges that the rising national income may touch off inflation and thus decides to fight the inflation, it will decrease the money supply in the face of a rising national income. This is called ‘ leaning-against-wind’ monetary policy. All in all, the monetary authority can choose any of these policies. Mathematically, this means that there is no consistent functional relationship between the national income and the nominal money supply. In fact, nominal money supply has no consistent relationship with any economic variables.

2) Real Money Demand

(1) Uniqueness of Real Money Demand

A few important things to remember about real money demand:

First, note that the money market equilibrium should be defined in terms of real money supply and demand;

Nominal money supply is equal to nominal money demand at all times, i.e., at and out of equilibrium. The nominal quantity of money demanded by the society as a whole is always equal to the nominal quantity of money supplied by the government; MS = MD at all times. Suppose the government is handing out newly printed paper monies or notes on the street. IS there anyone who would refuse them? Every dollar of money supply will be gladly demanded.

Second, while an individual can control real money demand, the general public as opposed to the monetary authority cannot control real money demand;

When an individual receives some new paper monies, her/his nominal (and real) balances increase. S/he may succeed in decreasing the nominal money demanded or the real money balanced back to the initial level by spending the excess money holdings. However, because her/his expenditures will become someone else’s receipts, some other members are getting the increased money supply. So from an individual’s view point the nominal money demanded may be controllable, while it is not controllable from the entire society’s viewpoint. What is true for individuals is not necessarily true for the society as a whole. This is the ‘fallacy of composition’ commonly founded in macroeconomics.


As individuals are busy getting rid of the excess of money holding over the desired level of demand (“I would like to have $200 in my pocket, but as government gives me a new $100 bill, now I have the excess of money holding by $100. I would like to go back to the desired level of money demanded, that is $200 by spending $100 away.”) The increased money becomes a kind of ‘hot potato’. What does this mean in terms of the real money demand? The real money demand, which is the nominal money demand (= the nominal money supply) divided by the price level, is going back to the initial level. The increased speed o spending and expenditure will eventually push up the price level. The general public are collectively changing the price level and thus controlling the real money demand.

Suppose MS = M = MD = $200 billion and P = 1.00 initially in the equilibrium; the real money demand is MD/P = 200/1 = 200 and should be equal to the real money supply at the equilibrium. This real money demand is at the desired level at the equilibrium in light of all the determinants of the demand including the income level and the interest rate.Now the monetary authority increases the nominal money supply MS to $400 billion.

First, all the increased nominal money supply will be demanded. So the nominal money demanded is equal to the new nominal money supply; MD’ = MS’ = M’ = $400 billion.

In the short-run, the price does not change, and thus the actual amount of the real money holding will be m’ = m’’ = M’/P = $400/1.00 = 400. This is much larger than the desired real money demand, that is, 200. As there are no changes in the determinants of the real money demand, there should not be any change in the level of real money balances the general public wishes to hold. There is an excess of real cash balances over the desired real money demand; ‘actual’ real money balances > ‘desired’ real money balances.

As individuals with excessive money balances try to recover the desired real money balances by spending the excess money receipt, the price level is going up to P’. At this new price level, the new ‘actual’ real money balances (M’/P’) become equal to the desired level of real money balances.

Specifically, the price level will go up to the level of 2 (or the index number 200). The actual real money demand will be 400/2 = 200, the same level as before any changes.

(2) Functional Form of Real Money Demand

The real money demand is given a functional form such as

md = L ( i, Y ).

The above equation defines the real money demand as a decreasing function of interest rates and an increasing function of national income. What determines the desired level (quantity) of real money demand? Just as the desired quantity of hamburgers is determined by the consumers’ income and the price of hamburger, the real demand for money is determined by the income


level of the economy, that is the national income, and the price of the money, that is, the interest rate.

Let us examine the second point in the above statement: the price of money is the interest rate. In other words, the opportunity cost of holding money balances is the interest rate.

Money is one of many assets, which include bonds, stock, equities and real assets. Money and other assets are substitutes. The major difference between money and other assets is that money does not bring in any positive pecuniary returns. Actually it is very often subject to the erosion of real value due to inflation, and other assets do have pecuniary returns. However money, or cash balances in a precise term, renders a unique non-pecuniary service, which is known as ‘liquidity’. Money is the most generally accepted medium of exchange and most ‘liquid’. So when you decide to hold assets in the form of cash balances instead of any other, you are showing your preference for liquidity over pecuniary returns. This is the reason why the money demand is called’ liquidity preference and the money demand function ‘liquidity preference function.’

(Digression: Diversity of various interest rates) The pecuniary returns of other assets are, in fact, no uniform because the risks associated with other assets differ: risky assets have higher rates of returns an safe assets have a lower rate of return. The difference in the rate of returns is compensation for entering the risk, in buying risky assets. However, for simplicity, let us simply suppose that the rate of return on other assets than money can be represented by a certain representative ‘interest rate’.

The interest rate represents the foregone pecuniary return or the economic sacrifice you have to take when you are choosing cash balances over other assets, as your mode of holding assets; in other words, the interest rate is the opportunity cost of holding cash balances. When the interest rate goes up, the cost of holding cash balances increases and naturally you would like to hold less assets in the form of cash balances and more interest bearing assets. This means that the demand for money is inversely related to the interest rate.

Now we have another major factor to be considered, which affect the real money demand; the income level. When real income increases, in most cases, the demand for money increases in real terms, too. To name one reason, when real income increases, there occur more transactions, and then more cash balances should be held to back up the increased transactions.

We can give the liquidity preference function the following specific functional form;

Md = kY – h i + u,

where K is the elasticity of real money demand with respect to the national income; h is the elasticity of real money demand with respect to interest rates; and u is the random component of real money demand.


The liquidity preference curve is negatively sloped when drawn with the interest rate on the vertical axis and the amount of real money on the horizontal axis. The variables Y and u are the shift parameters of the real money demand curve.

(Note: Y and u are shifting parameters)

Also, we can draw a set of liquid preference curves for different levels of income; the higher the level of national income, the larger the demand for real money balances. You may remember, from the class of introductory economics, that an increase in income shifts the demand curve to the right.

3) Money Market Equilibrium and LM Curve

As emphasized, the money market equilibrium should be defined in real terms; the money market is in equilibrium when real money supply is equal to real money demand ex-ante. If the demand is larger than the supply, the price will go up. With an increased price some people will give up their demand. The price, which adjusts to equate the supply and demand, is nothing but the interest rate. The money market interest is set at such a level as to make the supply equal to demand ex-ante.

1i

0i

dm

L (Y, u )



(1) Algebraic Solution

LM Curve: Money market equilibrium condition ms = md yields the following equations. Rearranging the equation with ‘i’ on the left hand side and ‘Y’ on the right hand side, we get a

LM Curve. Real money supply = , = L(i,Y,u) = kY – hi + u

Y hk + )u +

PM (-

h1 = i

u + Y k + PM -= i h

u + i h - kY = PM

0

0

0

↓ ↓ intercept slope

We can draw a LM curve with the interest rate on the vertical axis and the national income on the horizontal axis. The LM curve is upward-sloping, or in other words, it as a positive slope. (Along LM )

(2) Intuitive Explanation

Why is the LM curve upward-sloping LM?

Let us start with an equilibrium, ms = md.

PM s

dm

ds mm


When the interest rate increases there will be a decrease in the real quantity of money demanded, (a new md < an old md = ms).

How can we recover the equality between the real money demand and the real money supply? The real money supply cannot change unless the government changes the nominal money supply MS or M to a higher level, or the price level changes. So the real money demand should rebound back to the initial level in order to re-establish the equality. One way of doing it is to increase Y*. When the national income increases, the real money demand will increase. This increase in real money demand offsets the previous decrease in real money demand. So we can observe that the interest rate and the national income move in the same direction.

(3) Graphic Derivation of LM curve:

The real money demand and supply mainly carve up the relationship between the interest rate and the real money balances. However, we are interested in getting the LM curve which carves up the relationship between Y and i*.

To get the relationship between the two, we have to change the value of Y and look at the responsive change in i* or the money market equilibrium interest rate;

When Y increases from Y1 to Y2 the real money demand curve shifts to the right. Here the Y variable is a shift parameter I the real money demand function.

When the real money supply remains unchanged, the increased real money demand will push up the equilibrium price of the money in the market, that is, the equilibrium interest rate I the money market. Previously Y1 corresponded to i1, and now a higher Y2 to i2.

So a higher level of income means a higher level of interest rate. Y and i are moving in the same direction. The LM curve should be upward sloping.

4) Comparative Statics of LM curve

i iPM

ms

1i

2i

i

Yds mm /

),( 1 uYmd

),( 2 uYmd

1Y 2Y Y

),( uPMLM


(1) Change in the Slope of LM curve.

i) Elasticity of real money demand with respect to Income, or income elasticity of real money demand (K):

The larger the income elasticity of real demand, the steeper the LM curve.

For instance, when Δ Y = 1% for the following two cases:

Case I with K = 1 : md = Y – 20 i+ u

Case II with K = 0.5 : md = 0.5 Y – 20 i + u

ii) Elasticity of real money demand with respect to Interest rate, or Interest rate elasticity of real money demand (h): the elasticity of real money demand with respect to the interest rate, or in short interest elasticity of money demanded.

i iPM

ms

1i

2i

i

Yds mm /

),( 1 uYmd

),( 2 uYmd

1Y 2Y Y

),( uPMLM

i iPMms

1i2i

Yds mm /

),( 1 uYmd

),( 2 uYmd

1Y 2Y Y

),( uPMLM


In general, the larger the value of h, or the more (interest rate) elastic the real money demand, the flatter the real money demand.

In the following two cases, assuming that K = 0.5 and u = 20 for both in the money demand function md = K Y – h i + u,

Case 1 with h=0.5; Inelastic money demand, md = 0.5 Y – 0.5i = 200

Case II with h =20; Elastic money demand, md = 0.5 Y – 20 i +200

In the above graphs, we can see that with a flat md curve with a large interest-rate elasticity, a very small drop in the interest rate will bring about a very large increase in m d. We may also review some extreme cases.

When the real money demand is perfectly inelastic with respect to interest rate (the interest elasticity h = 0)

KYhiKYPM

i iPM

ms

1i

2i

i

Yds mm /

),( 1 uYmd

),( 2 uYmd

1Y 2Y Y

),( uPMLM

i iPMms

1i2i

Yds mm /

),( 1 uYmd

),( 2 uYmd

1Y 2Y Y

),( uPMLM


This is the case where interest rates do not enter the real money demand or liquidity preference function. In other words, real money demand is not responsive to the change in interest rate all; real money demand is completely inelastic with respect to the interest rate; real money or liquidity preference function is drawn as a vertical line, and the derived LM curve is also vertical.

Under what conditions will the elasticity of real money demand with respect to its own price, that is, the interest rate become equal to zero?

The magnitude of the (own price) elasticity is determined by the availability of alternatives or substitutes. If people regard non-money assets, such as bonds, equities, and so on, as completely useless as substitutes for money, the (own price) elasticity of real money demand should be equal to zero. As there are no substitutes for money, regardless of the cost of holding money (whether it is high or low), there would be a certain amount of real money balances that they think they must absolutely hold.

At the equilibrium in the money market, where real money supply is equal to real money demand as:

Thus

In this case, there is a strict proportionality between the National Income (Y) and the Real Money Supply (ms). Only money supply determines the equilibrium national income. The goods market is completely irrelevant in the determination of the equilibrium national income.

When the real money demand is perfectly elastic with respect to the interest rate (h is infinitely large): the Keynesian ‘Liquidity Trap’.

When a small change interest rate leads to a very large change in real money demand; real money demand is extremely responsive to a change in interest rate; real money demand is

i ism

ds mm / Y

kYmd LM

KYP

Ms

KPMsY


infinitely interest rate elastic. Graphically, the real money curve is horizontal. With a horizontal money demand curve, changes in money supply would not affect the interest rate at all. The interest rate will be stuck at the same level. The derived LM curve is also horizontal at that level of interest rate.

Here monetary policy is ineffective, as any increased money supply will be gobbled up as soon as it is injected into the economy. The public has a hefty appetite for liquidity, or money, and thus, it will swallow it up even with little incentive to do so, that is, a very small drop of interest rate. Therefore, the increased money supply would not have had much of a change to exert any downward pressures on interest rates. This situation is called a ‘liquidity trap’. It could have been named ‘liquidity blackhole’ if Keynes had been well versed in astronomy.

Interest Pegging Monetary Policy: When the monetary policy which involves changes in money supply is completely ineffective, the LM curve is horizontal. However, the reverse is not necessarily true. The horizontal LM curve does not necessarily mean that monetary policy is ineffective. Even if the real money demand curve is downward sloping in a normal way, when the monetary authority or the central bank is dedicated to maintaining a fixed interest rate at all cost, the LM curve will be horizontal.

Let us illustrate this point. There are a set of money demand curves which correspond to different levels of income. This gives the LM curve, linking different levels of Y and i. Let’s suppose that now changes in some factors other than Y and i cause a decrease in money demand: the money demanded decreases at a given level of interest rate and income, and thus real money demand curves with different level of national income shift all down or to the left at the same time.

In this situation, if the government is not doing anything, thus the money supply is fixed, obviously this decrease in real money demand will bring about the decrease in the money-market-equilibrium interest rate at all level of income: ms = md. Initially, and md i – md’ < m’ – i'. Therefore the LM curve shifts to the right. This will be an ordinary case.

i ism

ds mm / Y

LMidm

smsm

a b c

For these different money market equilibrium a, b and c, the money market equilibrium interest rate is the same, and is fixed.


However, if the central bank stands ready to offset any change in the interest rate, as is assumed in this question, it should decrease the money supply. If the money supply is changed exactly by the same amount as the changes in the money demand, there will be no change in the money-market equilibrium interest rate. The interest rate will be always constant at a fixed level. This implies that the LM curve is horizontal at that level of interest rate.

We can also think of the reverse case. The interest rate will be still kept at the target level. In this monetary policy regime, monetary policy is effective in pegging the interest rate. Here the policy target is the fixed interest rate, and the monetary authority changes money supply in response to the uncontrollable changes in real money demand.

(2) Shift of the LM curve.

i) Change in nominal Money Supply; Δ MS

The LM curve shifts to the right when the monetary authority increases the nominal money supply: An increase in nominal money supply leads to the increase in real money supply when the price level is fixed.

i ism

ds mm /

),( 1 uYm d

),( 2 uYm d

1Y 2Y Y

),( uPML M

),( 1 uYmd

),( 2 uYm d

),( uPM

L M

i i

sm

i

ds mm /

),( 1 uYmd ),( 2 uYmd

Y

),( uPMLM

),( 2 uYmd

smsm


ii) Change in Real Money Demand unrelated to any changes in the interest rate or the income level: ∆ u

The LM curve shifts to the right when the real money demand decreases at the given interest rate and income level.

Under what circumstances could this happen? Think about the case where people lose their confidence in currency due to the imminent currency reform. The domestic residents will decrease the demand for money and seek safe haven for their wealth elsewhere. Also, in an open economy situation, the demand for domestic currency could decrease as the foreigners wish to convert the domestic currency that they are holding into foreign currencies.

Suppose that due to a decrease in the residual term of the money demand function, an initial money demand md = K Y – h i + u (eg: md = 0.5 Y – 20 i +200, and here u = 200) is reduced to md’ = K Y – h i + u’ (eg: md = 0.5 Y – 20 i +100, and here u’ = 100). The entire set of money demand curves for different levels of income should decrease.

Note: md (Y2, u) and md’(Y2, u’) have the same Y2; and md (Y1) and md’ (Y1) have the same Y1. Initially, Y1 corresponds to i1, and Y2 to i2. With a decrease in real money demand and consequent shift of the demand curves, Y1 corresponds to i1,and Y2 to i2. When md decreases as u decreases to u’, the LM curve shifts to the right.

i i

sm

ds mm /

),( 1 uYmd

),( 2 uYmd

1Y 2Y Y

),( uPMLM

sm

),( uPMLM

i iPMm s

ds mm /

),( 1 uYm d

),( 2 uYm d

1Y 2Y Y

),( uPML M

),( 1 uYmd

),( 2 uYm d

),( uPML M


5. Equilibrium National Income and Interest Rate in the IS-LM Framework

The intersection of the IS and LM Curves give the equilibrium national income and the interest rate that satisfy the market clearing condition in both goods markets and money markets; ex-ante all the goods produced are demanded, and real money supply is equal to the real money demand.

1) Graphic Solution

2) Algebraic Solution

Steps1. Get the IS and LM curve2. Equate the IS and LM curve3. Solve for Y*

4. Substitute the solution of the Y* for the variable Y and the LM equation to get the value for i*;

5. Differentiate the above equations for multipliers.


Case 1. All taxes are lump-sum or autonomous. T = T0. (Assume NX= 0 for simplicity)

Recall the IS Curve: Goods market equilibrium condition AE = Y yields

{Note: (- ) = slope of IS Curve} Recall the LM Curve: Money market equilibrium condition ms = md yields

(Note: = slope of LM curve, h↑ ↓, thus, LM gets flatter)

where K is the elasticity of real money demand with respect to the national income; h is the elasticity of real money demand with respect to interest rates; and u is the random component of real money demand.

Equate the above two equations for i or Y: The Simultaneous Equilibrium of Goods and Money Markets yields

u) - PM(

hkb + c-1

hb

+ )G + I + T c - C(

hkb + c-1

1 = Y

get, weabove the Rewriting

u) - PM(

kb + )c-(1b + )G + I + T c - C(

kb + )c-h(1h = Y

01

00010

1

*

0100010

1

*

Y b

c - 1 - )G + I + T c - C( b1 = i

)G + i b - I + T c - C( c - 1

1 =Y

100010

000101

bc11

Y hk + )u +

PM (-

h1 = i

u + Y k + PM -= i h

u + i h -ky = PM

0

0

0

hk

hk


Multipliers:

i)Impacts on Y*

We may remember that in the simple Keynesian model of income determination (the Cross-Diagram with Y = YS and AE) the multipliers were obtained by differentiating the equilibrium national income equation.

Now, in the IS-LM curve model, another set of the multipliers can be obtained by differentiating the first equation, which describes the equilibrium national income in the goods and money market, with respect to the Autonomous components of AE ( C, T, I, G and M). The result of differentiation is the coefficient of each variable in the above equation.

(Note: the above two are business cycles)

(Note: = “Fiscal Policy Multiplier”)

The first two multipliers have something to do with business cycles as the C0 and I0 show cyclical movements over time beyond the control by government.

The third one is called the ‘Fiscal Policy Multiplier’. It measures the ratio of the change in the goods and money market equilibrium national income to a change in government expenditure. Note that this new multiplier or the fiscal policy multiplier in the IS-LM framework is smaller than the government expenditure multiplier in the Cross-Diagram setting. Both measure ∆Y* due to ∆G. However, the fiscal policy multiplier takes account of the resultant change in interest rate and the consequent crowding out effect while the government expenditure multiplier does not; the difference between the government expenditure multiplier and the fiscal policy multiplier is the crowding-out effect which results from an increase in interest rates and its suppression of private

hkb + c-1

1 = CY

1

*

0

hkb + c-1

1 = IY

1

*

0

hkb + c-1

1 = GY

1

*

0

0

*

GY


investment. Because of the secondary feedback in the money market, the magnitude of fiscal policy multiplier is smaller and thus ∆G has a smaller impact on Y*.

The following multiplier measures the change in income to a change in a lump-sum tax responsible for it.

The following multiplier is called the ‘Monetary Policy Multiplier’. It measures the ratio of the increase in income to an increase in money supply.

“Monetary Policy Multiplier”

ii) Impacts on Interest Rates:

Remarks: Note that compared with the equilibrium national income equation without the LM curve

(in the previous handout), there is an additional term kb/h in the multiplier for the autonomous expenditures.

A $1 increase in G shifts the IS curve by $1/(1 - c1), and y* by $1/(1-c1 +kb/h). What makes the difference?

Now, let’s extend our model to more complex cases of aggregate expenditures as we have seen before.

i

*0i

*1i

1e

0e

SI

IS

LM

*0Y *

1Y*2Y

Crowding out effect

hkb + c-1

c =

TY

1

*1

0

hkb + c-1

hb

pMY

1

*


Case 2. There are Autonomous and Proportional Taxes. T = T0 + t1Y, IS Curve: Goods market equilibrium condition AE = Y yields

Y b

)t-(1c - 1 - )G + I + T c - C( )t-(1c

1 = i

)G + i b - I + T c - C( )t-(1c - 1

1 =Y

1100010

11

0001011

LM Curve: Money market equilibrium condition ms = md yields

y hk + )u +

PM (-

h1 = i

u +y k + PM -= i h

u+i h -ky = PM

0

0

0

Simultaneous Equilibrium of Goods and Money Markets

u) - PM(

hkb + )t-(1c-1

hb

+ )G + I + T c - C(

hkb + )t-(1c-1

1 = Y

get, weabove the Rewriting

u) - PM(

kb + ))t-(1c-(1b + )G + I + T c - C(

kb + ))t-(1c-h(1h = Y

011

00010

11

*

01100010

11

*

Note: compared with the equilibrium national income equation without the LM curve (in the previous handout), there is an additional term kb/h in the multiplier for the autonomous expenditures.

Case 3. There are proportional taxes, and Imports are proportional to national income.

NX = X - M;

M = M0 + m1 Y;

X = X0,


where M0 denotes the Autonomous imports and m1 denotes the Marginal Propensity to Import.

IS Curve: Goods market equilibrium condition AE = Y yields

Y b

m+ )t-(1c - 1 - )M - X + G + I + T c - C( m+)t-(1c

1 = i

)M - X +G + i b - I + T c - C(m + )t-(1c - 1

1 =Y

1110000010

111

0000010111

LM Curve: Money market equilibrium condition ms = md yields

Y hk + )u +

PM (-

h1 = i

u + Y k + PM -= i h

u+i h - kY = PM

0

0

0

Simultaneous Equilibrium of Goods and Money Markets

u) -PM(

hkb +m +)t-(1c-1

hb

+)M -X +G +I +T c -C(

hkb +m + )t-(1c-1

1= Y

get weabove the Rewriting

u) -PM(

kb + m+)t-(1c-1b +)M - X +G +I +T c-C(

kb + )m+)t-(1c-h(1h= Y

0111

0000010

111

*

01110000010

111

*

,

Note: compared with the equilibrium national income equation without the LM curve (in the previous handout), there is an additional term kb/h in the multiplier for the autonomous expenditures.

3) Comparative Statistics: Business Cycle, Fiscal and Monetary Policies

The above equilibrium equations for Y* and i* indicate that

(1) Business Cycles

∆I0, and ∆C0 are beyond direct control by government and cause undesirable fluctuations in Y*: The factor by which the changes in autonomous investment and consumption are multiplier into


larger changes in Y* is given by the coefficient of I0 and C0 in the above equilibrium income equation.

(2) Fiscal Policy:

i) ∆G0 leads to an increase in Y* and an increase in i*

ii) ∆T0 leads to a decrease in Y* and an decrease in i*.

(3) Monetary Policy

i) An increase in money supply leads to an increase in national income:

ii) An increase in money supply leads to a decrease in the interest rate.

Let us examine the above (2) and (3) in a formal and rigorous way:

5. Fiscal and Monetary Policies in the Conventional IS-LM Curve Model

1) Fiscal Policies

Government expenditures may be financed either by taxes or by deficits. In the latter, the deficits should be made up by issuing bonds. Perversely, a bond-financed increase in government expenditures has a larger impact on national income than a tax-financed increase in government expenditures. This inequivalence in terms of financing is a main feature of the conventional IS-LM model. We will later discuss the problem of this view and present an alternative view developed by Barro-Richardo. For now, we are simply having a review of fiscal policies in the IS-LM model.

(1) A Bond-Financed Increase in Government Expenditure: ∆G = ∆B

When government increases its expenditure without increasing tax revenues, there occur deficits. The government has to make up for deficits by borrowing funds. The certificates of borrowing by the government are bonds. So deficit-financing is the same as bond-financing. There is no corresponding increase in taxes when government expenditures increase.

In the Keynsian Cross-Diagram, ∆G0 shifts the AE curve up by ∆G0 and the Y (note that there is no longer * on Y because this Y is just an equilibrium in the goods market as opposed to the Y *

which is the equilibrium in the goods and money markets) increases by ∆G0 times 1/(1-c1).

Accordingly, in the IS-LM curve model, there occurs a parallel shift of the IS curve to the right by ∆G0/(1-c1). This results into the increase in Y* by ∆G0 times 1/(1-c1 + Kb/h) which is smaller than ∆G0 (1-c1).


The increase in Y*, shown as the rightward movement of Y*in the graph, is smaller than the rightward shift of the IS curve. The reason is that ∆G0 leads to ∆Y*and this increased income increases real money demand. An increase in real money demand pushes up the interest rate when real money supply is fixed. A higher interest rate decreases investment and through the multiplier, income falls. This mechanism partially offsets the initial increase in the income due to ∆G0. This is called ‘Crowding Out’. The increased government expenditure crowds out the private investment by raising the interest rate.

(2) A Tax-Financed Increase Government Expenditure: ∆G = ∆T

When government is increasing its expenditure with revenues raised through taxation, it is engaged in balanced budget operation.

In the Cross Diagram, ∆G = ∆T leads to a rightward shift of Y or the goods market equilibrium national income by ∆G times 1.

Accordingly, in the IS-LM curve model, the IS curve shifts to the right by ∆G. This results into the rightward shift of Y*, goods and money market equilibrium national income by ∆G times (1- c1)/(1- c1 + Kb/h) which is less than ∆G. Also the interest rate goes up.

2) Issues of Monetary Policies

We will examine some relevant issues in the separate chapter.

3) Policy Mix

The crowding out effect shows that as long as the IS and LM curves are normally shaped, a change in G will bring about undesirable side effect of a higher interest rate and a smaller investment.

A: the horizontal distance of IS curve shift

B: Y*

C: i*


Now the policy mix enables a desired Y* and a desired I* to achieved simultaneously if and only if Y* is below Y1 or the full employment national income (maximum potential national income).

CASE STUDY: “House or Gun” for the Americans during the Vietnam war(Credited to Professor R. Gordon, Northwestern University)

The 1965-67 period, during which U.S. government spending expanded rapidly as our involvement in the Vietnam war deepened, provides an unusual case study of the consequences of fiscal expansion while the real money supply remains fixed. In the fourth quarter of 1966 (October through December), written as 1966:Q4, the real money supply was almost exactly the same as five quarters earlier, in 1965:Q3. An LM curve corresponding to this fixed level of Ms/P is drawn in the figure. During this five-quarter interval the level of real government purchases grew by 12.2 percent, represented in the figure by the rightward shift in the IS curve from IS0 to IS1.

How did real income and the interest rate behave over the five-quarter interval? Real income increased by $129.9 billion, more than the $60.2 billion increase in government spending, because of the (fiscal policy) multiplier effect. And the higher demand for money forced an increase in the interest rate from 4.7 to 6.0 percent to keep the total demand for money equal to the fixed real money supply.

The immediate victim of the higher interest rates was investment in residential housing. By 1966:Q4 this component of investment had declined 17.9 percent from the level reached in 1965:Q3. This is the Crowding out effect. (Nonresidential investment including inventory change and expenditures on plant and equipment-continued to grow despite the increase in interest rates through 1966:Q4. The reason for this growth stems from the delay between the increase in the interest rate and the subsequent decline in nonresidential investment, a factor our IS-LM model does not take into account.)

A basic principle of economics holds that a wartime economy cannot boost military spending without decreasing civilian expenditures; that is, the economy “cannot have both guns and butter”. In this case the economy could not have both “guns and houses”.

The principle is not true in a recession or depression which has some buffer in productive capacity and has the actual national income below the full employment income level. With expansionary monetary policy which shifted the LM curve, the interest rate was brought down. This is the policy mix. In 1967 and the early 1968 the economy tried to have both “guns and butter” due to this policy mix of the simultaneous use of expansionary fiscal and monetary policies.

President Lyndon Johnston delayed proposing a tax increase, which was not finally approved by Congress until Jul 1968. Consequently, the money supply began to grow rapidly, and this allowed private spending as well as defense spending to grow.

The problem arose when the resultant Y*exceeded the full employment income Y*. The excessive spending growth of 1967 –68 in an economy that was straining at the limit of its


productive capacity unleashed a serious inflation. Many analysts think that an underlying cause of the inflation suffered by the United States sine the late 1960s dates back to President Johnston’s refusal to “pay for” the Vietnam war in 1966.

The IS-LM curve model shows that there could be a number of policy mixes or the combinations of fiscal and monetary policies to achieve a certain level of national income. For instance, when the economy is stuck at the equilibrium with Y* and i* which is below Yf or full employment equilibrium, the government can attain Yf by entirely relying on ‘expansionary fiscal policy’ (case I), by entirely relying on ‘easy money policy’ (case II), or even the combination of the two policies (case III).

Although the equilibrium income is the same for both cases, the relative composition of private and government sectors will be different. In the first case, at the given level of income, the share of private investment and consumption compared to that of the government sector is smaller than in the second case. The reason being, the increased government expenditure raises the interest rate and thus decreases private investment. In other words, the relative share of the public sector rises at the expense of the private sector.

(4) Effectiveness of Fiscal and Monetary Policies

The degree of effectiveness of fiscal and monetary policies depends upon the magnitude of the underlying parameters.

1) Effectiveness of Fiscal Policies

Depending on the magnitude of the elasticity of real money demand with respect to interest rate (=h), the LM curve could be vertical (h=0), upward sloping (0<h<infinity), and horizontal (b is infinitely large).


An expansionary fiscal policy (∆G or ∆T) shifts the IS curve to the right. The same shift of the IS curve could bring about different degrees of ∆Y* depending on the slope of the LM curve.

Cf. Now you may remember that the Interest Pegging Monetary Policy leads to a horizontal LM curve: The interest rate is constant at a fixed level. In this case of the horizontal LM curve, the fiscal policy will be very effective because there is no crowding out; the expansionary fiscal policy does not increase the interest rate and thus does not have any dampening effect on investment or partially offsetting effect on national income. However, the bad side of the horizontal LM curve (which would not have any crowding out effect) is that a decrease in consumption or investment will bring about a larger decrease in national income in this horizontal LM curve than when the LM curve is upward sloping.

.

2) Effectiveness of Monetary Policies

i

*0i

*1i

SI

I S

1LM

*3Y

2L M

3L M

Y

*2i

c la s sic a l (c o m p le te c ro w d in g o u t )

n o rm a l (p a r tia l c ro w d in g o u t)

keynesian (no crowding out)


6. Controversies and Pitfalls of the IS-LM curve analysis:

1) Ricardian Equivalence

IS-LM curve model suggests, “Bond-financed government expenditures have a larger impact on the national income than the same amount of tax-financed government expenditures.”

“A tax cut without an equal decrease in government expenditures leads to an increase in government budget deficits. This switching from one method of financing government expenditures to another should alone increase the national income.”

“An increase in government deficits due to tax cuts will lead to an increase in national income.”

(1) Illustration: What does the IS-LM model imply?

This is just to paraphrase the Keynesian position that in the simplified Keynesian model the government expenditure multiplier ∆Y/∆G = 1/(1-c2) is larger than the balanced budget multiplier ∆Y/∆G + ∆Y/∆T = 1 or that in the IS-LM model the fiscal policy multiplier ∆Y*/∆G = 1/(1-c2 + Kb/h) is larger than the balanced budget multiplier (1- c2/ (1-c2 + Kb/h).

Graphically,

Keynesian school gives a very clear answer: when the bond-financed government expenditure increases, the AE increases, and thus IS curve shifts to the right which results in an increase in Y*

and i*.


The upshot of the Keynesian theory is that ∆G will have different impacts on Y* depending on how ∆G is financed, or the method of financing ∆G. ∆G financed by bonds does shift the AE and the IS curves more to the right than ∆G financed by taxes.

To corollary is that the switching of revenue sources from taxation to bond-issues without any changes in G will lead to a net increase in Y*: A tax-cut increases disposable income, which in turn increases consumption by a lesser amount, AE, and finally Y*.

A gullible mind would conclude that deficit financing is more effective and thus better than tax-financing. We are now experiencing the legacy of this line of thinking by having the problem of the accumulated amount of deficits. That is a huge amount of public debts.

(2) Uncertainty from Intergenerational Transfer and Bequest

Whether the above statement is correct or not depends on (1) the degree of farsightedness of the consumers, and (2) their sense of responsibility towards the welfare of the future generation. The crucial problem is that the beneficiary of the present tax cut may be different from those who will eventually pick up the tap in the form of an increased tax in the future.

Let us examine the following concrete real world examples faced by consumers:

As soon as the NDP party came to power in the province of Ontario in 1989, it increased government expenditures drastically. Sensible and far-sighted people predicted that as the government did not hit any bonanza, it would soon have to increase taxes. In 1992, in fact, the government proposes major tax hikes. It has turned out that the government was riding a fiscal time-machine, and simply playing the game of transferring resources from 1992 to 1990. Back in 1990, what would be the impact of the increased government expenditures on those who benefited directly from it and correctly foresaw the future tax-liability attached to it?

In the year 1992, the government announces that it will decrease taxes in 1992-93, and issue bonds with a maturity of 100 years. It will raise taxes to retire the bonds in the year 2092. Let us suppose that the average life expectancy is 75 years. What will be the impact of this proposed tax-cut on Y*?

The following two scenarios are possible:

First, if the consumers are short-sighted or myopic, or have no concerns about the welfare of the future generation on whom the tax burden will be imposed after their death: they will be just


concerned about their life-time income. The tax-cut increases disposable income now, but the corresponding tax increase will come after their death in 2092. So this tax-cut is free lunch for these people. They will spend the part of increased disposable income on consumption, which increases AE, and eventually, through the multiplier effect of the A, Y*.

Alternatively, if the consumers are far-sighted and responsible for the welfare of the future generation: They foresee the price tag of an increased future tax liability attached to the goody of the present tax cut. They do not want the future generation to be affected by the tax-hike. They would not spend their increased current disposable income on consumption. They save it and leave the savings as the bequest to the future generation so that the future generation may cash the savings to pay for an increased tax liability in the future. The consumption by the current generation does not change, and thus neither the AE nor Y* change. The IS curve will not shift to the right.

(3) Ricardo-Barro Equivalance

Ricardian Equivalence states that there is equivalence between bond and tax-financed issuing bonds instead of increasing taxes, the Canadians used increases in disposable income in raising their standard of living rather than increasing savings for the future generation. The present generation cannot help feeling that they are forced to pick up the lunch bill for the past generation. To that extent, Ricardian Equivalence failed. This failure does not reduce the need to learn the theory itself, but rather strengthens it: it will help the current generation to remember that there is no such a thing as free lunch in the economy and that the tax-cut for the current generation comes at the expenses of an increased tax liability of the future generation.

2) Timing and Expectations

The IS-LM curve model simply suggests, “Investment tax cut will boost economy.”

According to the Keynesian theory, ∆Y*/∆I = 1 /(1- c1) in the simple cross diagram model without the crowding out, and ∆Y*/∆I = 1/(1- c1 + Kb/h) in the IS-LM model with the crowding out.

When we introduce the element of time and expectations, the results could be uncertain.

Example: Carefully analyze the following economic situation.

The Canadian economy is caught in a serious recession. Some measures to boost investment are needed. Now in January of year 2010, the concerned Canadian government announces that it


will give an investment tax credit, which will last only for four months. But it says that it will take eight months from now to pass through the parliament.

What will be the instant impact of this supposedly ‘expansionary measure’ on the economy during January to August?

The firms will delay the preplanned and newly planned investment until the bill passes through the parliament. During January to September, there will be very little investment to be made. This decrease in investment will decrease Y* through the multiplier effect.

Would this measure more expansionary between September and December than a permanent investment-tax-break at the same rate? Why?

If the tax break is only for a limited time, then the investors would like to take advantage of it by rushing investment during the period of the tax break. They will delay and forward the investment projects. In the case of a permanent tax break, there is no reason to forward investment projects along the time scale: the tax cut will be effective forever, so why hurry to invest? There will be only delaying investment projects from the time of the announcement to the time of the tax break coming into effect. In other words, as far as investment is concerned, a temporary tax break has a larger expansionary impact on the economy than a permanent investment tax break.

3) Time-lags

It takes time for any economic problem to get recognized, for any remedial decisions to be made, and for the policies to be formulated and executed. These are Recognition Lag, Decision Lag, and Execution Lag of an economic policy. It also take time for the economy to respond to an applied policy; this is the Effectiveness Lag. The former is Inside Lag, and the latter Outside Lag.

Due to time lags, contradictory fiscal or monetary policies may come into effect at a wrong time.

4) Lucas’ Critique of Economic Policy Evaluation

Government economists use some version of the IS-LM model in order to predict and to evaluate a proposed economic policy.


The equilibrium national income equation shows the quantitative relationship between Y* and various variables such as G, I, C and T: they are related through the coefficients, such as 1/(1- c1

+ Kb/h), which in turn consist of many parameters, such as h, b, K, c1, and so on.

Econometrics enables us to estimate the magnitude of h, b, K, c1 with past data. We use these estimated values of parameters in the IS-LM model, and thus make some quantitative evaluation of newly proposed policy. For instance, if c1 is estimated from past data to be equal to 0.8, K to be equal to 0.5, b to be equal to 20, h to be equal to 20, a proposed decrease in government expenditures by $50 billion will lead to a decrease in national income by $ 75 billion, that is, 50 times the multiplier of 1.5 (1 over 1 minus c1 plus Kb/h) in case of no crowing-out.

This use of econometrics along with the IS-LM curves could lead to problems under certain circumstances.

When government changes its whole set of rules of the game, there occurs a ‘regime change’. This is different from a mere ‘policy change’, a quantitative change in government expenditures or money supply. If the general public takes a regime change as permanent and credible, they will accordingly change their behavior. This change in behavior is reflected in the parameters of behavioral equations such as consumption function. This is a ‘parameter drift’ due to regime change. The use of estimated parameters under the old regime to a new policy under the new regime would give a wrong prediction of the proposed policy. This is the core of Professor Lucas’ Critique against Econometric Policy Evaluation: when there is a regime change which causes a parameter drift, the use of estimated parameters from the past regime would give the wrong evaluation of the new proposed policy.

Case I (a mere policy change). There is no regime change. Now government is going to decrease its expenditure by $50 billion. The econometric technique gives you that the marginal propensity to consume is estimated to be 0.8 from the past 10 year data. In this case, the use of the old parameter 0.8 for a new policy is justifiable as there was no change in government’s rule of game or regime change and thus the consumers have no reason to change their behavior. The IS curve will shift to the left by ∆G times 1 over 1 minus 0.8 or $250 billion. There will be a decrease in Y*

by a less amount.

Case II. (a regime change). Government announces that it will change the rules of game entirely. It will turn away from the past ‘spending’ regime to a new ‘saving’ one. Now as part of such fundamental change, the government is decreasing its expenditure by $50 billion. What will be the change in Y*? The past behavior of the consumers under the old regime was that a $1 increase in disposable income increased consumption by $1 time the marginal propensity to consume, say, 0.8. Now as they expect leaner days ahead of them, they would like to practice thrift, too. This change in consumers’ behavior will be reflected in the change in the marginal propensity to consume or c2, say 0.6, will be smaller than the c2 before the regime change. The IS curve will move to the left by ∆G times 1 over 1 minus 0.6, that is, %50 times 4 = $200 billion, not by $50 times 1 over 1


minus 0.8 = $250 billion. Of course, the resultant decrease in the equilibrium Y * will be smaller due to the crowding out effect.

Macroeconomics 109 Chapter IV. Appendix I

Appendix I. Review Questions

In the IS-LM curve model, the general price level is assumed to be fixed. This is a reasonable assumption if the economy is operating under the full employment income level.

The IS Curve

1. From the Keynesian cross diagram, derive the IS curve, which shows various combinations of interest rate and national income in the goods market equilibrium, 1) when the investment function is independent of interest rate, and 2) when investment is inversely related to interest rate.

The LM Curve

2. Derive the LM curve, which shows various combinations of interest rate and national income in the money market, 1) when the money demand is independent of interest rate (h = 0 in the real money demand function Md/P = KY – hi), 2) when the money demand is inversely related to interest rate, and 3) when the money demand is infinitely elastic with respect to interest rate (h is infinitely large): Draw money demand and supply curves in a graph, and the LM curve in the other.

3. Show graphically what happens to the LM curve when the central bank increases money supply.

4. The following question shows what happens to the LM curve when there occurs a decrease in money demand which is caused by other things than changes in income or interest rate:

Suppose that in a country called ‘Erehwon’ there breaks out a rumor of the currency reform which would penalize the holders of money balances. People naturally scramble to make a flight from cash balances and to buy up alternative assets. Describe the situation with the graphs of the liquidity preference function and the LM curve. What will be its impact on national income?

5. Let’s suppose that the money supply and demand curves are normally shaped, and that the Bank of Canada is committed to maintaining interest rate at a certain level. This means that the Bank of Canada stands ready to change the nominal money supply in response to changes in the real money demand which could affect interest rate. What will be the resultant shape of the LM curve in this case? Explain why, under this monetary regime, the impact of a reduction in investment on national income would be felt more painfully than under alternative monetary regime?

Equilibrium of IS-LM: Crowding-Out Taken into Account

[Can you tell the difference between Fiscal Policy Multiplier and Government Expenditure Multiplier: the first takes Crowding-out Effects into account while the second does not. Accordingly, the first is usually smaller in magnitude than the first.]


6. Suppose that the following report was made by an economist who offers consultation to an opposition party ‘Libertarian’ in a country called ‘Erewhon’. If you ar the opposition leader who is properly trained in economics, why would you feel like switching to another consulting company? – Let’s assume that the facts used are all correct. Indicate the missing points which lead to the drawing of the underlined wrong conclusion from the correct facts.

“My econometric analysis using a very sophisticated programme and the data of the past 10 years shows that the marginal propensity to consume is 0.67 in this country (fact). Now the government treasury is cleaning its house, and ready to cut down on its expenditures by 50 billion this year (fact). Therefore, I can forecast that the accumulated total decrease in national income over time will amount to 50 billion dollar times the implied multiplier equal to 1 over 1 minus 0.67, that is, about 150 billion dollars. (opinion). Everyday the news media is pounding into the head of the citizens that the idea that the citizens should be prepared for lean days (fact). However, one social study show that the thresh-hold point is a 100-billion-dollar reduction beyond which the citizens will prefer a political regime change to the economic sacrifice however necessary it might be (fact). Therefore, it is my prediction that with the reduction of national income by 150 million dollars the present ruling party ‘Troy’ will most likely lose the next election (opinion).”

7. Answer the following questions:

1) Let’s suppose that the IS-LM curves are normally shaped: the first is downward-sloping and the second upward-sloping. Evaluate the following argument within the Keynesian framework:“The government spending raises interest rate, which chokes off private investment. As now the Canadian economy is heading toward recession, the government spending should be reduced, thereby lowering the interest rate and preventing recession from taking its toll any further.”

2) In each possible case of the LM curves given in Question 3 on Page 3, what is the extent of Crowding-out effect when government increases its expenditures?

Policy Mix

8. Suppose that two administrations, one the Liberal and the other Socialists, all use fiscal and monetary policies to raise the national income to a target level which is still below the maximum potential national income, and that the Liberal administration relies relatively more on the expansionary policy while the Socialists relies more on fiscal policy.1) On a single graph, show how the IS and LM curves of these two administration differ.

2) Indicate whether the following variables will be higher under the Liberal or Socialist administration: interest rate, private investment, and government spending.

Alternative Frames of Reference

9. Keynesian ‘Non-equivalence’ and Ricardian Equivalence.At time t, the government announces that it will decrease taxes on consumers’ income, and issues bonds to make up for the decrease in government revenues. The bonds will be paid back


in 90 years with an increase in taxes at that time. The average life expectancy is 75 years, which means that the current generation of consumers will not be hit with the tax-hike in their life-time.

Note that government expenditure has not changed, but some part which used to be financed by taxes is now financed by bond issues.

1) The Keynesian framework assumes that the consumers are near-sighted or selfish, and thus do not have any concern for the welfare of the future generation. What will be the impact of such a tax cut on national income? Illustrate it with the IS-LM model.

2) Now let us assume that the consumers are far-sighted and responsible for the welfare of the future generation, and thus do have bequest motive for their descendants. What will be the impact of the tax cut on the national income at time t and time t + 4?

A

B

Macroeconomics 112 Chapter IV. Appendix II

Appendix II: Summary of Chapter

1. Fiscal Policies: G (Case 1: all taxes are lump sum)

A : y = 11 - c1

(C0 - c1 T 0 + I 0 + G0 )−b

1−c1i

B: y¿ = 1

1- c1 + kbh

(C0 - c1 T 0 + I 0 + G0 ) +

bh

1- c1 + kbh

( MP0

- u )


2. Monetary Policies: M (Case 1: all taxes are lump sum)

MP0

= ky - h i+u

A : y = MkP0

+ hk

i −1k

u

i = 1h (

MP0

+ u ) + kh y

B : y¿ = 1

1- c1 + kbh

(C0 - c1 T 0 + I 0 + G0 ) +

bh

1- c1 + kbh

( MP0

- u )

A

B

Y

i


3. Effectiveness of Monetary Policies in Various Settings: How much Y results from M

b=0 normal b b-> (h = 0)

IS & LM is perfectly inelastic

(Normal h)

( )

LM is perfectly elastic

ISLM

IS

LM

IS

LM

IS LM

IS

LM

IS

LM

hIS LM IS

LM ISLM


4. Effectiveness of Fiscal Policies in Various Settings: How much Y results from G

b = 0 normal b b - >

h = 0

normal h

h - >

Macroeconomics 116 Chapter V. AS-AD Model

Chapter V. Aggregate Supply & Aggregate Demand Curve Analysis

1. Aggregate Demand

1) Algebraic Derivation

You may remember that the equilibrium national income from the IS-LM curve is

Let’s focus on the relationship between Y and P.

If all variables are constant except for Y and P, we can get an equation showing the relationship between the two variables Y and P, such as Y = 500 + 200/P. This equation carves up the relationship between two variables, Y and P, is called the AggregateDemand Curve.

In the discussion of monetary policy which involves a change in money supply M and its impact on P and Y, we deliberately drop the intercept A, which is related to fiscal policies, and frequently use Y = B/P = B’ (M/P) to carve up the relationship between the three key variables, M, P, and Y (real income).

If we draw the graph of the above equation with Y on the horizontal axis and P on the vertical axis, this is a hyperbola.

We know that Y = 1/X is a rectangular hyperbola. Y = A + B/X is simply Y = 1/X shifted up by A and outward along the Y =X line by B.

P

u) - PM(

kb + c-1b + )G + I + T c - C(

kb + )c-h(1h = Y

0100010

1

*

P

Y

AD

);;;;( 0000 MGITC s h i f t p a r a m e t e r s


The quantity theory of money postulates that the equation of exchange is M V = P Y, or Y = V (M/P), where M is the supply of money, and V the velocity of circulation of money. This equation is exactly the same as Y = B’ (M/P). This is a special case, featuring monetary aspects, of the AD curve which embodies the impact of fiscal policies along the others (∆C, ∆I) in the first term and that of monetary policies along with monetary shocks (∆u) in the second term of the equation Y

2) Graphic Derivation

We derive the AD curve by examining the impact of a changing price level on the LM curve and consequently on the AD.

When the price level falls from P1 to P2, the real money supply rises from M/P1 to M/P2. This shifts the LM curve to the right.

The equilibrium national income level rises in the IS-LM curve. The corresponding point shifts in the AD setting. By linking the two points, we get the

AD curve.

3) Shift of AD curve

∆ C0, ∆I0, ∆G0, - ∆T0 ∆IS ∆AD

∆ M ∆LM ∆AD

∆ md = ∆u ∆LM ∆AD

AD

P1

P2

LM (M/P1)

LM (M/P2)


In summary, the AD has six shift-parameters, C0, I0, G0, T0, M, and u. Out of them, C0, I0 and u are beyond the control of the government;

C0, I0 and u are called Aggregate Demand Shocks;

specifically, C0 and I0 (X0 and M0 as well in the open economy) are goods market shocks, and

u is a monetary shock;

G and T are fiscal policy instruments;

M is monetary policy instrument.

To countervail the Aggregate Demand Shocks and thus to eliminate any impact on the equilibrium national income, the government may control G, T, and M in counter-cyclical ways. This is called ‘the Counter-cyclical policy’ or ‘Income stabilization policy’.

2. Aggregate Supply

1) What is the aggregate supply?

AS versus YS

The aggregate output is the sum of all the supplies of goods and services in the economy. You may remember the 45 degree line of YS = Y in the Keynesian Cross Diagram. When the aggregate output YS is drawn against a particular price level, that is the aggregate supply. The only difference is that the AS is drawn again at the price level while YS is not. In a sense, AS comes from YS. Then, our next question is, what determines YS?

2) Aggregate Production Function

AS is the aggregate outputs at a particular price level. Output results through production process from inputs. The production function shows the relationship between the inputs and the outputs: production combines production factors with a certain technology. The production function summarizes all three aspects of the supply: Inputs, outputs, and technology.

N

YS

Aggregate Production Curve


(1) Functional Form

In microeconomics theories, an individual production function, say, a hamburger or i th industry, is given by

Qi = f (K,L),

where K and L are capital and labor inputs, and Q output at the firm or industry level. Technology is implied in the functional form.

The aggregate production function is obtained by summing up the production functions of all industries. The aggregate production function shows the aggregate output YS as an increasing function of capital and labor inputs. Again technology is implied in the functional form. We use notation K for the capital stock or the amount of capital, and N for labor input at the aggregate level of economy.

YS = F (K, N; T ).

Note that unlike the microeconomics which uses L for labor input, we use N for the aggregate labor inputs, which is called the ‘level of employment’ in an economy. N may be measured in total hours worked for a given period of time, which is equal to the number of workers employed times the number of hours worked by each worker. Here T stands for Technology employed in production.

(2) Derivation of the Aggregate Production Curve Note that in the short-run, K remains fixed and T does not change. Thus the short-run aggregate production function can be expressed as an increasing function of one variable N or the level of employment of existing workers: the more workers employed for longer hours, and then more aggregate output.

N

YS


Let’s take a numerical example for the Short-run Aggregate Production Function:

YS = 100N – 0.3 N2

If the level of employment is given at 40 (say, million hours worked for a year), what is YS? The answer is YS = 100 x 40 – 0.3 (40)2 = 3520.

If N increases up to N = 60, then the aggregate outputs rise to a new level: 100X60 – 0.3 (60)2 = 4920.

These two points give us an aggregate production curve. It is upward sloping, and is convex upwards. In the short-run, there is a one-to-one relationship between the level of employment and the aggregate outputs: N*’ – AS* t in the short-run. An increase in the level of employment leads to a movement along the given aggregate production function.

Note that the slope of the tangent line to the Aggregate Production Curve is the Marginal Product of Labor.

The shape of the above Aggregate Production Curve is part of a so-called ‘S curve’ of the total (aggregate) production curve:

The first phase or Phase I shows the concave upward and implies that as the input of labor force or the level of employment goes up, the output increases by more than proportion due to an increase in efficiency coming from specialization and cooperation, etc. That is an increasing marginal product of labor or MPL increases in this phase.

Then there occurs a point of inflection. The curve become convex upwards and implies that as the input(labor forces or level of employment) rises, the output increases by less than proportion: This is the area where the diminishing marginal product of labor takes place. As the level of N increases by one unit, the output increases but it does so by less and less. It is called ‘Decreasing Marginal Product of Labor’. This is due to some imbalance between the size of (given) capital

N

YS


(equipment and facilities) and the number of workers working in and with them, and the resultant inefficiency such as congestion(too many workers collide and crowd, free-riders(some workers are not carrying their fair work load) etc.

Our earlier aggregate product curve is a cut out of the above S curve from and beyond the inflection point. Why cut here? Because Phase I is important and beneficial for the producer, but it is uninteresting. All the decision to be made is trivially to keep expanding the employment (N up). When the inflection point comes, now the entrepreneur has to start thinking of a very critical question: When to stop? He has to weigh the inefficiency, which has started setting in, against other benefits, and has to make a decision to stop at the right level of N. Thus, this part of S curve is important in terms of the entrepreneur’s corporate decision making, and we are only looking at this part of the S curve of the total production curve.

(3) Shift of Aggregate Production Function

In the long-run, i) an increase in N, ii) an increase in K, and iii) the enhanced level of technology are all possible, leading to an increase in Aggregate Output. However, an increase in N leads to a movement along the Aggregate Output Curve, and the two others, such as an increase in K or/and T leads to a shift of the Aggregate Output Curve.

i) Capital Accumulation: ∆K

With more capital inputs, each level of employment will lead to a larger amount of aggregate outputs: With more capital equipment, each worker can produce more outputs.

This will send the Aggregate Production Curve outward, or upward.

YS

N


Let’s take a numerical example,

Before: Y* = 100 N – 0.3 N2 (a Old production function) N = 40 – Y* = 3520; N = 60 – Y* = 4920.

After: Y* = 250 N – 0.2 N2 (a New production function)N = 40 – Y* = 5680; N = 60 – Y* = 8280.

Therefore, capital accumulation (∆K) leads to a upward shift of the production curve. When the Aggregate Production Curve shifts up, at each level of N, the slope of the

tangent line gets steeper: The slope is equal to the marginal product of labor, and thus the MP of labor rises.

Think about the decrease in capital, which will send the Aggregate Production Curve downward.

Capital naturally wears and tears over time and it is called ‘Depreciation’ Capital can be destroyed during a war.

ii) Technical Innovation , or Technological Advances: ∆T

With an improved production technology, each level of employment will lead to a larger amount of aggregate outputs.

Let’s take a numerical example:

Before: Y* = 100 N – 0.3 N2 ( a Old production function)N = 40 – Y* = 3520; N = 60 – Y* = 4920.

After: Y* = 150 N – 0.2 N2 ( a New production function)N = 40 – Y* = 5680; N = 60 – Y* = 8280.

YS

N


Therefore, technological advances also lead to a upward shift of the production curve. The marginal product of labor rises, too.

iii ) A Growing Number of Workers: ∆N s This is a rightward shift of the labor supply curve. The equilibrium nominal wage rates fall: So does the real wage rate. The equilibrium level of employment rises, which increases the aggregate outputs along the aggregate production function.

This can happen in the long run due to population growth, or open-door immigration policies. As N is on the horizontal axis, this leads to a movement along the aggregate production curve.

3) Aggregate Labor Supply and Demand Curve: Labor Market

Then, the question in order is how the level of employment or N* is determined to enter the aggregate production function. N*

is determined in the labor market through the interplay of the aggregate labor supply and aggregate labor demand. Now, we note that we are introducing one more market into the picture, and that is the labor market.

The supply of labor is an increasing function of real wages, which are money wage over the price level ( w = W/P), and the demand for labor a decreasing function of real wages.

(1) Aggregate Labor SupplyThe labor supply is an increasing function of real wages, which are equal to nominal wages divided by the price level;

Ns = f (W/P; other variables)

For a given level of P, as W rises, Ns rises as well.

If you put Ns on the horizontal axis and W on the vertical axis, the curve should be positively sloped. And P becomes a shift parameter.

(for P=1)


Numerical Example:Ns = 100 + 3 (W/P).

If the nominal wage or money wage (rate per hour) is $10 per hour and the price level is equal to 1, then the real wage (rate per hour) is 10/1 = 10, and the aggregate labor supply would be 100+ 3 times 10/1 = 130.

The above is sufficient for the labor supply curve in macro. Note that the vertical axis is in the real wage W/P. The labor supply is an increasing function of real wage.

However, in the macroeconomics, we would further separate real wage W/P into nominal wage W and price level P. If we draw the aggregate labor supply curve Ns against the nominal wage W, we can see impacts of P more clearly.

How can we do that? First, hold P = 1 constant, then W/P becomes W, and draw the N s curve of the same shape:

Note that now the vertical axis is W or nominal wage, and the horizontal axis is the level of employment or N, and finally that the Ns curve or the aggregate labor supply curve is drawn with the fixed price level of 1. Thus we should note that the price level is now the shift variable of the Ns curve.

What will happen to the Ns curve for P =1 if the price level rises from 1 to, say, 2 while the nominal wage (rate for hour) is held constant?


A Shift of the N s curve:

In the short-run, a change in the price level shifts the Ns curve. As P rises, the Ns curve shifts up as well; As P rises, for a given level of W, the real wage of W/P falls, and thus labor supply falls.

There are other variables that shift the Ns curve.

For example, in the long-run, as population grows, the aggregate labor supply curve shifts to the right.

W

When P rises from P=1 to P=2,

Ns decreases

Ns (for P=1)

Ns (for P=2)

W

When population grows or more immigrants come, the N s shifts to the right

Ns increases

Ns’

Ns


In summary, for the dimension of W and N, we can write the aggregate labor supply curve as:

Ns = f (W(+) : P(-) , other variables such as population, immigration, etc.)

All other variables, except W and Ns, become shift variables. A change in these shift variables leads to a shift of the Ns curve.

Remember that an increase in the price level or P leads to the visually upward movement of the N s curve or a decrease in N s .

(2) Aggregate Labor Demand:Let us examine the labor demand first:

The aggregate labor demand is a decreasing function of real wages:

Nd = g (W/P; other variables).

If we draw a curve which shows the relationship between Nd and W. It will be downward-sloping; as W goes up, the entrepreneurs demand for labor falls. The third variable P becomes a shift parameter.

By holding P = 1 constant, we can get a Nd curve corresponding to P=1.

W/P

Nd


Background-You may recall the following Microeconomics theory of labor demand:

The entrepreneur does demand labor and hires workers. If s/he is maximizing profits, at the margin or for the last worker hire, the cost is equal to the benefit. The cost of hiring the last worker in monetary terms is the money wage W, and the benefit from hiring the worker is the marginal product MP (units of output the worker produces) times the price of the output P. So at the profit maximizing level of employment, W = P x MPL.

Numerical example) It costs $10 to hire a worker because W = $10. The last worker increases the total products or outputs by 5 (5 units of outputs), and each unit of output has the price of $2 in the market. The cost of hiring the last worker is $10, and the benefit from hiring her/him is 5 times $2, being equal to $1.

We now know that at the equilibrium for the profit maximizing firm

W = P x MPL in dollar terms, or W/P = MPL in physical terms.

MPL is a decreasing function of the amount of labor inputs.The real wage w= W/P is set by market forces, and is paid uniformly to all workers, regardless of whether there are many or few workers.

When the real w = W/P is set at a certain level in the labor market, the entrepreneur who is a price taker will hire workers in such a number that the last worker’s marginal product is equal to the real wage set in the market. The entrepreneur is making profits from hiring intra-marginal workers (all the workers except the last worker hired) as their marginal products are higher than the real wage. S/he is not marking any profit from hiring the last or marginal worker (MP = W/P) This implies that the MPL curve itself drawn against real wages is the labor demand curve.

A Shift of the N d curve:

W/1

Nd

Nd (P=1)


As P or the price level rises, the real wages (W/P) falls for a given level of W. And thus Nd rises: this is a rightward movement or upward movement of Nd curve.

where P =1, and P’ = 2 in this case.

There are other variables that shift the Nd curve:

In the long run, ∆K or an enhanced technology increases each worker’s productivity or marginal product. The MPL shifts up, and the labor demand curve shifts up (or to the right): some workers who used to be unproductive and thus unemployable become now productive due to technical innovations and become employable. There is an increase in the aggregate labor demand by the entrepreneurs.

In summary, for the dimension of W and N, we can write the aggregate labor supply curve as:

W

N

As P rises, say from 1 to 2, while W is held constant,

Nd rises

Nd(P)

Nd(P’)

W

NNd rises

Nd

Nd’


Nd = g(W (-) : P(+) , other variables such as population, immigration, etc.)

All other variables, except W and Ns, become shift variables. A change in these shift variables leads to a shift of the Nd curve.

Remember that an increase in the price level leads to the visually upward movement of both N d and N s curves.

(3) Labor Market Equilibrium

The interplay of the Nd and NS determines the equilibrium level of employment N* and the equilibrium level of real wages w*;

At equilibrium,

f(W/P) = g(W/P), or

f(W: P ) = g (W: P)We can solve for the real wages or W/P at this equilibrium in the labor market.

And then, for a given price level, we can also get the nominal wages W for this equilibrium.

Graphically,

By plugging the value of W* back into the aggregate labor supply or demand function, we can get N*

W*

N*

W

Nd


In summary, As – YS – N*- w* - W for a given level of P.(4) Responses of Nominal Wages to Changing Price Levels: Flexible or Not?

We would revisit the question of what will happen to the equilibrium real wage W/P = w when the price level rises? This depends on what will happen to nominal wage or W when the price level rises.

In the microeconomics, which belongs to the world of classical economics, there is an assumption of flexibility of nominal wage. In other words, the nominal wage W will rise in an exact proportion to the increase in P. As P rises, W rises by the same amount. Thus, W/P = w or real wage does not change. There will be no change in the level of employment N, and thereby no change in aggregate output YS or real national income Y.The flexibility of nominal wage W ensure the separation of the world of nominal variables such as W and P, and the world of the real variables such as N, YS, and Y. There is a dichotomy between the real and the nominal variables.

However, in macroeconomics, there are different schools which have different assumptions about the degree of flexibility of nominal wage. And the different degrees of flexibility of nominal wage opens up the possibility of W not exactly following the movement of P and thus lead to a change in real wage or w =W/P, level of employment N, aggregate output YS, and real national income Y. An increase in the price level, which is a change in nominal variable, can affect the real variables.

Let’s elaborate on this point:

I f W is viewed to be flexible , just as assumed in the classical economics, and follows the movement of P, a change in P will be accompanied by an equal movement of W, leaving w unchanged.

First, the rising P shifts both the labor supply and demand curves up;

The new equilibrium occurs at E;

The new equilibrium nominal wages are proportionally higher than the previous one: In other words, the increase in W is proportional to the increase in P;

Therefore the real wages (w= W/P) do not change;

The level of employment is the same as before.

W 0

W E

W1


This flexibility of money wages and thus the consequent constancy of real wages belong to the classical world, where i) there is no information asymmetry between the entrepreneurs and the workers: There is no money illusion on the part of workers (it goes without saying that any working, let along successful, entrepreneurs should NOT have any money illusion at all); ii) there is no structural rigidity which hinders flexible changes of money wages in response to a change in price level, particularly of downwards changes or falls to a falling price level in the case of recession, such as labour unions, and finally iii) it is in the long-run – enough of time has passed to make a full adjustment of money wages to a changing price level.

However, John Maynard Keynes saw the real world differently: First, he argues that yes, in the long-run, the money wages will adjust fully to a changing price level and everything will be fair and square, but that in the long-run ‘we are all dead’. We may live through a series of short-terms, and constant changes in equilibrium. In the short-run, money wages can be rigid for many reasons. For one thing, it may be confusion on the part of the workers, such as money illusion. Even in the long-run, money wages can be rigid even amid recession, and they are so mainly due to institutional elements such as labor unions. Why did the Great Depression last for such a long period of time – 10 years or so? It was mainly due to the rigidity of money wages backed by labor unions, and also due to ‘confusion’ by a political leader. Let’s listen to Professor G. Smiley in her contribution of ‘The Great Depression” in the Concise Encyclopedia of Economics:

“….In previous depressions, wage rates typically fell 9-10 percent during a one- to two-year contraction; these falling wages made it possible for more workers than otherwise to keep their jobs. However, in the Great Depression, manufacturing firms kept wage rates nearly constant into 1931, something commentators considered quite unusual. With falling prices and constant wage rates, real hourly wages rose sharply in 1930 and 1931. Though some spreading of work did occur, firms primarily laid off workers. As a result, unemployment began to soar amid plummeting production, particularly in the durable manufacturing sector, where production fell 36 percent between the end of 1929 and the end of 1930 and then fell another 36 percent between the end of 1930 and the end of 1931.

Why had wages not fallen as they had in previous contractions? One reason was that President Herbert Hoover prevented them from falling. He had been appalled by the wage rate cuts in the 1920-1921 depression and had preached a “high wage” policy throughout the 1920s. By the late 1920s, many business and labor leaders and academic economists believed that policies to keep wage rates high would maintain workers’ level of purchasing, providing the “steadier” markets necessary to thwart economic contractions.

W 0

Nd


When President Hoover organized conferences in December 1929 to urge business, industrial, and labor leaders to hold the line on wage rates and dividends, he found a willing audience……”

Perhaps, it wasn’t Mr. Hoover who found the audience, but it was the general public (workers) that found Mr. Hoover as a populist politician. He meant to have represented the workers by supporting an artificially high money wages, but in the end, he prolonged the depression into the Great one in history.

Thus the Keynesian world goes as follows:

If W is fixed , particulary downwardly rigid: An increase in P may or may not be accompanied with a commensurate increase in money wages or W, and thus may lead to a decrease in real wages or w. However, more apparently, a decrease in P during the recession may not lead to a corresponding fall in money wages or W. It may be due to three things: money illusion on the part of workers; labor unions, and/or in the short-run. In any case, it will lead to an increase in real wages or w: an increase in the real labor cost on the part of entrepreneurs and thus their demand for labor decreases.

First, the increasing P shifts both the labor supply and demand curves visually up.

However, the nominal wages are set at a fixed level, shown by the horizontal line; nominal wages cannot be nothing other than the fixed level.

The new equilibrium should come at E where the labor demand curve and the horizontal nominal wage line (effective labor supply curve) intersect.

At the new equilibrium, compared with the previous equilibrium, the nominal wages are the same, and the equilibrium level of employment N is lower.

The first position is taken by the classical economics, which is the same as the microeconomics, and the second is by the Keynesian economists. The second is true when there is structural impediment to the flexible mobility of W or nominal wage. This is the case when there is a union which insists on having fixed nominal or monetary amount of wage. In other words, when workers’ unions have ‘money illusion’ and thereby focus on the

W sN

E E

*N *0N

dN

(effective labour supply)

dN


nominal value of wage instead of real value or purchasing power of the wage. This is also the case when the time-period of observation is too short. In a very short-run, the change in the price level is not reflected in the wage level. The third possibility is when the people (= the workers) have some kind of ‘money illusion’. The money illusion refers to the situation where, being faced with a changing price level P, the people really should focus on the real wages w = W/P but they in fact have ‘hang-up’ on the nominal wages, and thus they try to stick to the fixed nominal wage( W bar). The end result is that real wage instead changes and so do N*, YS, and Y.

On the other hand, if there are no impediments on the mobility of nominal wage W and workers are more or less fully employed W will move in the same direction as the changing P in the long-run. ∆P means an increase in living –costs for workers, and workers will eventually demand a higher money wage or ∆W.

Basically, the AS analysis hinges upon what is happening when the price level changes: What is the impact of a change in the price level on real wages and on the equilibrium employment level?

4) Derivation of Aggregate Supply Curve

(1)Different Aggregate Supply Curves

You may remember that the AS is assumed to be vertical in the classical economics, and horizontal or upward sloping in the Keynesian economics.

You may recall that the classical AS curve is vertical; the AS is fixed at a certain level. The fixed level of AS is called ‘the full employment level’.

Note: The full employment does not mean zero unemployment, but a low yet positive rate of unemployment. A certain positive rate of unemployment is inevitable for an economy where new comers are looking for best-fitting jobs and some workers are upgrading their skills and consequently searching for another jobs. Some unemployment is even desirable as it provides some reserves in the economy; without it the man/women-power situation is too tight, and a firm which is faced with even temporary rise in the demand for its products would have extreme difficulties in hiring extra workers. As a consequence, we will observe a shortage of the good or a rise in its price. We need a small ‘buffer’ of unemployed workers. This positive rate of unemployment compatible with a smooth working economy at the ‘full employment level’ is called ‘the natural rate of unemployment’. The corresponding national income is the ‘natural real national income.’

In the short-run, there may be some temporary deviation of the actual national income from the full employment N.I., but the price level will adjust to push the economy back to the equilibrium. The Business Cycles can occur due to the demand shocks. However, it is only temporary, and is


of no big concern as the economy, if left alone, automatically gravitates toward a unique equilibrium N.I.

What is the role of the government in the economy?

If there is no factor in the economy which blocks the above tatonnement, the government should not create anything which can get in the way of this natural adjustment process of recovering the equilibrium. Actually it should eliminate any impediments in this process and facilitate the adjustment process by promoting competition.

You may also recall that the Keynesian Aggregate Supply curve is upward-sloping; the AS responds positively to the (output) price level.

(2) Fundamental Cause of Different AS curves.

Flexible Nominal/Money Wages A vertical AS curve. (Neo Classical)

Rigid Nominal./Money Wages a Positively Sloping AS curve. (Keynesian)

The reasons for rigidity: Money Illusion; a kind of stupidity at the individual levelUnion, etc: a kind of ‘social’ and ‘structural’ rigidity

To derive the Aggregate Supply Curve, first you need a Four-Panel graph of AS-AD, Ns and Nd, and Aggregate Production Curve and a 45 degree-line of converting YS into Y.

The AS curve shows the relationship between the different levels of prices, or Ps, and the corresponding levels of real national income, orYs. Thus, you have to kick up and down the price level or P, and to find the corresponding Y.

(3) Classical Aggregate Supply Curve: A Vertical AS Curve

Under what circumstances would the money wage be flexible?

i) The economy is at full employment level: all available workers are fully employed; there are no other workers who are willing to work for the real wage lower than the prevailing rate;

ii) There is no structural rigidity of money wage: no impediment on the equilibrating force in the labor market;

iii) The workers are free of ‘Money Illusion’;

iv) In the long-run: an enough amount of time has elapsed since ∆P.

This is a graphic and somewhat mechanical derivation:


1.) Choose a price level, say, P1.

2.) For this given price level, we can have the labor supply and demand curves;

Ns = f (W/P); and Nd = g (W/P) become

Ns = f (W: P1); and Nd = g (W: P1).

Or, by simply showing the shift variables, we can write down

Ns (P1); and Nd (P1).

3.) The intersection of the labor supply and demand curves gives the equilibrium real wage w= W/P, in the labor market; N* and W* for a given P (thus w*).

4.) The equilibrium N* feeds into the aggregate production function of

YS = F (K, N*; T) for a given K and T in the short-run.

5.) YS = Y the third panel.

6.) Y goes down to the fourth panel and matches the starting price level P1.

7.) Suppose that the price level goes up to P2.

8.) As P rises, both labor supply and demand curves shift up.

Now we get Ns (P2); and Nd (P2).These are shown with broken lines in the graph below.

9.) We get the new equilibrium. At this new equilibrium, the new nominal wages are higher than the previous nominal wage by the same proportion of the increase in P. And thus, the real wages do not change; the level of employment does not change, either.

10.) The same level of employment feeds into the aggregate production function, and leads to the same level of YS.

11.) The same level of Y in the third panel.

12.) The same Y goes down to the fourth panel and matches the new price level P2.

13.) By linking the two points in the fourth panel, we get the AS curve.


Note that along this AS curve the real wage is constant but money wage is not: at point 1 the corresponding money wage is W*1, and at point 2 the corresponding money wage is W*2. However, at both points, the real wage is equal to w.

An int uitive explanation is as follows:

When P rises, W will rise proportionately. The revenues (P Q) and the costs (W L) are increasing proportionately, and thus the profit margin does not change. There is no reason for entrepreneurs to attempt to expand production scale. The AS remains constant at the macroeconomic level, too.P increases and W increases W/P remains unchanged N remains unchanged YS remains unchanged Y remains unchanged, and thus a vertical AS we get.


(Supplement: Why does W/P determine the profit margin?)

Production decisions are made ultimately by producers, or entrepreneurs who weigh the situations in the output market (which determines revenues) and the input market (which determines costs).Entrepreneurs make supply decisions by weighing the ratio of output price to input price, which is the key variable for their profits which constitute their prime motivation. Entrepreneurs are orchestrating production processes (borrowing capital, hiring workers, etc.) in order to earn profits.

Formally, the aggregate production function shows the relationship between inputs such as capital (K) and labor (L), and outputs. These aggregate outputs are the aggregate supply or Y in Y – YS: Y = F (K,L)We know that an increase in K and L leads to an increase in Y. However, it does not happen by itself. In order to have a larger amount of inputs and consequently more outputs, entrepreneurs should exert themselves to organize more K and L. What would be the incentive for entrepreneurs to produce more? They respond to a larger profit margin. Profit is revenues minus costs. Revenues are Output Price times Quantity.Costs are Input Price times Input Quantity. Profit = Total Revenue – Total Cost = P Q – ( r K + W L). In the short-run, P and W determine the magnitude of profits; an increase in P increases profits, and an increase in W decreases profits.

(4) Keynesian Aggregate Supply Curve

Basic a ssumptions are as follows:

i) The time is too short for W to change, orii) There are impediments on the flexibility of W, oriii) There is unemployment; there are other workers other than the present employees,

who are willing to work for less than the present real wage.

Graphic Derivation is as follows:

Start with P1.

For the given price level, get the labor supply and labor demand curve in the second panel.

The intersection of the labor supply and demand curves gives the equilibrium level of employment N1.

This feeds into YS1 in the aggregate production function. YS1 = Y1 in the third panel. Now in the fourth panel, Y1 matches with P1.

Suppose that the price level goes up to P2.

This sends both the labor supply and demand curves up. However, the level of nominal wages does not change due to unions or money illusion. It

is the effective labor supply curve; note that it replaces the shift labor supply curve,


which is meaningless. The new equilibrium level of employment is given at N2.

This feeds into the aggregate production function to give YS2 = Y2.

Y2 goes down to match P2. By linking the two points of Y in the fourth panel, we get the Keynesian Aggregate

Supply Curve. It is upward-sloping.

Along the Keynesian AS curve, the nominal wage rates are fixed at W*. However, real wages vary along the AS curve. That is because the money wage is fixed along the AS curve, but the price level varies: The real wage (=W/P) must vary along the curve.

This contrasts with the fact that along the previous classical AS curve, which is vertical, the real wage is fixed but money wage varies.

Suppose that there is a huge excess capacity of production: this is possible as the economy is just coming out of a big recession. Even a very small increase in the price level leads to some increase in the revenues of companies (= P x Q), and the entrepreneurs will respond to this increase in revenues in a big way by hiring a lot of new workers back to the production process. We can have a very flat AS curve as well.

Depending on the elasticity of the supply side, we can get the almost horizontal SAS curve as we have seen in Chapter 1.



Intuitive Explanation for the upward sloping AS curve is as follows:

When P rises, W remains constant. The revenues increase while the costs are fixed, and thus the profits increases. The larger profits will give a greater incentive for entrepreneurs or employers to expand production scale by hiring more workers. If this expansion of output happens to all firms, the aggregate supply will increase.

P increases with W being fixed w(=W/P) decreases Nd increases N* increases AS = y = F (K, N) increases

The opposite can happen, too.

P decreases with fixed W w(=W/P) increases Nd decreases N* decreases AS = y = F (K, N) decreases

Let us explain the same thing in terms of real wages, which is nothing but the ratio of W and P or W/P. The profitability is related to the ratio of W to P (=W/P), which is real wage or constitutes ‘real’ cost of hiring workers.

1) When W/P falls, the real cost of hiring workers is falling, the profit margin widens, and thus more (incentive for) production (on the part of the entrepreneurs):

Real wage (W/P) decreases Nd increases Actual N* increases AS = y = F (K, N) increases

2) When W/P rises, the real cost of hiring workers is rising, the profit margin is reduced, and thus less (incentive for) production (on the part of the entrepreneurs).

W/P increases Nd decreases Actual N* decrease AS = y = F (K, N) decreases

Note: a larger W/P sounds like good news for the workers. You may be wrongly reasoning: “a larger W/P means a larger incentive for the workers to work. The longer and harder the workers are working, the larger the output. And the workers will have more money to spend.” (This is the very wrong idea that Mr. Hoover had during the Great Depression).

But it is not workers but entrepreneurs that make production decision. In the above case, who will hire the larger number of more willing workers at such a high real wage level? The willing workers will not be hired as they cannot force the entrepreneurs to hire them above and beyond the latter want to.

So we are assuming that the actual amount of employment is determined along an entrepreneur’s labor demand curve, not along the worker’s labor supply curve, and the effective labor supply curve, which is basically the horizontal line from the fixed money wage or W.


Can you mathematically express the AS curves of the Keynesian and the Classical economists?

Classical AS curve: Y = F(K, Nf) = Yf, say, 1000.

Keynesian AS curve: Y = F(K, Nf + dN) = Y – a (W/P), say = 1500 – 100 (W/P):

(W/P) increase then dN <0, so N < Nf and Y decrease,(W/P) decrease then dN >0, so N > Nf and Y increase.

If W/P goes up, the real cost of hiring workers is higher now, and thus entrepreneurs would like to hire less workers. The resultant output or AS will be smaller. If W/P falls, the real cost of hiring workers is lower now, and thus more workers will be put into production process and the resultant AS will be larger than the previous equilibrium or the full employment level national income.

Some may argue that the Classical AS curve is valid in the long-run; and the Keynesian AS curve is valid in the short-run;

Short-run AS = Keynesian ASLong-run AS = Classical AS

One might have the SAS curve in the short-run when the time is too short for W to change and the LAS curve in the long-run when enough time elapses for the adjustment of W.

5) Shift of Aggregate Supply Curves

The Long-run AS shifts (to the right) when

i) ∆Kii) ∆Technologyiii) ∆Populationiv) Positive Supply shocks

As the long-run AS shifts to the right, the level of long-run real national income or full-employment real income rises.

The first two shifts the Aggregate Production Curve up and, at the same time, the Aggregate Labor Demand curve up.

Population growth shifts the aggregate labor supply curve to the right (downward visually).

The last one, positive supply shocks, may send the aggregate production curve up.


Combined or not, the shifts of the aggregate production curve and the corresponding aggregate labor supply or demand lead to an increase in YS and Y as we can easily illustrate on the 4 panel graph. Over time, the first three happen to a growing economy. And it is called ‘economic growth’, and the annual economic growth rate is measured by a percentage change in real national income.

These issues will be examined in details in a later chapter of economic growth theories.

The Short-run AS shifts (to the right) when

The above four shift factors, and

v) ∆ Decreases in Money Wage

When the LRAS curve moves, the SRAS shifts, too, at all times.

However, it is not necessarily the case that when the SRAS shifts, the LRAS shifts: When there is an increase in money wages, the SRAS shifts to the left (visually up), but the LRAS stays put.

(1)An Increases in Money Wages or W:


Suppose that unions raise the fixed nominal wages to a higher level;

Along the AS curve, the nominal wage rates are fixed at W*.


(2)Technical Innovation

If we assume that there is no change in labor demand, but the technical innovation shifts up the aggregate production function only, then N1

* remains to be the equilibrium level of employment in the labor market. However, the corresponding out level is higher and thus the long-run AS curve as well as the SR AS will shift to the right to a new point of Y2.

We can see that the LAS and SAS curves all shift to the right by the same amount and at the same time: the height of the intersection of the SAS and LAS curves stays the same.

However, most technical innovations increases the productivity of labor forces as well. Thus the demand for labor forces increases. In other words, technical innovation shifts up the aggregate production function as well as labour demand curve. In this case, the equilibrium level of employment will be at N2, and the corresponding level of national income is Y3. And thus the SAS and LAS shift more to the right than the previous case.

E'

(W )

¿W ¿ P1

N1¿ N2

¿ Y 1 Y 2 Y 3


(3)An Increase in Production Cost(except for money wages) such as Oil Shock

In general, this is called ‘adverse or negative supply shock’. It shifts the aggregate production function downward.

This permanently shifts the LRAS and SRAS to the left by the same amount.


3. ‘Grand Equilibrium’ of Aggregate Demand and Supply

1) Grand Equilibrium

P

Y

The intersection of the AD curve and the Long-run Aggregate Supply curve gives the long-run equilibrium.

The intersection of the AD curve and the Short-run Aggregate Supply curve gives the short-run equilibrium.

There are the corresponding equilibrium national income and the equilibrium price level for the short-run and the long-run equilibrium respectively.

2)Short-run Adjustment to the Long-run equilibrium

What if the long-run equilibrium and the short-run equilibrium do not coincide with each other?

The long-run adjustment depends on the flexibility of Money Wage: If nominal wage or W is flexible, then the SAS curve will move around so that the intersection of all three curves, i.e., LAS, SAS, and AD, come to one point.

However, please note that the above adjustment of the SAS to the LAS is not automatic. It critically depends on the background of the economy, particularly on the flexibility versus rigidity of nominal wages.

If for some reasons money wage or nominal wage is not flexible in the long-run, the SAS will stay suspended. This was the case of the Great Depression.

Y*

Long-run AS Short-run AS

AD curve

P*


Suppose that the short-run equilibrium Y < long-run equilibrium Yf;

P AD LAS SAS

-- deflationary gap Y leads to more competition among workers

For instance, Yf is below the long-run equilibrium or full employment income Yf. The deflationary gap leads to a competition among unemployed workers and thus lower nominal wages. The falling nominal wages shift the short-run aggregate supply curve to the right. Eventually, a new short-run equilibrium will coincide with the long-run equilibrium.

However, if there is an impediment to the flexibility of money wages, the SAS will stay suspended, and will not move to the new position given by the solid broken line as shown above. And the equilibrium national income Y1 will last for a long period of time, which is below the full employment national income Yf. It is a sustained economic recession.

If initially short-run Y*>long-run Yf* and money wages are flexible, then there will be an inflation gap developing, which will lead to upward pressure on money wage. As money wage goes up, the SAS goes up as well. Eventually all the three curves of SAS, LAS and AD, intersect at one point:

P

---

inflationary gap

Y1

P

Y


The short-run equilibrium national income exceeds the long-run or full employment national income. This inflationary gap leads to an increase in the price level. The labor supply in the market is tight. The competition for workers leads to a rising nominal wage. Thus the labor supply curve will shift to the left until it passes through the long-run equilibrium point where the AD and the Long-run AS curves intersect.

3) Applications of the AS-AD Curve Model: Economic History of the U.S.

(1) Industrial Revolution (1869 – 1897)

Statistical data shows:

- mainly due to LAS (SAS), which was in turn due to K, L, T during the American Industrial Revolution

- AD was stable due to no (slow) increase in (gold) money supplyAn increase in population might have added, through an increase in C, I, and so forth, but the overall it is no stronger than an increase in AS.

When LAS0 moves to LAS1, SAS0 moves to SAS1 by the same amount at the same time(note that the intersections of the LAS and SAS before and after have the same height). That is not the end of the story.

Note that the SAS moves once again from SAS1 to SAS2: Because the short-run equilibrium national income given by the intersection of SAS1 and AD leads to a short-run equilibrium national income Y (not indicated above: you may do so), and it is below the new full employment or long-run equilibrium national income Yf

1987.

Yf1897(299.00)

Yf1869(100.00)

P1897(63.40)

P1869(100.00)

LAS0 SAS0

AD

LAS1

SAS1 SAS2

Y* P*1869 100.00 100.001897 299.00 63.40

Y* P*

LAS

AD1929AD1933AD1939

P

YY* << Yf

SAS


In this case, just as we have learned, the SAS should move to the long-run equilibrium. As SAS moves to the right for this reason, there is an additional increase in Y and a fall in P.

(2) The Great Depression (1929 – 1939)

Y* P*1929 100.00 100.001933 70.00 75.001939 105.00 100.00

- puzzling question: Why SAS did not shift to the right when P level fell between 1929 and 1933?

The answer lies in the institutional downward rigidity of money wages that kept the SAS there for a long period of time.

LAS

AD39AD29

P

Y

SAS099SAS1

**LRSRf YYY


If the money wages had fallen, YSR* would not have stayed below Yf for such a long period of time:

(This situation did not happen in 1929-1939)

(3) Pax Americana (1945 – 1962)

- a resumed economic growth, shifting LAS and SAS (and is coupled with an increase in AD due to the post-war expansion of government expenditures, consumption, and investment)

P

fY*1Y '

fY

0LAS 1LAS0SAS

1SAS

e

'E

Y


(4) Evolution of Inflationary Spiral (1968 – 1969 – 1980’s)

-:

Where people to do not have inflationary expectations, the economy moves from (a) to (b) in the SR. As the general public catch on what is happening to the price level, they demand a higher money wage and the higher wage is reflected in the shift of the SAS curve from (b) to (c) in the LR.

:When people revise inflation expectations at the same time along with the actual increase in the price level: one movement is from (c) to (d).

:

When inflation expectations are excessive, being higher than the actual increase in the price level, and, in addition, the excessively higher money wages are actually obtained by strong labour unions, one movement is from (a) to (e) The result is a decrease in Y below Yf, and it is called STAGFLATION, which is the combination of STAG(nation) plub (in)FLATION.

P

fY*Y

0LAS1LAS

0SAS1SAS

Y0AD 1AD

2AD

3AD

2SAS

3SAS

ab

c

d

e


(5) Oil Shocks (1972 – 1975)

: Oil shocks – permanent (negative) AS shocks, shift LAS and SAS to the left

: Additional adjustment of AS curve

P

fY'fY

0LAS1LAS

0SAS1SAS

Y0AD

2SAS


4. Rational Expectations Revolution and New Classical Model

1) Assumptions

(1) Revised Labor Supply and Demand Curves

The entrepreneurs make a decision on labor demand on the basis of the actual real wages, which are equal to nominal wages divided by the actual price level;

Nd = f (W: P, other variables).

This is the same as any previous models.

On the other hand, the workers make a labor-supply decision on the basis of their ‘perceived real wages’, which are equal to nominal wages divided by the ‘expected price level’ of the current period, being carried from the last period.

Ns = g (W: Pe, other variables).

We draw Ns curve with W or money wages on the vertical axis and N on the horizontal axis. Pe

becomes a shift parameter.

(2) Information Asymmetry is a norm for Unannounced Policies.

At time period t-1, workers and employers do form expectations as to the price level to prevail at time period t, that is, Pe.

W

W 1

N1 Y

Ns (Pe1)

Nd (P1)


At time t, the actual price level turns out to be equal to P. Of course, there is no guarantee that Pe = P.

As soon as the price level reveals, the employers or entrepreneurs are updated, and do have correct information about the current price level P. On the other hand, the workers do not have information about it. The workers do have just the expected price level Pe, which is carried from the last period.

Derivation of Lucas Aggregate Supply Curve for a fixed Price Expectations on the part of Workers:

i) Information Asymmetry and the New Classical Labor Supply and Demand Curve:

Suppose that there is an increase in P, which the entrepreneurs recognize but the workers do not. In other words, let us assume that there is information asymmetry between the employers and the employees about the price level.

In this case, what will happen to the Nd (P1) and Ns (Pe1) curves?

This increase in P is unexpected on the part of workers, and thus Pe remains unchanged. Thus the labor supply curve stays put.

However, the entrepreneurs are updated on the increase in P. Thus the labor demand curve shifts up.

W

Y

Ns (Pe1)

Nd (P2)

Nd (P1)

Lucas’s AS


ii) Information Asymmetry and the New Classical AS Curve:

P > 0Pe = 0W* >0

P > W* > Pe = 0

Along the Keynesian AS curve, the nominal wage rates are fixed at W*.

The resultant AS is called “Lucas’s AS curve” or “Expectations-Augmented AS curve”.

Note that along this Lucas AS curve, the expectations about the price level are constant. In other word, the expected price level is the shift variable for Lucas Aggregate Supply Curve. As the workers or the general public revise their expectations as to the price level (up: it is a numerical increase), Lucas’s AS curve shifts (it is visually a upward movement, but a numerical decrease in AS).

Note that the increase in the nominal wages W is smaller than the increase in P.

Lucas AS ()

Lucas AS ()


As a result, in the mind of a worker, the perceived real wages have gone up: The expected price level remains unchanged while the actual nominal wages have gone up somehow. The labor supply rises along the curve.

However, the actual real wages, the nominal wages divided by the actual price level, have gone down; the numerator has changed less than the denominator has.

iii) Revised Expectations and the Shift of Lucas Aggregate Supply Curve

Recall that, as P1 goes up to P2, Nd curve shifts up on the part of entrepreneurs but Ns remains constant reflecting a constant Pe on the part of workers: This is needed to derive LAS(Pe

1 ) curve.

Now what will happen if the workers revise their expectations? The N s will shift up as shown below, there will be two corresponding points to the two different price level P1 and P2.

Note that Y1 here coincides with the full employment national income.

iv)A vertical Long-Run Aggregate Supply Curve or LRAS is still valid here as well. This is the line passing through the points where expected price levels are the same as actual price level. In the long-run the perception will come in line with the reality.


(3) Policy Invariance Theorem for Fully Anticipated Government Policies

How convincing is the assumption of Information Asymmetry as assumed above?

Generally it did make a sense prior to the 1980s. However, in today’s world of the post-information-revolution society where the general public has access to all kinds of information including government policies, information asymmetry may not be sustainable. The general public has the same access to information of the government’s policy model and all the input data. With this parity-of-information between the general public and the government or the policy maker, the assumption of information asymmetry between the employers(entrepreneurs) and employees(workers) is unsustainable. It is all the more so in a democratic society where every has equal access to all kinds of information and information is efficiently propagated. This is particularly so when government announces its proposed policy and its forecast economic impacts in advance. The ‘honest’ government may be educating the general public in this case.

A well-announced economic policy with deterministic rules will not have any impact on the real variables such as real national income- Policy Invariance Theorem

Suppose that even the workers are fully updated on a change in the price level: The government announces its policy well in advance to the general public and carries out the policy in the honest and open way. The general public have time to understand the impact of the proposed policy on the price level and thus to revise their expectations about the price level. What will happen to the labor supply and demand curves?

Note that P = Pe = W* > 0 in this case.

W

P

Ns (Pe1)

Nd (P2)

Nd (P2)

Ns (Pe2)

AS


What is the resultant AS curve in this case?

Along the Keynesian AS curve, the nominal wage rates are fixed at W*. The resultant AS is the same as the long-run AS curve. Note that the increase in the nominal wages W is proportional to the increase in P.

This happens in the long-run when the workers are fully updated on what is happening to the price level, and the money wages become flexible even if they are not so in the short-run.

LAS ()

LAS ()


Another way of looking at the above is as follows:

We can think of the above vertical long-run AS curve as Lucas’s AS curve shifts up as the expectations are revised as given below:.

Along the Keynesian AS curve, the nominal wage rates are fixed at W*.


4. New Keynesian AS curves

1) Assumptions

i)Rigidity of Nominal Wages; In the New Keynesian model of labor market, the nominal wage is set at t-1 through labor contracts, and the level of employment is to be determined at time period t.

ii) Long-term Non-indexed Labor Contract: Just like the Keynesian AS curve model, the wages are set in advance through the long-term non-indexed contract.

iii) The labor contract sets nominal wages at time t-1. The workers are bound by the contract to work at the set wage rates as much as is required by the entrepreneurs. The level of employment is flexible to be determined according to the labor demand at time t.

Ex-post revisions of expected price levels do happen, and shift the labor supply and demand curves around. However, the labor supply curve is redundant as it is effectively replaced with the wage line, which is set through the contract. The equilibrium takes place where the horizontal nominal wage line intersects the newly shifted labor demand curve.

2) Derivation of New Keynesian AS curve

Graphic Derivation is as follows:

Start with P1.

For the given price level, get the labor supply and labor demand curve in the second panel.

The intersection of the labor supply and demand curves gives the equilibrium level of employment N1.

This feeds into YS1 in the aggregate production function. YS1 = Y1 in the third panel. Now in the fourth panel, Y1 matches with P1.

Suppose that the price level goes up to P2.

This sends both the labor supply and demand curves up. However, the level of nominal wages does not change due to unions or money illusion. It

is the effective labor supply curve; note that it replaces the shift labor supply curve, which is meaningless.

The new equilibrium level of employment is given at N2.

This feeds into the aggregate production function to give YS2 = Y2.

Y2 goes down to match P2. By linking the two points of Y in the fourth panel, we get the New Keynesian Aggregate

Supply Curve. It is upward-sloping.



3) Comparison of the New Classical and the New Keynesian AS curves

Note that the slope of New Keynesian AS curve is flatter than the corresponding New Classical AS curve: if we look at the labor market only for a unexpected rise in the price level, the comparison is as follows:

YS = Y

450

(New Classical)

NKASP1

P2

Fixed W*

N1* Y1N2*

Ns (Pe1)

Nd (P2)

Nd (P1)

New Keynesian Eq.

New Classical Eq.

Y2


Comparison of New Classical and New Keynesian equilibriums:

Note that the slope of New Keynesian AS curve is flatter than the corresponding New Classical AS curve: if we look at the labor market only for a unexpected rise in the price level, the comparison is as follows:

YS = Y

450

New Classical

NKASP1

P2

Fixed W*

N1* Y1N2* Y2


5. Putting them all together in a complete macroeconomic model with the AS and AD curves.

So far we just assume that there is an increase in the price level P. Why or how does it happen, or what causes this rise in the price level?

In reality a rise in the price level or inflation is most likely the result of government’s expansionary fiscal or monetary policies, which shift the AD curve.

Suppose that government increases nominal money supply or MS. It will put a train of economic sectors in motion:

First, the real money supply curve ms will shift to the right.

Second, the LM curve will shift to the right.

Third, the AD curve will shift to the right.

Now, when it comes to the response of the AS side, there are different assumptions for different circumstances:

1) If the increase in Money Supply is unanticipated or unexpected for the workers or the general public, then the SAS curve does not move at all in the short-run.

2) Even if the expansionary monetary policy is unexpected, eventually in the long-run the general public will figure out the consequent increase in the price level. Suppose that there is no institutional wage rigidity in the labour market. As they demand a higher money wage so as to recover the real wage, the money wage will rise and the SAS will reflect the wage(labour cost) increase and thus decrease(shifting to the left or up visually).

3) If the expansionary monetary policy is announced well in advance and is executed by the monetary authority as announced, and at the same time, if there is no institutional money wage rigidity, then there is the Policy Ineffectiveness Theorem holding once-for-all, i.e., in the short-run as well as in the long-run.

Macroeconomics 165 Ch VI. Consumption

Sectoral Analysis

Chapter VI. Consumption Function

1. Keynesian Theory

1) Background

We have learned that the Keynesian consumption function in general takes the form

where C0 is the basic consumption, c1 the marginal propensity to consume, and Yd the disposable income which is equal to income minus taxes. Implicit herein is the assumption that changes in income and changes in consumption are contemporaneous.

So by introducing time subscript, we can rewrite the above as

Keynesian economists estimated consumption function by obtaining a best fitting line with time-series data of disposable income and consumption.

For instance, with the U.S. yearly data of the period 1929-1941, the consumption function for the whole U.S. economy was estimated as

Ct = 47.6 +0.73 Ydt

(unit: in 1972 Billion U.S. dollars);

With the Canadian yearly data of 1926-1940, the consumption function for Canada was estimated as

Ct = 3.0 + 0.69 Ydt (in 1972 Billion Canadian dollars).

So we can make a prediction as to the magnitude of consumption if we have a reasonable forecast about income. Alternatively, as we have seen in the above Question #1, we can get the value of the APC for a predicted level of national disposable income

Question #1: Suppose we have obtained the consumption function in Question #1 from the past data. What is the APC for a personal disposable income of $ 150 billions in 1972 dollars? The answer is 0.71; the consumption is 3.0 + 0.69 times 150 from the equation, and is equal to 106.5. The APC is this consumption $ 106.5 billions divided by the total disposable income $ 150 billions.

), T -Y ( c + C =

Yd c + C = C

10

10

). T - Y (c + C =

Yd c + C = C

tt

tt

10

10


Question #2: Suppose we have obtained the consumption function in Question #1 from the past data. What is the APC for an personal disposable income of $ 200 billions in 1972 dollars? The answer is 0.705; the consumption is 3.0 + 0.69 times 200 from the equation, and is equal to 141. The APC is this consumption $141 biiions divided by the total disposable income $ 150 billions.

2) Implications of Keynesian Consumption Model

Two corollaries we can draw from the above equation are

Average Propensity to Consume (APC) is larger than Marginal Propensity to Consume (MPC); more importantly, the APC decreases as income increases. This implies a non-proportionality between an increase in income and the responsive increase in consumption. As income rises, a smaller and smaller portion of income will be spent as consumption. The above questions #1 and 2 illustrate the APC falls as income increases.

The estimation of the Marginal Propensity to Consume (MPC) enables government policy makers to compute the multiplier and thus to know exactly how much government expenditures or taxes should be adjusted in order to increase the national income by the target amount.

Quite important implications behind the two points are as follows:

The first point is a terrible prognosis for a growing economy. The APC shows the proportion of the total income to be consumed. A small APC means a small portion of income to be transformed into expenditures.Savings are, in the circular flow model of the Keynesian theory, a leakage, which lowers the Aggregate Expenditures and subsequently the level of the national income in the next round. As the APC decreases in a growing economy, an increasingly larger proportion of income is saved away and thus there occurs a deficiency of aggregate expenditures. The aggregate output continues to grow while the aggregate expenditures stagnate due to an increasingly larger proportion of income to be saved away. The result is a secular stagnation. This implication that a growing economy will be inevitably faced with Secular Stagnation due to a deficiency of aggregate expenditure or an excessive saving is in line with Marxists' argument that the capitalist economy is bound for general glut due to excessive savings by stingy capitalists.

In the Keynesian view, the second point is a miracle cure for the problem of a falling APC: By using the multiplier government may know exactly how much it has to supplement the aggregate expenditure which is not sufficient if left to the private sector.

3) Keynesian Justification


The Keynesian Proof of the first point of a declining APC in the face of a growing income is as follows:

By definition, in general, the marginal propensity to consume (MPC) is the ratio of the responsive increase in consumption to a unit increase in income. It measures what proportion of an incremental increase in income is consumed. The average propensity to consume (APC) is the ratio of the total consumption to the total income. It measures what proportion of the total income is consumed.

(1) Illustration

Graphically, the MPC is the slope of the consumption curve and is constant over the entire range of income.

The APC measured at a certain level of income is the slope of the ray which links the origin and the corresponding point on the consumption curve.

At Y1, MPC = c1; APC = Slope of the OR1 ray.

At Y2, MPC = c1; APC = Slope of the OR2 ray.

(Note: the OR1 is steeper than the OR2, and therefore; APC at Y1 >> APC at Y2.)

Algebraically, we can also show that

As Ct = C1 + c2 Ydt,

0

R1 R2

.dYdC= MPCand ,

YC = APC

.c + YdC =

YdYd c+

YdC

= YdC

tt

t

tt

t1

01

0


So the APC is the MPC plus a positive term. And thus APC - MPC = C0/Ydt which is positive. Therefore, APC >> MPC.

We note that the term C0/Ydt is a decreasing function of income level; the numerator C0 is

constant regardless of the level of Yd. As Yd increases in the denominator, the ratio falls.

Therefore, the APC falls as income increases. A smaller and smaller proportion of income will be spent and thus be transformed into the aggregate expenditures. This means that the average propensity to save rises as income increases.

Ydt = Ct + St

Dividing the both sides of the above equation by Ydt, we get

As the income is increasing, the APC is falling and the APS is rising.

(2) Numerical Example

The consumption equation (unit: in 1971 Billion dollars) is given as

Ct = 3.0 + 0.69 Ydt.

What is the MPC?

What is the APS at Ydt = $ 150 billion? What is the APS at Ydt = $ 200 billion?

These feature, i) "dAPC/dYd < 0" or the APC falls as income increases, and ii) "APC > MPC", basically the same results from the fact that the consumption function has an intercept.

If the consumption function is a ray from the origin and thus without any intercept, the APC will be equal to the MPC and the APC would be constant all the time just like the MPC. The APS will be constant over the entire range of income. As income rises, the increase in consumption is proportional to the increase in income.

4) Two Empirical Anomalies

Upon the Keynesian theory, economists who have been working on historical data have found two empirical anomalies:

1) "The estimated consumption function underpredicted the consumption for a higher level of income";

.YdS +

YdC = 1

t

t

t

t


For instance, income has grown over time after World War II. We have seen that by substituting the forecasted level of national income into the estimated consumption function, we can get the predicted value of consumption and thus the APC. Economists did so in the pre-war time for the post-war era. Over time it was revealed that the consumption level predicted in the pre-war time for the post-war era was smaller than the actual post-war consumption. Also the predicted APC turned out to be smaller than the actual APC. For instance, when we predict the APC for the disposal national income level of $150 billions, it is about 0.71. However, historically, when the actual income was equal to $150 billions in Canada, the actual APC was about 0.85 rather than 0.71.

A few possibilities;

The first one is people have become more prodigal in the post-war period. The MPC might have increased in the post-war period compared to the MPC of the pre-war period. And thus the APC might have increased over time, too.

The second possible scenario is that the average and marginal propensities might have been wrongly measured in the estimation process. And there might have been a systematic error in estimating consumption.

If the first is true of the two possibilities, the Keynesian consumption function would be preserved, and there would be no further need for research geared to improving economic theory. This is an academically uninteresting case.

2) "The long-term APC thus APS were constant over a long period of time"

Professor Simon Kuznets estimated the long-run APC by observing the changes in consumption and income during a considerable long period of 1869 to 1933, and found that the long-run APC was constant at 0.89 over time. This result contrasts with the estimation result from a relatively short-period data.

This implies that there are two kinds of consumption curve, short-term and long-term:

The long-run consumption curve can be drawn as a ray from the origin;

There, long-run APC = long-run MPC as there is no intercept; the APC and APS are constant over the entire range of income.

long-run MPC >> short-run MPC if the short-run consumption curve is based on the yearly changes in income as shown above.

In attempts to resolve these anomalies, some alternative hypotheses about the consumption behaviour were proposed. These alternative consumption theories differ in the length of the time-horizon over which consumers are assumed to make consumption decision.


2. Permanent Income Hypothesis

1) Basic Ideas

M. Friedman says that the current consumption is a function of permanent income Yp.

Permanent income is a sort of income stable in the long run. Its calculation requires an observation over multiple periods of time. ctrue is a true value of marginal propensity to consume measured out of permanent income. This contrasts with c1 or the simple and conventional Keynesian type of marginal propensity to consume measured out of current income.

2) Fictitious Keynesian Consumption Function

He argues that in order to get the correct consumption function we should lengthen the period of observation, or should observe income and consumption for a sufficiently long time. Trying to attribute changes in current consumption to changes in current income would lead to a fictitious or erroneous consumption function.

The following example will be helpful in your understanding his point;

For instance, suppose that in an economy all the people are identical and homogeneous who are all paid $ 110 per week. The only inter-personal difference is that the one sixth of workers are paid on each day of the weekdays. So 1/6 are paid on Monday, another 1/6 on Tuesday, and so on... Let suppose that the workers spend more, say $ 40, on the pay day, than on other days of the week, say $10 per day. So they save $ 10 each week.

A Keynesian economist would like to examine the relationship between current income and current consumption. And s/he chooses a day of the week, say, Monday, and observes the receipts and expenditures of the workers on the very day.S/he will find two groups of people with different income and consumption;

─────────────────────────────────────────────Monday’s Income Consumption

─────────────────────────────────────────────1/7 of the workers $ 110 $ 40The rest of them $ 0 $ 10────────────────────────────────────────────

The economist would (wrongly) reason that the basic consumption (C1), which is necessary even there is no income, is $ 10, and calculate the MPC = dC/dYd = approximately 0.3 because dY = 110 and dC = 30 between the two groups of the workers. So s/he will get a Keynesian consumption function C = 10 + 0.3 Y.

However, when lengthening the period of observation or time span for the calculation of income and consumption from a day to a week, the above fictitious Keynesian consumption function will disappear; there is only one kind of workers who are all paid $ 110 and consume $ 100: about 90% of income is spent on consumption. The

(1). Y c = C ptruet ........


resulting consumption function will be C = 0.9 x Y (which has no intercept). Friedman thinks that extending the time horizon to a year would not completely eliminate the above error. He does not specify the time horizon.

3) Two Period Model of Permanent Income Hypothesis

Permanent income is a weighted average of the past and current incomes. How far back into the past? The PIH itself is silent as to the specific length of time-horizon the consumer look over in making consumption decision. For practicality's sake, we have to cut it off somewhere in the time-point of the past. In a simplified version of the two-period model;

where θ is in the range between zero and one, and indicates the extent to which people regard the current increase in income as permanent.

For instance, people assign 1 to θ when they regard the entire increase in income as permanent or persisting in the future. Then all the change in the current income will become the change in permanent income, and the c1 (=MPC) fraction of the increase in permanent income will translate into a change in consumption.

However, they will assign 0 to θ when they regard the entire increase in income as transitory or temporary. The increase in current income will not affect the permanent income, and therefore there would not be any change in consumption.

What is the MPC? There are multiple MPC's depending on what income to use in measuring the MPC.

When the MPC is measured against the permanent income: MPC measured out of permanent income = dCt /dYp .

Differentiating both sides of equation (1) with respect to Yp, we get

dCt / dYp = cture.

The MPC measured out of current income (Yt) = c1= dCt / dYt;

Substituting equation (2) into equation (1), we get

Differentiating the above equation with respect to Yt, we can get

c1 = d Ct/dYt = ctrue θ.

),( Y )-(1 - Y =

)Y - Y( + Y = Y

1-tt

1-tt1-tp

2.......

.Y )-(1 c + Y c =

} Y )-(1 + Y { c =

Y c = C

1-ttruettrue

1-tttrue

ptruet


Obviously, ctrue > ctrue θ, because 1 > θ and thus cture x 1 > ctrue x θ.

The larger θ is, the larger the impact of changes in current income on permanent income and consumption;

(1) When θ is equal to one, the MPC measured out of permanent income will be just equal to the MPC as is the case of the Simple Keynesian consumption function.

(2) When θ is equal to zero, the MPC measure out of permanent income will be zero because there is no change in permanent income and thus no change in consumption. The increase in income will be mostly saved, and thus the ratio of saving to income will rise.

(3) Usually 0 < θ < 1. The MPC is measured out of.

Historical Evidence that a transitory increase in income or windfall of income does not increase consumption very much.

(1) There was a one-time restitution payment from Germany to the Israeli citizens. The payment was equal to the average annual income per household. Only 20 % of the amount received was spent out as consumption.

(2) In 1950, there was a unanticipated, one-time payment of life insurance dividends to the U.S. Word War Two veterans. It was $ 175, which amounted to 4 % of annual household income. Consumption rose only by 1 % that year (less than 30 % of the windfall increase in income was spent).

4) Life Cycle Hypothesis

Life Cycle Hypothesis specifies (1) the time horizon, which the consumer consider in making consumption decision, as her/his life time, and (2) include wealth in the income and thereby regarding wealth as making differences in consumption for a given level of labor income.

(1) A consumer's time horizon is equal to her/his life time;

the consumer will first figure out the total amount of resources available for consumption during his/her entire life time. This total amount of resources available during the life time is called 'Life-time Budget Constraint', which is specified, assuming life span is 75 years, as

Note that the Life-time Budget Constraint is the Present Discounted Value of all income over the life span; the future income is discounted with the relevant interest rates for the time interval between the present and the future time points; So the life cycle budget constraint is

.)r + (1)r+ )(1r + (1

)T- Y( +

+ )r + )(1r + (1

)T - Y( + )r + (1

)T- Y( + )T - Y( = Y Disposable

75+t1+tt

75+t75+t

1+tt

t2+t

t

1+t1+tttlcbc

.......

.......2


the Present Discounted Value of the present and future income over the entire life span.

The consumption will be given as

If we assume that r = 0 at all time periods, fist the life-time budget constraint becomes

Secondly, consumption function becomes

Note that consumption is equalized over time, and the actual level of consumption depends on the life-cycle budget constraint which in turn is a function of the current and future income over life time. Broadly speaking consumption function is given as

Let us examine some implicit assumptions behind this life-cycle hypothesis before making more realistic modifications to them;

(1) There is No Uncertainty. The L.C.H. assumes perfect foresight for the consumer; s/he is assumed to know the entire profile of current and future incomes. When s/he is born at time t, s/he knows what the current and future personal disposable incomes are and what the current and future taxes are. Government is acting along a preannounce path of policies.

(2) The preference of the consumer is that s/he can maximize her/his utility over time by smoothing the consumption profile or by spreading consumption evenly over time.

The equal amount of consumption for each period will maximize the total utility, because of the decreasing marginal utility of consumption.

Here a tax cut or decrease in tax (dTt+25), say, at time t+25, does bring about no increase in consumption at time t+25 compared to that at time t+24 or dC t+25 = Ct+25 - Ct+24. It means dCt+25/dTt+25=0. That is because the tax cut was already correctly and completely predicted and thus consumption was already adjusted (at time t or at the beginning).

(2) Wealth matters;

Consumption is a function of life-time labor income and wealth;

Ct = c YL + a WL, where

YL is the (life-time) labor income and WL wealth.

.)r + (1)r + )(1r + (1

C = =

r + )(1r + (1

C = )r + (1

C = C

75+t1+tt

75+t

1+tt

2+t

t

1+tt

..............

.)T- Y( + + )T - Y( + )T- Y( + )T - Y( = Y Disposable 75+t75+t2+t2+t1+t1+tttlcbc .......

.C=C = = C = C = C 75+t2+t1+tt .......

(c).)T,Y, ,T ,Y ,T ,Y ( f = C 75+t75+t1+t1+tttt ...............


For a given level of labor income, at a personal level, the larger wealth one has, the larger APC will be when it is measured against (conventional labor) income;

Ct/Yt = c YL/Yt + a WL/Yt.

5) Modern Frontier Consumption Theory

(1) In the real economy, there is uncertainty to the future. The best one can do is to make an educated guess, or to form expectations by efficiently utilizing information contained in 'news'.

Now consumption depends on the current and all the expected future incomes during the life time; A revision of expectations provoked by the receipt of news about the occurrence of shock or unanticipated events involving future disposable income will lead to changes in consumption; the modified Life Cycle Model in the presence of uncertainty will be

where * means expected future variables.

Example:

For instance, government may suddenly announce at time t that it will decrease tax at time t+25. This comes as surprise or shock as it was an unanticipated, unforeseen, unpredicted event. The 'news' leads to the revision of the expectations of the future income (Tt+25

*). Therefore, the Expected Life-cycle Budget Constraint will be revised upward at time t, and accordingly consumption level will be raised once-and-for-all at time t.

When actually the tax is raised at time t+25, nothing is out of blue. The event has been fully anticipated, and perhaps by this time all the necessary adjustments have been made. Thus the tax cut at t+25 would not bring about any adjustment in consumption at time t+25.

The changes in tax and consumption are not contemporaneous any more; at time t, consumption changes even if there is no change in tax or current disposable income. At time t+25, there will be no change in consumption while there occurs changes in disposable income due to the tax cut. Probably, by now, all the necessary adjustments have been made in response to this fully anticipated tax cut.

(2) The time-horizon may extend beyond life-time if the consumer cared about the welfare of her/his descendant(s), and so on for each subsequent generation.

Suppose there is a tax cut at time t+25, and the decrease in government revenue due to the tax cut will be offset by an increase in the revenues from issues of bonds. As the bonds have maturity and should be retired sometime in the future. Let us also suppose that government is planning to retire these bonds by increasing tax at the year t+76, a year after the death of a particular consumer. Within the framework of L.C.M. which regards the time horizon of a consumer as being limited to her/his life time, the

(d).)T,Y, ,T ,Y ,T ,Y ( f = C 75+t*

75+t*

1+t*

1+t*

ttt ...............


consumer can enjoy the benefit of tax cut and avoid the future tax-liability (s/he dies at the year t+25). So the tax cut will be regarded as bonanza or windfall gains and lead to increases in consumption.

However, it s/he cares about the future generation, s/he will give weight to the disposable income and expenses of the future generation. In the above case, s/he would like to lessen the future tax liability to be imposed upon her/his children. So s/he will save the benefits from tax cut by buying bonds newly issued, and bequeath bonds to the descendant. At the year t+76, the descendants will cash the bonds and pay the increase in tax-liability which is necessitated for the repayment of government debts. In this case, all the government does is to move tax over the time horizon, and thus to delay taxation. That kind of ìntertemporal reallocation of taxation' does not alter the total amount of resources available for a consumer. The consumer will not change her/his consumption behaviour. Therefore there is no further impact on economy. So the Ricardian Equivalence holds (which says that switching from one method of financing to another does not matter, or that deficit-financed and tax-financed government fiscal policies are equivalent, unlike the Keynesian argument that there is no equivalence between the two because the former is more effective with the associated multiplier (=1/{1-c}) having a larger magnitude than the latter with the corresponding multiplier which is equal to one). Here the consumer acts as if s/he would live an infinite life. The inter-generational link is the bequest (motive).

Now in the infinite time horizon model, a general form of consumption function should be again modified as a function of income and tax variables of the current and all the future time points up to the infinity;

(3) Liquidity Constraint

L.C.H. assumes that the consumer can completely smooth the consumption profile by effectively financing current consumption with future income. This is possible when one has an unconstrained access to credit market, and thus can borrow or lend freely.

In reality, a lot of people have only limited access to credit market. Particularly this is the case for those who have wealth in the form of human capital. For instance, most people agree that students will earn more income in the future. But risk-averse people will not give unlimited credit to students. The students are faced with liquidity constraint and their consumption is below the desired level. When the liquidity constraint is lifted up, there will be increase in consumption because the previous consumption is somehow suppressed.

(e).) T,Y, ,T ,Y ,T ,Y ( f = C 75+t*

75+t*

1+t*

1+t*

ttt ...............


Application:

1) Consumption Function and Tax Cut (Fiscal Policy)

Why does the specification of consumption function make difference in fiscal policy implications?

The consumption function is important because it characterizes a most important link within the mechanism of fiscal policy.

Once a renowned economist Professor Edmund Phelps asked in the class, “What is the ultimate purpose of tax?". The answer is that through Taxation and consequent changes in disposable income the government can affect Consumption. Changes in consumption, which is the largest component in the Autonomous Expenditure or YD, will bring about changes in equilibrium national income. So the sequence of fiscal policy involving tax cut is that dT (changes in T) dPDI dC dYD = dAE dYe.

It can be explained in the following details;

The tax multiplier or dYe/dT can be broken into the chain of functional relationships such as

Note that the first component is the multiplier which is equal to 1/{1-c1}. The second one is always one because YD = C + I + G; C will increase YD at the one dollar-to-one dollar ratio. The third is the MPC whose magnitude depends on the specification of consumption function. The last component dPDI/dT = d(Y-T)/dT is one in the Keynesian consumption theory, while in the PIH dPDI/dT = dYp/dT = θ.

The purpose of this chapter is that depending on the link dC/dPDI and dPDI/dT, the impact of tax cut on national income is not that simple, and varies much. We will examine how the modification of the simple Keynesian consumption function could alter the implications of fiscal policy, particularly tax-cut.

2) Permanent Income Hypothesis

In the context of the PIH, the tax multiplier which indicated the impact of tax cut on equilibrium national income can be broken into

We can show the following:

.T

dPDIdPDI

dCdC

dYDdYDdY =

dTdY ee

.T

dPDIdPDI

dCdC

dYDdYDdY =

dTdY ee

.G + I + C = Y tttt

).T - Y( )-(1+)T - Y( = )T - (Y= YdPermanent 1-t1-tttpt

.G + I + }T - Y( )-(1+)T - Y( { c =G + I + PDI permanent x c = Yd

tt1-t1-ttt

tttt


At equilibrium YS = YD, where YS = Y and YD is as given as above,

The PIH suggests that the tax cut will shift the IS curve only by the θ fraction of the distance of shift of IS as is suggested by the Keynesian model.

3) Life-cycle Income Hypothesis

We know that the present tax cut leads to budget deficit at the margin, and necessitates the issue of bond. The crucial point is when the bond will have to be retired sometime in the future, and that this retirement will be done by a tax increase. So basically all the government does in cutting tax is to delay tax over time. The crucial matter for the consumer is whether the bond will be retired and at the same time tax will be increased for that purpose; if the present tax cut has a tax increase within the life time, the consumer knows that s/he cannot escape the future tax liability and thus will not regard the present tax-cut as `free lunch.' S/he saves the increase in income which results from the decrease in tax by buying bonds, and will keep them until the tax raise. Then s/he will cash the bonds and pay the increased tax. In this way her/his consumption is kept smooth, and needs not be swayed by the whimsical government policies against her/his preferences.

4) Modern Frontier Consumption Function

(1) If the L.C.H is true and correct, and if the government will correct the future tax after her/his death, then the present tax cut is regarded as `free lunch,' whose bill will have to be picked up by the future generation s/he does not care about. Her/his consumption will increase upon the news that there will be a tax cut. So in this case of finite time-horizon model, the Ricardian Equivalence fails to hold.

If the time horizon is infinite because a generation cares about its subsequent generation, the consumer will behave as if s/he lives an infinite life; s/he equally weighs the present tax cut and the future tax liability. S/he will save the benefit from the present tax cut and bequeath the saving to the future generation or ‘bequest’, which will be cashed to pay the (future) tax liability, which originated from the tax cut. The bequest motive is the operational link between generations.

. ) 1-T- 1-Y( )-(1 = B where

,G + I + B + )T - Y( c =

G + I + )}T - Y( )-(1+)T - Y( { c = Y

tt

tttt

tt1-t1-tttt

}. tG + I + T {-c c- 1

1 = Y

sot,G + I + T -c= Y ) c- 1 (

ttet

ttt


(2) Rational expectations theory says that in the real world with uncertainty, consumption is a function of the current and all expected future incomes. Therefore expectations about the future affect current consumption behaviour. Whenever there is a revision of expectations about the future, which is prompted by the receipt of news about unanticipated event, there will be changes in consumption.

Anticipated changes in income, or fully foreseen tax cuts would not bring out any concurrent changes in consumption, when actually the tax cuts happen. Because the tax cuts were fully anticipated in the past and were acted upon it at that time of perception, by the time when actually the even occurs, all actions have been taken and no further actions will be left to be taken.

In summary, only unanticipated shocks will bring about changes in consumption, and therefore the changes in consumption will be unpredictable or 'random walk.'

Example: There is no actual tax cut now at time t. But there is 'news' about the future tax cut of time period t+5. The consumer will revise expectations about the future income upward. The extent to which s/he revises expectations also depends upon her/his judgement as to whether the tax cut is permanent or temporary, or in other words, whether it is for one period or for multiple periods. As her/his expected future income increases, her/his consumption will increase now at time t. At time t+5 when actually the fully anticipated tax cut happens, there would not be any change in consumption.

Macroeconomics 179 Ch VII. Investment

Chapter VII. Investment Function

1. Definition

Investment consists of

Fixed Capital Investment: Machinery, Equipment, Non-residential Building, and Residential Construction Addition to Inventory: finished goods and materials on the pipeline, and also buffer

stock of finished goods.

We can also divide the total or gross investment into replacement investment or capital consumption allowances and net investment;

Gross Investment = Net Investment + Depreciation

There are suggestions to include Consumer Expenditures for Durables in Investment.

2. Biggest Issue: Volatility of Investment

Investment is much more volatile than income or consumption; Inventory Investment is still more volatile.

3. Explanations for Volatility of Investment.

1) Keynesian Accelerator Model of Investment

(1) Model

Inverting the following Aggregate Production Function with labor input being held constant

we can rewrite the above equation into;

We can also apply this to the last period;

Investment is the increase in capital stock which is proportional to the increase in (the production of aggregate output, which is equal to) national income;

Differentiating both sides with respect to time t, we get

). N ,K ( F = Y ttt

1. > ,Y = K tt

. Y = K 1-t1-t

).Y-Y( = K - K = I 1-tt1-ttt

.dt

)Y - Y( = dtdI 1-ttt


The rate of change in investment depends on the acceleration/deceleration of the growth rate of income, or the change in the rate of change in income.

(2) Numerical Example:

Assumption: Ct = 50 + 0.8 Yt, It = 3 (Yt - Yt-1). Note that v =3 here.

────────────────────────────────────────────────── Year Yt % change Ct % change Kt It % change────────────────────────────────────────────────── 1

450 410 1350 2 500 11 % 450 10 % 1500 150 3 600 20 % 530 17 % 1800 300 100 % 4 660 10 % 580 9.5% 1980 180 -40 % 5 726 10 % 630 8.6% 2178 190 5 %─────────────────────────────────────────────────

Note that the % change in income and the % change in consumption go hand in hand in a similar proportion. However, the % changes in investment are much more volatile than those in national income or consumption.

In fact it is in a proportion to the % change of the % change in income; the % change in the % change in Y between years 2 and 3 (from 11% to 20%) is 82%. The % change in the % change in Y between years 3 and 4 (from 20% to 10%) is -50%. The % change for the subsequent period is 0%. These numbers, 82%, -50%, and 0%, are in line with the % changes in investment, 100%, -40%, and 5%.

Therefore,

Acceleration in Y (an increase in the growth rate of national income) I

Deceleration in Y (a slow-down of the growth rate) I

Whether investment will increase or decrease this year in comparison to the last year's investment depends on whether the growth rate of this year is larger or smaller than the growth rate of the last year;

For instance, suppose that the real income grew 3% last year, and grows 1% this year. The economy is still growing; income increases this year and so does the consumption. But the investment will decrease compared to the last year's level because the growth rate drops from 3 to 1 % or the growth decelerates.

(3) Implications of the Keynesian Accelerator Model;

i) When the above investment function as a function of changes in income is substituted in the equilibrium national income equation, the only exogenous variables left over are autonomous consumption (C) and government expenditure (G). So what ultimately determines the equilibrium national income is G.


ii) Substituting the above investment function into the equilibrium income function, we get a first-order difference equation; Yt = A (G + C) + B Yt-1. Depending on the value of B, there could be different patterns of business cycles.

(4) Problems

i) This is a circular argument; Y changes as I changes, which changes as Y changes. Therefore this is rather a mechanical illustration than a explanation which touches the fundamental causes of volatility of investment.

ii) There is some factor which attenuates the volatility of investment; the adjustment cost makes actual fixed capital, investment or increases in fixed capital, take place over time in a gradual fashion rather than over night. But the adjustment cost is minimal for inventory investment.

The actual change in capital stock or dK cannot take place overnight. The time lag involved in increasing K is fairly long (think about the construction period, and the time lag between the order and the shipment of equipment and machinery). Inventory Investment does not involve any significant lag.

2) Neoclassical Model of Investment

Investment is the demand for new capital stock (dK). The demand for dK is determined by weighing the cost (Present Price) and the benefit (PDV) of the capital good;

so It = dKt = f (Cost versus Benefit of New Capital Stock)

The cost is equal to the present price of New Capital Stock.

The benefit comes over time in the form of the stream of revenues generated from the capital stock over its life-time. To compare it with the present price of new capital stock, we should get the present value equivalence of the revenue streams by discounting the revenues with interest rate of the times and summing them up. This leads to the Present Discounted Value of the stream of future revenues. So the Benefit of New Capital Stock is a function of the stream of future revenues and future interest rates. In reality where there is uncertainty, the future values are unknown. The best the investor can do is to make a rational guess about the future variables. This means that the PDV becomes the function of expected future variables such as expected future revenues and expected future interest rates;

.)r+1()r+)(1r+(1

R +

+ )r+1)(r+(1

R + r)+(1

R= PDV

20+t*

1+t*

t

*20+t

1+t*

t

1+t*

t

......

......

where * denotes expected future variables, Rt+i is the stream of revenues from the investment project, r interest rate.


The revenue is the value of sales of output (= the price of output multiplied by the amount of output demanded and thus produced) minus tax, and so on;

Implications:

(1) There are a lot more expected variables in the investment function than in any other function; the expectations matter more in the investment function than in other functions.

(2) The expectations change all the time, reacting to 'News', which may not be necessarily correct.

(3) Among the expected variables which affect the PDV of the investment project, in percentage terms, the interest rate is the most volatile. For instance, at the aggregate level, revenues rarely change by 50% (due to such changes in sales or price) while the interest rate often changes by 50 % (from the 11 % to 15 % level or the other way around). So ultimately, a substantial part of the volatility of investment can be explained by the volatility of interest rate. What makes interest rate volatile? It should be considered in the context of Money Supply and Demand. Naturally this has a lot to do with the next topic of this course.

3) Rental Cost of Capital

Investment is the demand for new capital stock or an increase in capital stock (ΔK). The demand for ΔK is determined by weighing the cost and the benefit (or revenue) of the capital good at the margin.

Marginal Revenue = Marginal Cost.

Let's suppose that you are an investor or entrepreneur. You are borrowing money from a bank at the interest rate of i for a year and buy a capital good. You produce outputs from the use of the capital good, and sell it in a year to repay your loan from the bank.

Your revenues come from two sources: During the year, there will be product generated from the machine. At the end of year when you sell the machine you will have gains or loss as the price of the machine has changed.

The marginal revenue is the sum of the marginal product of capital MPK (for a year) and the capital gains or loss due to the changes in price of the capital good (when you are selling your company at the end of a year):

).r ,R ,r ,R ,r ,R( f = I 2+t*

2+t*

1+t*

1+t*

ttt .....

.r ,T ,Q ,P

,r ,T ,Q,P

,r ,T,Q ,P( f = I

2+t*

2+t*

2+t*

2+t*

1+t*

1+t*

1+t*

1+t*

ttttt

....)

.PP+MP = MRK

KK


You incur two kinds of cost: one is the interest ("i") you pay to the bank. The other is that the machine needs repairs, that is, depreciation. Let's suppose that with the payment for depreciation the machine is maintained in as good a condition as a new one:

Here the interest rate i is determined in the money market. The percentage change in the price of the capital good may be in line with the rise of the general price level:

MPK is primarily a decreasing function of capital stock. It is also an increasing function of technical innovation and a decreasing function of any event which adversely affects productivity of capital (for instance, oil shocks).

By transposing the rate of inflation, we rewrite the equilibrium condition as follows:

We call the right-hand side express the user (rental) cost of capital.

Note that the interest rate minus the rate of inflation is the real interest rate. Therefore, the equilibrium condition is that the marginal product of capital is equalized with the user cost of capital, the sum of the real interest rate and the depreciation rate.

Applications of Rental Cost of Capital Model: How does this model work in respond to variety of changes?

For some reason of external shocks (such as an increase in real interest rate) the MC may rise. To ensure the equality between the user cost and the MPK, the MPK should rise to re-establish the equality. MPK will rise when K decreases. Investment should decrease. Intuitive explanation is that when the user cost of capital rises, the least productive project of investment should go to enhance the marginal productivity of capital of the existing project. We will observe that the negative correlation between the interest rate and investment: An increase in the real interest rate will lead to a decrease in investment.

For some reason (such as oil shocks, which lead to cumbersome and disruptive energy saving measures) the MPK may decrease. The two forces will start working. In order to re-establish the equality, the MPK of the left-hand side should rise back. The capital stock should decrease to have an increase in MPK. The least productive project should go to enhance the productivity of capital. This decrease in the demand for capital will lead to a fall in the interest rate or th lending rate of the bank. In the right-hand side of the equality, the real interest starts falling. We will observe a positive correlation between the interest rate and investment.

. + i = MC

. = PPK

K

. + - i = T) ,KL (K,MPK


A decrease in the nominal interest rate will not necessarily lead to an increase in investment; For instance, in 1990, the nominal interest rate was about 12% and the rate of inflation stood around 7%. The user cost of capital was then 12 minus 7 % plus depreciation rate. Now the nominal interest rate is only 8%, and the inflation rate is 2%. The current user cost of capital is 8 minus 2 % plus depreciation rate. The current user cost is higher than that of 1990. What matters to the investor is not the nominal but the real interest rate.

4) Tobin's Q Theory

According to James Tobin, the `Q' index larger than one is a green-light signal for expansion of facilities or new investment. The Q index is equal to the market value of a firm over the replacement cost of a firm: The market price incorporates the market’s expectations as to the prospect of future business returns to the firm, while the replacement cost is simply the present market price of capital required to set up the firm.

Tobin's Q shows how or through what transmission mechanism, for instance, an increase in money supply leads to an increase in investment. If money supply increases, other things being equal, expenditures on all assets will rise. As the demand for stocks rises, the stock prices will go up. The market value of a firm is the stock volume times the stock price. As the market value of stocks rises, Tobin's Q exceeds one. There occurs a new physical investment.

5) Permanent versus Temporary Investment Tax Credits?

By nature, investment can be done in the discrete manner; investment spurts, making the best use of an auspicious investment environment, which comes occasionally ("Make hay while the sun shines").

Implication: A temporary tax cut on investment will have a larger expansionary impact on investment than a permanent tax cut. This contrasted with the case of tax cut on income; a permanent income-tax cut has a larger impact on consumption and aggregate expenditures than a temporary income-tax cut.

"....... Congress may revive the investment tax credit (ITC) in hopes of boosting spending on factories and equipment. Bush would probably sign on. Experts caution that ITC would be truly helpful only if the credit is temporary...." (The Times, "Does America Need a New Deal for the Nineties?", January 13, 1992).

Macroeconomics 185 Ch VIII. Money

Chapter VIII. Money

We have already learned that the LM curve shows the combinations of interest rate and income (i, Y), which satisfy the equilibrium in the money market. It comes from the money supply and demand curves: The equilibrium in the money market, that is, the money supply being equal to the money demand, yields the interest rate.

1. Nominal versus Real Quantity of Money

In economics we define the demand and supply in real terms, not in nominal terms. It is in line with the microeconomics expression of demand and supply. Let's take an example of the demand and supply of hamburgers. We say that 5000 units of hamburgers are demanded at the price of $4. If we say that $20,000 worth of hamburgers are demanded, the statement is not clear enough. If the price is $1, 20,000 units of hamburgers are demanded in real terms. If the price is $10, the demand for hamburgers in real terms is 2,000 units. We can dispel any ambiguity by expressing the volume of demand and supply in real terms- here `real' means no change in response to changes in prices. The nominal quantity of money (supply or demand) is the face value of the total amount of money, and the real quantity of money is the face value divided by price level;

Real quantity of money = Nominal quantity of money / Price level:

m = M/P

At the equilibrium in the money market, the money supply in real terms is equal to the money demand in real terms:

ms = md.

Nothing further will happen to national income, interest rate, and so forth. At disequilibrium, there occurs an excess supply of or demand for money. The equilibrating forces come in to push back the economy to the equilibrium. In this process there occur changes in such variables as income, and interest rate.

It is of great importance to understand the operation of the above equation describing the equilibrium money market condition. Unlike the usual demand and supply case, where the left-side supply is determined by the supplier(s) and the right-side demand by the demander(s). The left-side can be determined by the interaction of the supplier and demander(s). The above equation can be rewritten as

M/P = md

ms = M/P as will be seen shortly.

In case the right-side md is constant, an increase in nominal money supply M by the monetary authority can lead to an increase in the price level P: If the demanders have a very clear idea as to how much money they want to hold in real terms, an increase in nominal money supply will simply lead to a rise of the price level. The above equation can be rewritten as

M = P md.


When the left-side variable, that is, nominal money supply M increases, the price level will go up proportionally if the real money demand is constant. What it implies is that the monetary authority or government determines only the nominal money supply. The real money supply and the price level are both determined by the demanders of money.

2. Money Supply

1) Exogeneity of Money Supply

The nominal quantity of the money supply is determined by the monetary authority, which usually is the central bank.

MS = M

As just mentioned, the monetary authority does not determine the real money supply as it does not control the price level. The demanders of money or the general public determine the price level. To recap, the monetary authority determines the nominal money supply not the real money supply.

How does the monetary authority determine the nominal quantity of money supply? The monetary authority determines the money supply on the basis of a variety of variables. For instance, in the face of a high level of unemployment rate it may increase money supply (of the next period). In this case the money supply is positively related to the unemployment rate. Alternatively, the government may change money supply by accommodating money demand. In the booming stage of business cycles where more money is needed to back up a higher volume of transactions, the government may increase money supply. In that case the money supply is inversely correlated with the unemployment rate. The money supply must be positively correlated with government deficits if part of deficits is monetized or financed through printing of paper money. If deficits are financed through issues of bonds or taxation, they are uncorrelated with money supply. All these suggest that there is no clear-cut unchanging hard-and-fast relation of a great significance between any macroeconomic variables and the money supply. Depending on the government's current monetary and fiscal policies, the macroeconomic variables and nominal money supply could have different relationship. It is impossible to define any unchanging specific relationship between money supply and any variables. In this sense, we say that basically, the nominal money supply is exogenously determined, meaning that it is a good approximation to say that the nominal money supply is independent of any macroeconomic variables. Precisely speaking, the nominal money supply is also affected by interest rates, and so forth. However, their impacts are so small as to be dominated by the government's decision as to the money supply. At one point of time it is fixed, but over time it can be changed by the monetary authority.

The real quantity of money supply (ms) is the nominal money supply divided by the price level;

ms = MS/P = M/P

As the money supply is independent of the interest rate, when drawn in the interest rate and real quantity dimension, the money supply curve is vertical, being the same regardless of the level of the interest rate.


2) Detailed Studies of Money Supply: Money Multiplier

Here we would like to show that while there are determinants of money supply their impacts on money supply is all buried under the dominating factor, that is, the government decision of money supply. Roughly speaking, the money supply is independent of all variables including interest rates.

(1) Different scopes of money

There are a variety of alternative scopes of money. As you expand the scope of money, you are moving from a more liquid form of money to a less liquid one.

Monetary Base or High-powered money is the sum of Currency outside banks + Vault cashes in commercial banks and the reserve deposits at the Central Bank. This is close to the total amount of money that government or the monetary authority directly supplies to economy.

Cashes or Currency outside the banks or the banking institutions.

M1 = Currency + Demand Deposit

M2 = Currency + Demand Deposit + Time Deposit

The time deposits include personal notice and fixed-term deposits and non-personal notice deposits.

M3 = M2 + Non personal fixed term deposits + Foreign currency deposits

cf. There are some differences in terminologies between the U.S. and Canada:For the American terminologies, refer to Table 1 in Handout #1.For the Canadian terminologies, refer to Table 2.

As of November 1975, the Bank of Canada set a target of money supply defined as M2: M2 is regarded as the aggregate money supply variable which has the most direct impact on the aggregate expenditures. In the present Canadian setting `money' means M2.

(2) Money Multiplier Analysis

How the fundamental change in money supply, that is, a change in the monetary base or high-powered money (ΔMB or ΔH)lead to a change in M2 (ΔM2)?

Let's simply call the ratio of MB (H) to M2 the money multiplier. Money supply M2 is equal to the product of the money supply multiplier and the high-powered money;

M2

H=μ (1)


M 2=μH (1')

We recall that

M 2=C+D,

where D=DD+TD (2)

and H=C+R,

where R=Required/Legal Reserves+Excess Reserves (3)

Therefore, plugging (2) and (3) into (1), we get

μ=(2)(3)=C+D

C+R (4)

By dividing both the numerator and the denominator by D, we can rewrite equation (4):

μ= C /D+1C /D+R/D (5)

Therefore, by plugging (5) into (1'), we can see that the money supply M2 is a function of high-powered money H and the determinants of the money supply multiplier such as C/D and R/D:

M 2=μH=μ( RD

, CD )H= f (H , R

D, CD ) (6)

Questions:

i) What will happen to money supply around Christmas when people would like to hold more cashes for small transactions? Refer to the handout. The key is that as C/D ratio rises, as dμ /d(C/D) has a negative sign and thus μ declines, which leads to a fall in M2.

ii) What the impact on money supply would the zero reserve requirement system have? The R/D ration declines which leads to a rise in μ.

Equation (6) implies that government (monetary authority) can mostly control money supply but in a precise way. The interaction among the government, the general public and banks determines the money supply:

The government can fully control H: as will be seen, the monetary authority affects H mostly through the Open Market Operation (OMO). The central bank does have other means of controlling H such as the `Switching Operation' (= Withdrawal and Re-deposits of the central bank's account with the commercial banks), and so forth. However, we will just focus on the OMO.


The government has a printing machine with which to print money. Under the current fiat money system where no paper money is convertible into gold, silver, or any commodities, there is virtually no limit, except the self-restraint on the part of the monetary authority, to the supply of H by the government. Money has not much intrinsic values, and its value is just guaranteed by 'fiat' (decree) of the government.

It is under the fiat or fiduciary money system that paper money replaces commodity money and releases resources for other useful purposes. Gold and silver which is `locked up' for transactions purposes under the metallic standard system can now be used for other purposes under the fiat money system. Paper money or notes are now being used for transactions, which have very small intrinsic values. Only by the values of paper and ink used for the production of money, resources are being diverted from other useful purposes. This is the cheapest possible way of meeting the demand for media of exchange in an economy. This is a good side of the fiat money system: (paper) money is resource-releasing or resource-saving.

However, the bad side of the fiat money system is that there is no more discipline on money supply, except for the self-restraint by the government. Historical experiences reveal that under the fiat money system the printing machine tends to overwork. There frequently occurs an excess supply of money. It brings about inflation, which erodes the real values of money and thus implicitly transfers real resources from the holder of money to the producer of money. Inflation is a form of taxation for the government. This government revenue from inflation taxation is called 'seigniorage.'

Some epistemology may help us understand the term seigniorage. Coins of precious metals were capable of being debased. So arouse the need for certification. In the medieval age, the monarch stamped coins to certify their purity. The coins were made of bullion presented to be stamped The revenues from certification were collected by serrating the edges of coins. These revenues were called seigniorage. The seigniorage in general refers to some due taken by the `Senior' or lord by virtue of the prerogative of sovereign. It refers to government revenues from inflation taxation.

The government and the commercial banks together determine the R/D ratio: the fist sets the required or legal reserve ratio and the second the excess reserve ratio. Under the new Canadian system of zero required reserve system, the R/D ratio is controlled by chartered banks only.

The general public determines the C/D ratio by making decision as to the relative share of their money balances between cashes and deposits.

3) Control of Monetary Base and Interest Rate

Monetary policies involve changes in money supply and interest rate by the monetary authorities. How does the Canadian government control the money supply and the interest rate, particularly the Bank Rate? The Keynesian ideas are well illustrated in the IS-LM framework, with which we are all very familiar. We would like to look into detailed processes beyond the IS-LM picture.


(1) How does the government control the money supply? Open Market Operation

The government can control money supply (M2) indirectly by controlling the supply of high-powered money (H). The money multiplier, which is affected by many factors beyond control by the government, comes in between the two. To that extent the controllability of money supply by government is limited.

The open market operation is defined as the controlling of high-powered money and thus money supply through the government's purchase (H and M2) or the sales (H and M2) of securities or financial assets in the financial market.

There is no idiosyncrasy about the open market operation. First, it does not have to be financial assets or securities that the government buys and sells. For instance, it could be 'wheat.' When the government buys wheat from farmers, it pays them for the wheat with money it prints with the printing machine in the central bank. So there will be a flow of money from the government to the private sector, and the stock of money supply in the private sector increases.

One of the reasons why the government does not deal in wheat is that such operation will lock up wheat which has intrinsic values and uses - consumption as food. Another reason is that wheat is bulky and perishable, and thus it is costly to handle -transportation and storage costs. The financial assets do not have intrinsic values - except the small values as printed paper; they can be only used for igniting fire if the face value is gone-, and does not incur any considerable costs of storage or transportation. In this spirit, it may sound a rather odd suggestion, but what about the government buying birth certificates from the public, thereby increasing the money supply? At least, it does not bring about any distributional problems.

We can summarize the principle of the government operation affecting the money supply as follows:

Whenever the government buys "things", in fact anything, from the private sector which includes the public and the commercial banks, it pays for the things it buys with money it prints. Money flows from the government to the private sector. Therefore, the stock of money supply in the private sector increases.

Whenever the government sells "things", in fact anything, from the private sector including the public and the commercial banks, it receives money. Money flows out from the private sector, and the stock of money supply decreases in the private sector.

The above principle can be also obtained by studying the T-accounts of the banks in succession of transactions as are given in a handout distributed in the class.

Case I: The Canadian government participates in the Gulf War. Let's suppose that the Ministry of Finance sells newly issued bonds to the Bank of Canada and spends the acquired funds mostly on buying weapons from the American companies. Show the impact of the government action step by step on the money supply and other variables with the use of the IS-LM model. Please note that there are two stages of the government actions which affect the money supply: the open market operation or deals in financial assets and the fiscal activity or deal in weapons.


Case II: What will be the impact on the money supply when the Ministry of Finance sells newly issued bonds to the public and spends the acquired funds on Canadian wheat?

Let’s discuss the above two cases: First these questions do have two dimensions: (1) the sales of bonds or open market operation in a narrow sense, and (2) the purchase of goods and services from the private sector or the government expenditures.

Case I: When things are sold or bought among bureaus within the government sector, it does not affect the money supply: although some printed money moves from the Bank of Canada to the Ministry of Finance, it can be still regarded as the inventory of money which has not left the producer (of money) or the government. The MS does not change when the Bank of Canada buys bonds from the Ministry of Finance.

cf. Money residing in the government sector including the central bank is not `money supply'. It is inventory. In the microeconomics, products stockpiled in the warehouse of a factory are not called supply, but called inventory. Only when the products leave the factory or firm and enter the market where demanders are, then they are called supply. Therefore, the shift of stock of money from the central bank to the ministry of finance does not change the money supply. Precisely speaking, money supply is money supply in the private sector outside the supplier of money.

When the Ministry of Finance is engaged in fiscal activities or expenditure policy, buying domestically produced final goods and services and paying for them with the acquired fund, there will be an increase in the money supply in the domestic private sector. The MS increases as G increases. In the case, at hand, however, the acquired fund or newly created money is spent or injected into the American economy, leaving the money supply in the Canadian private sector unchanged.

The overall impact is no change in the MS. Therefore, the LM curve does not move. Neither does the IS curve, which has a shift parameter of the Aggregate Expenditures on the domestically produced goods and services or AE = C + I + G + X-M: In fact, G or government expenditures on goods, domestic and foreign, increases but M or imports increases, too, and thus they cancel out each other in the end.

Case II: In the first step of dealing in financial assets or the òpen market operation,' the Ministry of Finance sells bonds to the general public. As it receives money from the public in return, for them, the MS in the private sector decreases.

In the second step of fiscal activities, the Ministry of Finance buys goods or wheat from the private sector with the acquired fund. The fund in payment for the wheat flows from the government to the private sector, and there will be an increase in the money supply in the private sector.

The combined impact of the two steps on the money supply is nil, leaving the money supply unchanged. The LM curve does not move.

The IS curve moves to the right as G in AE = C + I + G + X-M increases.


(2) How does the Bank of Canada control the short-term interest rate?

The Bank of Canada controls the Bank Rate indirectly by controlling the yields on Treasury Bills (T-bills hereafter) or short-term certificate of government borrowing through its `controlled auction' of the T-bills. The Bank Rate is pegged at 25 basis point or a quarter percentage point (0.25%) above the average weighted yields on the most recently auctioned Treasury Bills of the maturity of 91 days. The detailed procedure of the auction is provided in the separate hand-out. The Bank Rate subsequently forms the basis for all other interest rates. To this extent the government can control interest rates.

This is the short-term interest rate as opposed to the long-term interest rate of bonds with one year or longer term of maturity. The relationship between the short-term and the long-term interest rates needs more scrutiny, and will be dealt under the heading of "Term Structure."

The principle is that if the Bank closes the auction at a relatively high bid, the (discounted) last bidding price of the T-bills is quite high and the corresponding yields should be low: you may remember that the discounted bidding price and the yield(rate of return) are inversely related when the face value at the maturity is fixed.

Consequently, the Bank Rate, automatically set at the rate of the yields plus 0.25%, will be relatively low, too. As the auction is closed at a relatively high bid, a relatively small amount of money in the private sector flows into the government. The left-over or not-auctioned-off bills will be absorbed by the Bank of Canada that makes payment drawing on its holding of existing stock of money or issuing new notes.

How does this affect the money supply? The Bank's purchase of T-bills itself does not increase the money supply (in the private sector): simply money flows between bureaus within government. As we have seen in part I, only when the fund, shifted from the Bank to the Ministry as the payment for the bills, is spent through fiscal activities on domestic goods, there will be increases in money supply (H).

In addition, the more of T-bills the Bank of Canada buys from the Ministry of Finance, the less of T-bills are purchased by the general public and thus the less squeeze is made on the private sector's liquidity or the stock of money supply. In other words, the Bank indirectly affects the amount of liquidity or money supply of the private sector in the process of controlling the yields and interest rate.

In this case we may observe that lower interest rates are usually associated with a larger amount of money printing on the part of the Bank of Canada and more liquidity or larger amounts of the money supply on the part of the private sector (liquidity effect).

Secondly, the Bank Rate may determine the amount of borrowing by the commercial banks from the central bank, which may constitute the reserves of the first in the creation of demand deposits: a low Bank Rate may lead to a large borrowing by the commercial banks from the central bank. The commercial banks may use the borrowed fund as the reserves (R) against which loans and deposits money are created (M2: M2 = m H = m (C+R), where H is high-powered money, and m the money supply multiplier). However, the Bank of Canada has discouraged the commercial banks from borrowing to replenish their reserves and applied a very


high penalty rate to the borrowing for reserves. In other words, in Canada the reserves of the commercial banks and consequent creation of deposit money as part of M2 do not respond to changes in the Bank Rate. This contrasts with the American situations: the (re)discount rate or the American counterpart of the Bank Rate is a major determinant of the money supply of the private sector.

One qualification we should keep in our mind is that the government sets the nominal interest rate or the observed interest rate but not the real interest rate. As we have seen in the early chapter of investment, the real interest rate is determined mainly by the marginal productivity of capital, which is in turn a function of capital stock.

2. Money Demand

1) Introduction

The demand for money or the demand for holding of real money balances should be expressed in real terms or the quantity (of goods the money balance can buy), not in monetary terms. We have already shown that there is little point in talking about the nominal money demand for an economy as a whole, and that the nominal money demand is always and thus trivially equal to the nominal money supply at the aggregate level.

What determines the desired level (quantity) of real money demand? Just as the desired quantity of hamburgers is determined by the consumers' income and the price of hamburger, according to some economists, the real demand for money is determined by the income level of the economy, that is, the national income, and the price of money, that is, the interest rate. Just like any other goods, Keynesians argue that the real money demand is related positively with real national income and inversely with the interest rate, which is the price of money from the Keynesian viewpoint.

Let us examine the second point in the above statement: the price of money is the interest rate. In other words, the opportunity cost of holding money balances is the interest rate. Money is one of many assets which range from financial assets, such as bonds, stock, equities to real assets such as land and gold. Money and other assets are substitutes. The major difference between money and other assets is that money does not bring in any positive pecuniary (monetary) returns - actually it is subject to the erosion of real values from inflation-, and other assets do have pecuniary returns. However money, or money balances in a precise term, renders a unique non-pecuniary service, which is known as `liquidity'. Money is the most generally accepted medium of exchange and thus the most `liquid' out of all forms of assets. So when you decide to hold assets in the form of money balances instead of any other, you are showing your preference for liquidity over pecuniary returns. This is the reason why the money demand is called `liquidity preference', and the Keynesian money demand function, or the `liquidity preference function.'

The interest rate represents the foregone pecuniary return or the economic sacrifice you have to take when you choose to hold your wealth in the form of money balances rather than in the forms of other assets: the interest rate is the opportunity cost of holding cash balances. When the interest rate goes up, the cost of holding cash balances increases and naturally you would like to hold less assets in the form of cash balances and more interest bearing assets. This means that the demand for money is inversely related to the interest rate.


Now we have another major factor to be considered, which affects the real money demand: When real income increases, as money is a normal good, the demand for real money balances increases, too. When real income increases, there occur more transactions and thus more money balances are needed to back up the increased transactions.

Random monetary shocks do affect the real money demand as well. They include not only truly turbulent shocks to the money or financial market, but also financial innovations which affect money demand.

2) Mathematical Presentation of Real Money Demand Function

where y is the real national income, i the nominal interest rate, and u the random term. K and h are all constants.

For simplicity we can specify the function in the linear form such as

In the log-log function, K is the elasticity of real money demand with respect to real national income, and h the elasticity of real money demand with respect to interest rate. The liquidity preference curve is negatively sloped when drawn with the interest rate on the vertical axis and the amount of real money on the horizontal axis. The variables y and u are the shift parameters of the real money demand curve.

In the case where money is defined in the narrowest scope, that is, cashes, the so-called ìnventory theoretic approach' by Keynesians do have specific numbers assigned to K and h such as

md = 0.5 y - 0.5 i + u.

Now we can see the reason why dmd/di or -h <0 , and dmd/dy or K > 0 in greater details:

i) Interest rate [Substitution Effect]:

How much money you would like to hold depends, among other things, on the sacrifice of pecuniary returns that resulted from holding money instead of interest-bearing assets. The foregone returns are the opportunity cost of holding money. They can be represented by the interest rate. So the higher the interest rate, the higher the opportunity cost is and thus the lower md will be.

ii) Income [Income Effect]:

When real income rises, households will add to all assets including money. Also, as real income increases, the volume of transactions increases and thus there is a need for more money balances.

],u i, y, [ L = m = P

M dd

.u + i h -y K = m = P

M dd


Keynes specified his money demand function such as Md = L1 +L2, where L1 = Àctive Balances' due to transactions motives and L2 = Ìdle Balances" due to speculative motives.

Our criticism against his idea is that one can think of different motives for holding money balances without dividing the actual holding of money into these two motives. Every dollar of money balances serves more than one function. Why can't the same dollar provide some transaction services, some precautionary services, some speculative services? Operationally Keynes's distinction is not meaningful as we cannot attach specific numbers to L1, and L2.

3) The Major Issues of Real Money Demand Function: Magnitude of Interest Rate Elasticity

We would like to make two major points: i) The magnitude of the interest rate elasticity of real money demand varies depending on the scope of money. ii) The magnitude also determines the relative effectiveness of monetary and fiscal polices.

The interest elasticity of 'money' will be all different depending on whether the `money' includes cash alone or other categories of money; cash does not bring any interest payment to the holder, while time deposit does. When there is an increase in interest rate, there will be a decrease in the demand for cash. If money includes both, the impact of the change in the interest rate on the demand for money will cancel out and thus the demand for that concept of money (= C + TD) could be rather constant.

First, what would be the benchmark? There is an old theory for the elasticity of real money demand with respect to interest and income. This would be a theoretical benchmark. However, the actual magnitudes of elasticity do change over time particularly with respect to interest rates. Ultimately, it is an empirical issue which employs data analysis and econometric regression of

(1) The Benchmark: Cash Inventory Theoretic Approach

Can we derive the sensitivity of the demand for cash with respect to interest rate?

The Inventory Theoretic Approach developed by W, Baumol has its own answer: K = 0.5 and -h = -0.5

Suppose that you are making and spending $ Y each month. The monthly income of $ Y comes at the beginning of the month and, as being spent, gradually runs down to zero toward the end of the month. During the interim period you are faced with two choices: you can hold your income either in deposits which pay the interest rate i(in fractional terms) or in money or cash that does not carry any pecuniary returns. Suppose you deposit the entire monthly income with a bank which pays interest on the deposit at the beginning of the month, and you make trips to the bank to withdraw $ Z each time. This trip is not without cost as it takes time or other resources. Suppose that each trip costs $ tc.

The first question you may ask is: How may trips would you make to the bank per month? Y/Z trips per month. The total cost of making trips to the banks to get cash withdrawal is $ tc (cost per one trip) x Y/Z (the number of trips). For instance, if you have $ 800 monthly income which


you deposit in the bank at the beginning and withdraw $ 160 per trip to the bank, you will have to go to the bank 5 times per month. If each trip costs $10 including loss of wages and use of other resources, the total cost involved in trips is $50.

The next question you may ask is: What is the average balance of cashes or money in you pocket? The amount of withdrawal of $ Z will slowly runs down to zero as you spend money. Therefore at the most you have $Z and at the least you have $0. The average cash balance is $(Z + 0)/2 or $Z/2. As 1/2 of $Z is always in you pocket rather than in the bank, you are foregoing the possible interest payment on it by $Z/2 x i: this is the opportunity cost of holding cash balances in your pocket instead of bank deposits. In the above case, the opportunity cost of the average cash balance of $80 is, if the interest rate is 0.1 (10%) per month, $8.

Therefore, the total cost is the sum of the costs of having money in the pocket and the costs of making trips to the bank:

Total Cost = Z/2 x i + Y/Z x tc.

You as a holder of cash balances would like to minimize the total cost by choosing an optimal value of Z;

Minimizing Z/2 x i + Y/Z x tc.

You are choosing $ Z here ( $ Y is given by your boss; i set by the bank; tc set by other things, such as bus fairs or your loss of wages for the time spent on trips) to minimize the total cost. The optimal value of Z* can be obtained from the first order condition: Differentiate the total cost with respect to Z and equate the first derivative with zero.

(f.o.c.) 1/2 i + Y x tc {-(1/Z)2} = 0.

as we know that d(1/Z)/dZ = - 1/Z2.

Solving the above for Z*, we get

1/Z2 = 1/2 x i x 1/Y x 1/tc

Z2 = 2 Y tc / i

Z = [(2 Y tc)/ i]½ , and

Md = Z/2 = [(Y tc)/ 2i]½

What is the income elasticity of the demand for cash balances? Answer: 1/2.

What is the interest elasticity of the demand for cash balances? Answer:-1/2.

(2) Changing Interest rate Elasticity, and Effectiveness of Monetary/Fiscal policies:


As we have discussed, alternative concepts of money have different demand elasticities with respect to interest rate. When money is defined as M2 = Cashes in circulation + Demand Deposits + Time Deposits, the interest rate elasticity of money demand will be very small. One may think that if the interest rate or the rate of returns on short-term T-bills goes up, the demand for all the components of money M2 will decrease. It is not true. Because of competition that induces the banks to bid up their interest rate on deposits, the demand for deposits does not have to decrease. In this case, what determines the money demand is not a particular interest rate, but the difference between the interest rate on bonds or T-bills and the interest rate on deposits. As they tend to move together, the interest rate itself does not lead to a large change in money demand.

Keynesians argue that h is quite large while classical economists and Monetarists argue that it is very small.

A large value of h means that the elasticity of real money demand with respect to interest rate is quite high: graphically the elastic real money demand curve is quite flat. The LM curve derived from the flat money demand curve along with the vertical money supply curve is quite flat, too. You may recall that the flatter the LM, the smaller the Crowding-out. Fiscal policies are quite effective. In this case monetary policies are not so effective. These conclusions are in line with the Keynesian basic doctrine that advocates fiscal policies and is skeptical of monetary policies:

A small value of h means that the elasticity of real money demand with respect to interest rate is quite low: graphically the inelastic real money demand curve is quite steep. The LM curve derived from the steep money demand curve along with the vertical money supply curve is quite steep, too. You may recall that the steeper the LM, the larger the Crowding-out. Fiscal policies are not so effective. In this case monetary policies are quite effective. These conclusions are in line with the Monetarists's basic doctrine that advocates monetary policies and is sceptical of fiscal policies:

The so-called Re-entry Problem illustrates skepticism of monetary policies: It states that once the government turned around from expansionary to stringent monetary policies, it is difficult to go back to use money to boost the economy and to raise the national income. In the stage of monetary policies as a means of boosting the economy, there is a `re-entry problem'. Once you go out of it, you may have difficulty in re-entering it.

It occurs under the following two conditions:

i) the money demand is quite interest rate elastic; andii) the nominal interest rate is falling.

it can be explained as follows: The money demand equation can be expressed in terms of percentage changes such as

ΔM/P = K Δy - h Δi + Δu

When the interest rate is falling, the term -h i is positive. Thus ΔM > K Δy .

So when there is the re-entry problem the rate of monetary expansion is larger than K Δy. This means that the same rate of money creation would lead to a smaller increase in the national


income. Put differently, in order to have the same rate of economic growth, the rate of money creation should be a lot higher with the re-entry problem than otherwise. The re-entry problem makes monetary policies quite ineffective.

eg) Let's assume that K=1 and h=0.5, and that interest rates have been falling from 15% to 7.5% (this is a 50% decrease as (7.5-15)/15 is equal to -50%). To have a 5% growth of national income, at what rate the money supply should be increased?

(Answer) ΔM/P = K Δy - h Δi = Δy - 0.5 Δ = 5 % - 0.5 (-50%) = 30 %.

A 30% increase in money supply will only lead to a 5% increase in national income. Under the given two conditions the effectiveness of monetary policy is smaller for a given rate of money creation than otherwise. The reason is that as the interest rate falls, the opportunity cost of holding money falls and thus the demand for real money demand increases. Put differently, when interest rates fall, people let money holding grow in their pocket or bank accounts. So a large part of the newly injected money supply will be held by an increased money balances rather than being spent around to boost the economy.

(4) In Search of Stable Money amid Financial Innovations

One of the main reason why real money demand is elastic with respect to interest rates is that money does not bring in any interest payment but its substitutes do. In the U.S., there has been so-called “Regulation Q”, which forbids any interest payment to money or cash balances. The U.S. financial institutions cannot pay interest payment to balances of checking account or demand deposits. On the other hand, when it comes to the means of payment, money or cash has the unique services of ‘liquidity’ as opposed other financial assets do not have ‘immediate’ liquidity. Thus, whether or not, and how much the real money demand is sensitive to changes in interest rates depends on whether there are any other substitutes for money which at the same time carry interest payment. If there is a non-money financial asset which must carry interest payment, and it also provides a comparable service of liquidity, then the demand for money will be highly sensitive to changes in interest rates as there will be an active substitution between money and the financial asset.

Over time, the banks have been engaged in financial innovation, and came up with interest-bearing financial assets which can also be accepted as a means of payment. For an example, some investment companies have come up with a checking account based on the balance of ‘money market mutual funds’. The customer earns interest payments as this is an investment on financial securities, and at the same time, he can write a check against the balance of his mutual funds. In this situation, when interest rate or rate of return on financial securities goes up in the financial market, people will move their wealth from money or cash to the money market mutual funds. The real money demand becomes large and unstable.

In the illustration of the ‘Re-entry Problem’, we have already illustrated that the monetary authority would like to secure a stable real money demand for the sake of control of economy via monetary policies. The controllability of economy depends positively on the stability of real money demand and negatively on the magnitude of the interest rate elasticity of real money demand.


From the viewpoint of policy makers, there is a simple solution to the problem of the real money demand becoming unstable due to financial innovations: Expand the scope of money for consideration. For the example at hand, due to the financial innovation of the checking account of money market mutual funds, the real money demand defined in terms of M2 has become ‘unstable’ and more sensitive to changes in interest rates. Now, if the policy maker expands his horizon so as to make a new definition of ‘money’ include the balance of the checking accounts of money market mutual funds, now the new real money demand will be less sensitive to interest rates. When interest rates go up, financial wealth will move from M2 to the checking account of money market mutual funds. However, that is still a flow within the scope of the newly expanded concept of money. In fact, the policy makers call the new scope of money ‘M2 +’. Now the real money demand, defined in terms of M2+ will be stable and be less sensitive to changes in interest rates. The monetary policy based on M2+ will have a clear impact on economic variables such as Y or P. Thus we can say that the monetary policy makers are always in search of ‘stable money’.

3. Equilibrium and Disequilibrium in the Money Market: Mathematical Analysis: Quantity Equation of Exchange

The relations between Money, Income, and Price Level can be viewed in light of the equilibrium and disequilibrium of real money demand and real money supply such as

M/P = K y - h i + u:

The left-hand side of the equal sign is real money supply, and the right-hand side is real money demand. At the equilibrium, nothing changes and the equilibrium levels of y, P, and i are shown in the equation.

In fact, the relationship between money supply M and income y and price level P can be best – in the sense that it is not clouded by the interest rate variable - with the Quantity Equation of Exchange. This is a very old model. It overlaps with the mathematical model of real money demand equation that we have examined. Compared to the mathematical version of the demand curve, the Quantity Equation of Exchange is simpler and thus has strength and weakness: It is easier and quicker to use in figuring out the impact of money on y or P. It is, however, not for a sophisticated analysis.

There are different versions of the quantity equation. However, the most common one is the Income Version of the Quantity Equation of Exchange such as

M V = P y,

where V is called the ìncome velocity of money' which means how many times a dollar changes hands for a given period of time.

There are also the `Transactions Version of the Quantity Equation' such as M V = P T, where T denotes the total volume of transactions, and the so-called Cambridge Cash-Balance Equation such as M = k P y where k = 1/V.

We can transform the above equation into;


Δ%M + Δ%V = Δ%P + Δ%y

If we look at the equation just mechanically, we can ask and answer the following questions very easily:

If the nominal money supply grows by 8%, the general price level rises by 6%, and velocity rises by 1%, what would happen to real income?

If income is growing at the annual rate of 4%, the money supply at 6%, and the prices at 1%, what must be the change in velocity?

If in the Canadian economy real income is growing along the long-run trend of 3% per annum, the velocity is expected to fall by 1%, what monetary growth rate is required to produce à zero inflation'?

The aggregate demand and supply are given by the following equations:

AD: P y = 3 M (no fiscal policies); AS: y = yf =300. Presently M = 100. What is the AD? Now if ΔMSe for the next time period t+1 is 30, what is ΔPe for t+1? Suppose that actually ΔMS at t+1 turns out to be only 20. What are actual ΔP at t+1, and forecast error respectively? What is going to happen to y in the short- and long-run?

The above equation itself does not specify what impact ΔM would have on P, V, or y. There are alternative views of causality and relationship among the variables appearing in the quantity equation.

Comparison to the mathematical version of real money demand is possible:

MV = P yM/P = K y - h i + u

Basically, V or the velocity corresponds to the part of – hi + u. In other words, the velocity of the quantity equation of exchange corresponds to the interest rate elasticity of real money demand and other random effects. Thus V reflects a lot of things without showing breakdown of the effects:

V= V(i, u, other economics customs related to payments and money use).

We know that the above nominal interest rate i= r+ : the nominal interest rate is equal to real interest rate plus expected rate of inflation. Thus the velocity of circulation V is a function:

V = V(real interest rate, expected inflation, random monetary shocks, other economic customs related to payments and money use).

For one thing, if people expect a higher rate of inflation, then V rises as they would like to spend their money before it loses real value. A higher expected inflation pushes up the nominal interest rate i, and in the mathematical real money demand function, a higher interest rate leads to a reduced real money demand.


4. What Does Money Do?: Relationship between Money and Real Income, Price Level, and Interest Rates.

Here we will look at what money does with respect to i) real national income(y), ii) price level and inflation, and iii) interest rates. The bridge between a change in money supply and changes in other variables is called the `Monetary Transmission Mechanism'.

Basically, the Classical School saw no connection between the real sector of economy to which investment, consumption and national income in real terms belong and the nominal sector of money and price level. They saw ‘Dichotomy’ or a big separation between the two worlds. Money is a veil and has impacts on nominal variables such as price level. As money increases, in the long-run the price level(P) goes up, and the nominal expenditures(=P times y) may increase but the real variables(y) do not change.

1) Relationship between Money and Real National Income: Neutrality versus Non-Neutrality of Money

There are two descriptions for the relationship between Money and Real National Income:

Neutrality versus Non-neutrality : If an increase in money supply does not have any impact on real national income or any other real variables such as investment, we say that money is ‘neutral’. If an increase in money supply leads to an increase in real variables such as investment and national income, money is ‘non-neutral’.

Note that this concept of ‘neutrality of money’ is in line with the tradition of ‘classical economics’ which sees the ‘dichotomy’ between the nominal sector variables such as money and price level, and the real sector variables such as ‘real’ interest rates, investment in real terms, consumption in real terms, and real national income.

Super-neutrality versus Super-non neutrality : If an increase in the rate of changes in money supply does not have any impacts on real national income, we say that money is ‘super-neutral’. If an increase in the rate of changes in money supply affects real variables, money is ‘super-non neutral’.

Note that here an increase in the rate of changes in money supply is the same as an increase in the speed of money creation, or in shorter terms, an acceleration of money creation. The accelerating money creation is different from a simple once-and-for-all increase in money supply which is related to ‘neutrality’ issues.

Here we will examine a few different schools of macroeconomics: First, the ‘Original Keynes’s view of money’, the Neo-Classical Synthesis, Monetarists, and New Classical or Rational Expectations.

(1) The Original Keynes’s Ideas on Money and Income


The Keynesian transmission mechanism is well illustrated by the IS-LM model which is the basic analytical tool for the Neo-classic Synthesis or Àmerican Keynesians'. An increase in money supply shifts the real money supply curve. The interest rate falls in the money market. The falling interest rate favourable affects the investment in the goods market, and the rising investment leads to an increase in the aggregate expenditures and the national income.

Keynes came up with a ‘new’ economics against the back drop of the Great Depression or a most severe recession or deflation in history. In the specific setting of the severe recession, Keynes was skeptical of any effective transmission of an increase in money supply to an increase in any variables: (i) If the money demand is almost perfectly interest-elastic, a given amount of an increase in money supply will lead to a very small fall in interest rate. This will be particularly true when the current interest rate is so low at the rock bottom that it cannot fall any further. And in addition (ii) If investment is not quite sensitive to interest rate, a falling interest rate will have hardly any impact on aggregate demand. In Keynes's view the investment is mainly determined by expectations of businessmen or ànimal spirits' rather than by interest rates.

In the Quantity Equation of Exchange MV = P y, any increase in M will be completely offset by the opposite movement of V. On the net, the left-hand side does not change, nor does the right-hand side: P or y does not change. Keynes empathetically said that during a severe recession “Money Does Not Matter”. This is what we have many times, by now, gone over as ‘Liquidity Trap’. Needless today, in this case money is ‘neutral’ in its strongest sense of the word.

(2)Neo-Classical Synthesis on Money and Income

This view is well illustrated with the standard IS-LM and AD-AD(long-run and short-run) curves.

When the monetary authority pours money supply or M into economy, then there occurs a dynamics of disequilibrium: for a moment at the beginning, the left-hand side of real money supply M/P exceeds the real money demand on the right-hand side. This inequality may – and may not- put a train of variables in motion. The disequilibrium in the money market makes the borrowing cost of money go down, and the (nominal) interest rate may fall. If the price level is constant for the moment, this will lead to a reduction in real interest rate which boosts real investment. Thus an increased investment will increase the aggregate demand of the economy. Thus, the national income measuring the expenditure side, that is, Gross Domestic Expenditures will automatically rise. This is the demand side of national income. Whether the increase in the demand side of national income leads to an increase in the supply side of national income such as Gross Domestic Products(GDP) depends on the size of room in the economy. If there is a room for an expanded production in the economy, the supply side of national income will increase. That is an increase in real national income ‘y’ or the aggregated quantities of goods and services. Going back to the above equation, as i falls and y rises, the right-hand side of real money demand rises. This dynamic change keeps happening until the right-hand side rises up to the equal level of the left-hand side of real money supply. Then, the economy has reached a new equilibrium and there would be no further changes. In this case, money is non-neutral.

A pure sense of non-neutrality may take place when M affects y only, but not P. This is possible when the economy has the almost perfect price(level) elasticity of (aggregate) supply: A small increase in the price level leads to an almost infinite increase in the aggregate supply. The short-run AS curve is horizontal.


In a hybrid case of non-neutrality, an increase in M would lead to an increase in both y and P. In this case, the short-run AD curve is upward-sloping. This is a true sense of ‘Synthesis’ befitting its name of school ‘Neo-classical Synthesis’.

If there is no room in the supply side, however, the increased aggregate expenditures or GDE will simply push up the price level of national income. The right hand side does not change. The result is an increase in P. Going back to the above equation, P on the left-hand side roses up until M/P goes back to the initial level. At the time when it is completed, the resultant change in P will be proportional to the change in P as long as there is no change in inflation expectations which will be shown as no changes in i (=r + as you may recall). In this case, money is neutral.

If we really want to split a hair, we will have to be exact here. Even when the economy is at the full employment level, the national income may rise for a short term. People may overwork and facilities may be put into use beyond capacity. In the short-run real national income rises. So we can say that even at the full employment level, money could be non-neutral for a short-term. However, in the long-run, people cannot overwork and facilities cannot be over-utilized. Eventually everything will come back to the full employment level. In the long-run, the increase in money supply will result into the only permanent increase in the price level. In the long-run, there will be neutrality of money. So remember that in this case there will be first a short-run non-neutrality and then a long-run neutrality.

Let’s have a look at the quantitative equations. This view basically believes that the velocity of circulation of money or V in MV = Py is stable. As M goes up and if y < yf , then y goes up. This is non-neutrality of money.

If y = yf, then M leads to an increase in y in the short-run, and an increase in P in the long-run. This is non-neutrality of money in the short-run to be followed by neutrality of money in the long-run.


(3) Monetarists' Ideas

The Monetarists are those who believe that money matters and money has the most far-reaching impacts on macroeconomic variables. They are headed by the late Professor Milton Friedman. His innovative ideas are summarized as ‘Monetarism’ and those who follow his ideas are called ‘Monetarists’.

Monetarists' transmission mechanism is direct and thus powerful. The money supply affects the aggregate expenditures directly. However, Milton Friedman did not say that the duration of the transmission is short. While it is direct, the transmission can take a varying length of time depending on the situation. In other words, there is a time-varying time-lag between a change in money supply and the manifest impacts on the economy. Thus, Professor Friedman was, for practical reasons, against the use of money as an instrument for an ‘active’ monetary policy geared to stabilizing the national income in the short-run. The ideal ‘monetary policy’ is, according to him, of the long-term nature, and is to be devoted to stabilizing the price level. The focus shifts from the national income to the price level. And then he took one step further to distinguish a simple increase in the price level and sustaining inflation. He analyses them in the context of real money demand, and their impacts on interest rates as well. Thus, Professor Friedman is known for his unique contribution of ‘real money demand’. M. Friedman should be heard in his voice:

"The quantity theory is in the first instance a theory of the demand for money. It is not a theory of output, or of money income, or of the price level. Any statement about these variables requires combining the quantity equation with some specifications about the condition of supply of money and perhaps about other variables as well." (M. Friedman, "The Quantity Theory of Money - Restatement, Studies in the Quantity Theory of Money, University of Chicago, 1956.)

Let’s run the risk of repetition and boredom, we may describe the transmission mechanism of money to other economic variables for the last time:

The nominal quantity of money demanded by the society as a whole is always equal to the nominal quantity of money supplied by the government; MS = MD at all times. The general public as a whole cannot control the nominal money supply but it can control the real money supply through their collective control of price level.

Suppose the government is handing out newly printed paper monies or notes on the street. Is there anyone who would refuse them? Every dollar of money supply will be gladly demanded. When an individual receives some new paper monies, her/his nominal (and real) balances increase. S/he may succeed in decreasing the nominal money demand or the real money balanced back to the initial level by spending the excess money holdings. However, because her/his expenditures will become someone else's receipts, some other members are getting the money being dumped on them by the first recipient. So from an individual's view point the nominal money demand may be controllable, while it is not controllable from the society's viewpoint. What is true for individuals is not necessarily true for the society as a whole. This is the `fallacy of composition' commonly found in macroeconomics.

As individuals are busy getting rid of the excess money over the desired level of demand("I would like to have $200 in my pocket, but as government gives me a new $100 bill, now I have


the excess money holding by $100. I would like to go back to the initial level of desired money demand, that is, $200 by spending $100 away.") The increased money becomes a hot potato. I dump money on you, you do on him, he does on her, and so forth. The total quantity of the nominal money demand of the society as a whole, which includes my money as well as yours, and theirs, remains constant. So we say that an individual can control nominal money demand but the society cannot.

Depending on the situations surrounding the aggregate supply, the increased speed of spending or aggregate expenditures can do two different things to the economy:

(i) an increase in aggregate expenditures may stimulate the aggregate supply of goods and services if there is room in the economy as the current national income is below the full employment level. The majority of impact will be on the real national income. The increase in the national income will consequently induce people to hold more money, which restores an equilibrium in the money market. In this case the real money demand rises up to the new higher level of real money supply: in M/P = md, an increase in M raises M/P to create a disequilibrium. The economy goes back to equilibrium as an increase in y leads to an increase in md. P remains constant.

(ii) If the economy is around the full employment level, an increase in the aggregate expenditures will eventually push up the price level. The general public are collectively changing the price level and thus controlling the real money demand, which is equal to the nominal money demand divided by the price level. What does this mean in terms of the real money demand of the society? The real money demand of the society as a whole or the macroeconomic real money demand is going back to the initial level.

Suppose an economy is around the full employment level, and MS =MD = $200 billion and P =1.00 initially in the equilibrium. Now the monetary authority increases the nominal money supply MS to $400 billion. What will happen to the economy?

The (macroeconomic) real money supply is MS/P = 200/1 = 200 for the society at the initial equilibrium. The MS in the numerator can be replaced with MD as they are always equal to each other. Let's us not have any distinction between nominal money supply and demand by using just M: MS/P = MD/P = M/P. At the equilibrium the real money supply is equal to the real money demand: M/P = md. This real money demand is at the desired level at the equilibrium in light of all the determinants of the demand including the income level and the interest rate.

What will happen as the nominal money supply doubles? First, all the increased nominal money supply will be demanded. So the nominal money demand is equal to the new nominal money supply(note that this equality of nominal money supply and demand does not mean at all as the equality of real money supply and demand is the condition for equilibrium): MD' = MS' = M' = $400 billion.

In the short-run, the price does not change, and thus the actual amount of real money holding will be M'/P = $400/1.00 = 400. This real money supply is much larger than the desired real money demand, that is, 200. As there are no change in the determinants of the real money demand such as interest rate and national income, there should not be any change in the level of real money balances the general public wish to hold. There is an


excess of real cash balances over the desired real money demand: àctual' real money balances > `desired' real money balances.

As individuals with excessive money balances try to recover the desired real money balances by spending the excess money receipts, the price level is pushed up to P'. At this new price level, the new àctual' real money balances (M'/P') become equal to the desired level of real money balances.

Specifically, the price level will go up to the level of 2 (or the index number 200). The actual real money demand will be 400/2 = 200, the same level as before any changes.

If you think that up to this part it seems to be, by and large, a repetition of what we have discussed elsewhere, you are missing a subtle but very important point. Indeed, there is some uniqueness to the Monetarists’ view. All explanations evolve around the real money demand, and its functional stability: If there is no change in the equilibrium level of real money demand, a change in money supply will be met by changes in such a way that the real money balance is to be restored. The functional stability of real money demand is the key to Professor M. Friedman’s ideas. The real money demand can change if there are changes in relevant determinants of variables such as y or i. However, the functional form is stable, and it is the Monetarism’s essence.

Which out of the two paths, an increased money supply go depends on a completely separate (auxiliary) assumption as to the aggregate supply condition. Some people think that the Monetarism always argues for neutrality of money. They erroneously think that in the Monetarists’ view an increase in M would just lead to an increase in P, and that it is the major part of the Monetarism. Simply it is a common misperception. The Monetarism itself is silent and neutral as to which one is correct. It requires a quite separate auxiliary assumption. We have already discussed the whole range of arguments as to the impact of an increase in aggregate expenditures or aggregate demand on the real income versus the price level: Classical school believes that the As curve is vertical and thus an increase in the AD or AE leads to a rise of the price level only, and Keynesians argue that it is upward-sloping and thus a higher AE leads to a higher equilibrium real national income. The New Classical economists argue that the unanticipated increase in the AD or AE leads to an increase in the real national income only in the short-run and that any anticipated change will have impacts only on the price level, not on real variables. Monetarism itself does not necessarily side with any particular argument.

(4) Rational Expectations Theory: New Classical Theory

The bottom line is that only unanticipated ΔM affects Y or national income in the short-run. This has been discussed in earlier chapters in relation to ‘Policy Invariance Theorem’.

Empirical studies on the Canadian economy of the last twenty years or so indicate the following conclusions:

i) Monetarist's transmission mechanism is correct for the entire period in question: Whenever monetary policies went against fiscal policies, monetary policies determined the changes in the


aggregate demand and the nominal national income. For instance, in the case when monetary policies were expansionary and fiscal policies contractionary, the nominal income increased.

ii) As a result, V or the income velocity was quite stable at least until the early 1980s. This means a proportionality in changes in the nominal income and the money supply for the most period of time: ΔM V = Δ Y.

iii) In the early 1980, V rose. This means that in the early 1980s the changes in the nominal income started to exceed the rate of changes in money supply: ΔM Δ V = Δ Y, and here M is defined as M1. This is not evidence against Monetarism, which does not preclude the possible changes in V. In the early 1980 inflation in Canada accelerated and the general public expected a continued acceleration. So people speeded up spending, and the income velocity rose. The income velocity changed in a systematic response to a changing opportunity cost of money holding. When they measured the velocity as a ratio of the nominal income to M2 as opposed to M1, the proportionality between the nominal income and money supply or the constancy of the velocity V (= Y/M) could be verified again. The most important determinant of the nominal income and the aggregate demand seemed to be M2. The Bank of Canada has changed its major money aggregate from M1 to M2 in managing the aggregate demand.

The New Classical Theory has brought a new dimension in out debate to “Neutrality” versus “Non-neutrality”. It argues that only unanticipated changes in money supply leads to a surprise inflation and consequently changes in real national income. This is called the (Monetary) “Policy Ineffectiveness Theorem”. They make a very clear distinction between Anticipated and Unanticipated Changes in the Money Supply.

(i) Short-run Neutrality for Anticipated Changes in Money Supply

Ultimately the question of whether a change in the money supply would affect national income depends on whether or not the monetary policy which involves the change in the money supply is anticipated by the public.

We have already examine this case in the section of the AS. In that graph, the economy moves from 1 to 3 directly, not through 2. Even in the short-run there is no change or increase in y.

Now let’s introduce some mathematical model as follow:

Remember that two kinds of random factors can make the actual national income deviate from the full employment income: the forecast error as to the future money supply, and aggregate supply and demand shocks.

Yt

= Y + ½(M – Met)+ ½( ),

where M is the actual money supply of period t, M denotes the money supply expected at time t-1 to prevail at time t.

Some authors may use different notation such as , They all denote the

same thing: expected at time t-1.

ft 1t tt

t 1tet

ttttett MEMM 1

*11

tM


and are aggregate demand and supply shocks following a random walk process. The examples of the aggregate supply shocks are war destruction(of negative value; -), drought(-), oil shocks(-), discovery of natural resources(+), and so forth. The example of the aggregate demand shocks may be something like a sudden foreign demand for domestic goods(of positive value; +), and so forth.

Anticipated changes in the money supply lead to anticipated changes in the price level there is no forecast error about the price level; there is no divergence, except for the one due to the aggregate supply and demand shocks, between the anticipated price level, which form the basis of setting nominal wages, and the actual price level; there is no change in real wages from the ones corresponding the full employment; there is no change in the level of employment from the natural rate of unemployment; there is no change in the national

income from the initial Yt. If there is a fluctuation in the national income, that is due to

aggregate supply and demand shocks.

An anticipated monetary policy means

Mt= M and thus M

t- M = 0.

Therefore

Yt

= Y + ½(0) + ½( ); Yt

= Y + ½( ).

Note that the monetary variables have disappeared from the income equation. Money is neutral in the short-run as well as in the long-run.

(ii) Short-run Non-Neutraility of a Unanticipated Change in Money Supply.

In the above equation, a unanticipated change in money supply leads to Mt

M and

thus Mt- M (forecast error) 0.

Here money could be non-neutral. There will be a possible forecast error as to money supply of the next period, which creates room for the national income to deviate from the full employment level in the short run. Unanticipated changes in the monetary supply lead to changes in real national income.

However, this does not mean that monetary policies should be used to control the national income. The forecast errors are random and thus the short-term deviation of national income from the long-run equilibrium value will be random as well.

An unanticipated change in the money supply increases the degree of variability of the national income: in order to defeat the general public’s expectations, the money supply should be changed in a random fashion. If so, the national income would also change in a

t t

1t*t 1t

*t

ftt f

tt

1t*t

1t*t


random way. As stability of the national income is an important element of society’s material welfare, the increase volatility decreases social welfare. This kind of nondeterministic or random monetary policy is not useful.

When there turns out to be a positive shock or surprise, the actual money supply increases more than what was anticipated in the last period, and the actual price level rises more than

anticipated: M - E M 0 (>0) and P - E P 0 (>0); the nominal wages for the

period t or W was determined on the basis of E P at the t-1. And thus the realized real

wages ( ) will be smaller than the desired or anticipated one ( ), which is equal to the full employment equilibrium; this relatively low wage will provide employers with an incentive to hire more labor; as the labor input increases, the output will increase and the national income will increase above the full employment level in the short run.

These are all beyond the control by the monetary authority or the government.

(iii) In the long run

Three alternative situations are possible:

First, if there is no further change in the monetary policy, in the long run, the general public will catch up with the reality and revise their expectations as to the money supply and the price level in line with the actual ones. Workers will demand a new level of nominal wages which recovers the equilibrium real wages. Then everything goes back to the initial full employment equilibrium.

Second, if the monetary authorities are engaged in nondeterministic ‘surprise’ monetary policies and thus changing the money supply in a purely random fashion, the general public will be continued to be ‘fooled’ and there will be always a deviation of the actual national income from the full employment one. However, the direction of the deviation, up above or down below the full employment one, is unpredictable as the deviation of

Yt from Y is the weighted average of the forecast error and the aggregate shocks, both of

which are intrinsically unpredictable under the rational expectations.

Third, when there are some structural rigidifies which hinder the flexible adjustment of nominal wages, actual wages do not return to the ones corresponding to full employment even if the general public may revise their expectations. An example is a legally binding non-indexed multi-period wage contract which carries to the current and future periods the previously set nominal wages based on the earlier expectations. In this case, the short-run deviation persists as long as the contract remains valid.

(vi) Empirical Evidence:

Early research on the United States and Canada, such as Robert J. Barro, “Unanticipated Money, Output, and the Price Level in the United States,” Journal of Political Economy, 1977, Vol. 86, and Gillian Wogin, “Unemployment and Monetary policy Under Rational

t 1t t t 1t t

1t t 1t t

t

t

PW

tt

t

PEW

1

f


Expectations: Some Canadian Evidence,” Journal of Monetary Economics, 1980, Vol. 6, indicated that money surprises were important - even more important than actual or forecasted money supply – in explaining the departure of the real aggregate output from the potential output.

In addition, in Y - Y = (Mt- E M

t) + (M

t- E M ), by using the data from

the U.S. economy of 1941 – 1977, Barro has found the econometrics test result that 0

and = 0, which means that Mt- E M

thas explanatory power while M

t- E M does

not. The first is the forecast error which is included in the information set or I . This confirms the prediction of rational expectations theory: only unanticipated changed in the money supply can affect the national income.

However, Barro’s findings might not stand up to attempts to deal with the longer-run movement in money in the 1970’s. In fact, his results have been brought into question by later researchers who have found that actual money supply explains the residual of the fluctuations of the national income from the potential one which cannot be explained by money surprise (F. Mishikin, “Does Unanticipated Money Matter? An Econometric Investigation,” JPE, 1982, Vol. 91; M. Askari, “A Non-nested Test of the New Classical Neutrality Proposition for Canada,” Applied Economics, 1986, Vol. 18).

Let’s take off from money supply and national income, and move on to the relationship between money supply and inflation.

2) Money Supply and Inflation

Real money (cash) demand has direct bearing on the social welfare. The change in real money demand is important. Real money demand is the ratio of nominal money supply to the price level. Therefore the relative movements or a relative change of the money supply and the price level determines the size of real money demand.

In this analysis, we would like to see whether an increase in the money supply would be accompanied with constancy of real money demand (M/P), or with a decrease in real money demand [(M/P) ↓].

In the first case, the price level increase in the same proportion as the money supply so M/P does not change. This can only happen when there is no change in nominal interest rate which determines the real money demand.

In the second case, the decrease in M/P with increasing money supply means that P rises more rapidly than M. So M/P decreases. This happens when the nominal interest rate increase.

(1) Once-and-for-all increase in money supply

If we believe neutrality, the only result is the proportional increase in the price level.

tf 1t 2t 1t

1t 2t 1t

1t


The holding of real balances does not change.M ↑ and P ↑ proportionately → M/P does not change.

The once-and-for-all increase in money supply does not increase interest rate unless it raises the inflation expectations. By definition, if the increases in real money supply is once-and-for-all, the moneys supply will only increase once and in the long-run it will never increase again, so the long-run rate of inflation or the expected rate of inflation does not change.

Therefore, a once-and-for-all increase in money supply will not result in a continuous rise in price level or the true sense of inflation, and will not induce the public to economize on the holdings of money and waste resources on the replacement of paper money. Thus, it does not impose any permanent cost on the economy.

.0 ee

PdP


Graphically:

(2) Continuous but Steady Increase in the Money Supply (dM > 0 but d M = 0)

The repetition of an once-and-for-all increase in money supply will result in the continuous increase in the price level. This is a constant or steady rate of inflation. Inflation occurs only with a sustained or continuous increase in money supply.

As long as the money supply increases at a steady rate, there is no complicating dynamics. The only problem is that compared to zero inflation there is a discrepancy between the social optimum and the private optimum in terms of money holdings; because the opportunity cost of holding money is positive, the public is trying to economize on the holding of paper money and this wasting resources and time.

As long as the rate at which the monetary authority increase money is constant, the rate of money creation is steady. In addition, if we accept the neutrality theorem, the steady rate of money creation will result in an equal and steady rate of inflation; dM/M = dP/P. The price level and the money supply increase at the same rate. The nominal interest rate, which is equal to the sum of the real interest rate and the rate of inflation, will be constant, too. So the opportunity cost of holding real money balance is constant and there is no reason why the real money demand should change. There is no worsening of the social welfare or no increase in social deadweight loss.

In this state, also = > 0, but constant.

M

Tim e

P

Tim e

Tim e

Ti m e

ri

r

2

e P dPe


Graphically:

(3) Continuous and Accelerating Increases in the Money Supply (dM > 0, and d M > 0)

An acceleration of continuous increases in money supply will increase the rate of inflation. This will in turn decrease the demand for real cash balances or the real money demand. Although M and P are increasing at the same time, the real balances should decrease. This in turn means that the speed at which P rises will exceed that at which M is increased.

Not only > 0, also d > 0; and > 0 and d > 0.So, i = r + ↑

Numeric Example:

Time Money Stock %change Price Level Inflation rate M/P Yt 100 100

1 100t + 1 110 10% 110 10 1 100t + 2 121 10% 121 10 0.86 100t + 3 145 20% 169 40 0.86 100

Note: Y is constant in the assumption of neutrality and superneutrality.

M

slope = % M

Time

P

slope = % P

Time

=

Time

Time

i = r +

2

e e

e


Graphic Illustration:

In stage I (a steady stage), the rate of money creation is 10%. If Y is constant, the rate of inflation is constant at 10%. So the nominal interest rate is constant at i = + r = 10% + r.

In stage II (another steady stage), the rate of money creation is 20%. If Y is constant and does not change (i.e. if superneutrality holds), the rate if inflation is 20%. There is no acceleration of inflation. The nominal interest rate is constant at i = + r = 20% + r.

In stage III (transition from a rate of inflation to higher rate), as the rate of inflation rises, the nominal interest rate rises, and thus the real money demand decreases [(M/P) ↓]. As the money supply (M) is increasing now, the price level (P) should increase more than the money supply to have M/P go down. As real money demand or real money balances decrease, the social welfare decreases and the social deadweight loss increases.

(Neutrality Revisited) The neutrality debates takes on another dimension. OK, we may accept the neutrality of a once-and-for-all increases in money. How about the accelerating increase in money? Would it still have n impact on the real national income? Those in favor of ‘superneutrality’ states that sustained and accelerating (/ decelerating) increases in money supply ( M) will just lead to an increase (/decrease) in the rate of changes in the price level or an increase (/decrease) in the rate of inflation ( P = ) but not the national income (Y kept being constant). On the contrary, those arguing for ‘Non-superneutrality’ states that an increase in the rate of growth of money supply (the acceleration of the rate at which to create money) will increase the real national income level.

The increase in the rate of growth of money supply will increase the rate of inflation. We all know by now that the increase in the rate of inflation will increase the opportunity cost of

holding cash balances or money balances (m = (M/P) falls). We know that the general public holds savings (S = Y – C) in the form of either increases in money holdings or in demand for physical goods or capital. In the face of the accelerating inflation rates, the

Time

M

I

II

Time

P

I

II

*

III

Time

I

II

III

Time

I

II

i

Time

I

II

III

PM = m

*

d


public switches from money holdings, which are subject to inflationary erosion, to other assets including capital, K, which are not vulnerable to inflationary erosion. If the supply of K is elastic, then there will be an increase in the equilibrium K stock in the economy. The increased stock of K will lead to a larger national income. This impact of the acceleration of inflation rates on the capital stock is called ‘Tobin’ effect.

(Summary)

M↑ and accelerates → ↑ → i ↑ → m = M/P ↓ → demand for K ↑ → Y = F (K, N) ↑(If the Tobin effect is correct.)

The major problem of the Tobin effect is that if focuses only on the ‘substitution effect’ of inflation, namely, the switching by the public from money holdings to the demand for capital; given the size of savings; the relative size of money holdings will decrease while that of K will increase. Inflation has also an ‘income effect’: inflation would decrease national income which is net of the resources to be wasted on transactions and this purely available for consumption. It will then crease savings (S = Y – C), which decrease the absolute sizes of money holdings and demand for K.

With the substitution effect (K↑; m ↓) and the income effect (K↓; m ↓), the overall size of K may not change while the real cash balances will surely decrease. If K, the stock of capital, does not change, there will be no change in national income. This is the superneutrality; an increase in the rate of growth of money supply will lead to an increase in the rate of inflation, but no change in national income.

Under superneutrality, whatever the rate of money creation might be, say 10% or 1000%, and whatever the rate of inflation might be, national income level dose not change.

3) Money and Interest Rate: Two Tales of Money and Interest Rate

Does an increase in money supply lead to a decrease or an increase in interest rate?There are two opposite views of this matter:

(1) IS-LM Model: Liquidity Effect: M and i move in the opposite direction

For a given money demand, an increase in money supply will lead to an excess supply of money and thus the interest rate will fall. Note that according to this view, the interest rate and money supply move in the opposite direction.

Graphically, in the real money supply and demand, and the IS-LM settings, the above case can be illustrated as

d

d d


(2) Expectations’ Theory or Monetarists’ View: M and i move in the same direction

Fisher’s equation saysi = r + ; andi = r + in the long-run,

The nominal interest rate is equal to the real interest rate, which is independent of monetary variables, and the expected rate of inflation. If any change in money supply increases the expected rate of inflation ( ), or the long-run actual rate of inflation ( ), then there will be a change in the interest rate. The implications are as follows:

i)the monetary authority can control only the nominal interest rate, not the real interest rate. The real interest rate r depends on the marginal product of capital which in turn depends on the amount of capital stock in the economy, the quantity and quality of labor forces to be combined with capital, and the level of technology and, over time, technical innovations. These are not what the monetary authority can control through monetary policy.ii) The net impact of an increase in money supply on the nominal interest rate is the sum of liquidity and expectations’ effects.

The natural question is what kind of increase in the money supply would lead to an increase in the expected or actual rate of inflation. For example, a truly once-and-for-all blip of increase in money supply does not change the expected or long-run rate of inflation. So only the liquidity effect works. Only an accelerating money creation will touch off a revision of the general public’s expectations to a higher level.

0i

1i

p i = r

i

LM

ML

IS

e

e


5. Advanced Theories of Monetary Economics

1) Revisiting the Relationship between Money and Income

Professor James Tobin sees the relationship between the relationship between money and real income in a different light. He has no problem with the neutrality of money: a once-and-for-all increase in money supply may lead to no change in the national income in the long-run. From there, what will happen if the rate of money creation increases or money supply increases in an accelerating fashion?

If the rate of money creation rises, the rate of inflation rises as well. Thus, the Fisher equation i = r + tells us that the nominal interest rate will go up.

Then the real money demand falls and the demand for all other assets rises. Particularly, people would substitute physical assets for money balances. As the demand for physical products increases, their supply and production will rise. The real national income will increase. This is called ‘Super Non-neutrality of Money’.

If Tobin’s argument is right, a mild yet ever-increasing inflation is beneficial for the economy. In some developing countries, people would like to minimize holdings of money for their assets and wealth, and to replace them with holdings of anything which is supposed to be protected from inflationary erosion of value.

However, the Monetarists have different view. Tobin’s idea focuses only on the substitution effect of inflation, and ignores the income effect. Inflation reduces overall national income. Why? It may not immediately and visibly decreases the nominal dollar value of national income. However, over time, inflation reduces efficiency of economy by increasing shoe-leather cost and menu cost. Eventually the real national income will decline. This is the negative income effect of inflation. Thus, if we look at the overall impact of inflation on the real national income, the positive substitution effect and the negative income effect cancel each other and, to say the least, the net result is uncertain. We may restore the dictum that an increase in the rate of changes in money supply or an accelerated increase in money supply has no impact on real national income. It is called ‘Super Neutrality’ of money.


2)Revisiting Inflation: The Phillips Curve

(1)The original Phillips curve and its Policy Implications

Phillips Curve shows the trade off relationship between the rate of inflation and unemployment rates. In other words, according to William Phillips’s empirical observation of the British economy of 1861 to 1957, there was a negative correlation between the rate of inflation and unemployment rate. In this Phillips curve, in order to achieve a lower unemployment or a higher level of national income, a policy-maker must pay the cost of a higher rate of inflation.

(2) How do you relate it to the Short-run Aggregate Supply curve?

We also know that there is a negative correlation between unemployment rate and national income. Thus, we can infer that according to the Phillips curve there is a negative correlation between the rate of inflation and national income. That is ‘almost’ the same as the short-run aggregate supply curve (SAS) except that the SAS shows the trade-off between the level of price and national income while the Phillips curve implies the negative correlation between the rate of change in price level and national income. Just as we can mark the full employment national income or Yf in the SAS, we can mark down the corresponding natural rate of unemployment or the non-accelerating inflation rate of unemployment(NAIRU), which means that as long as the actual unemployment does not exceed this threshold there is no pressure on inflation.


(3) Modification to the Expectation-augmented Phillips Curve

Later studies showed that the trade-off between inflation and unemployment rates became fuzzy and doubted the validity of the Phillips curve.

Edmond Phelps won the Nobel Prize(2006) for adding a third variable of inflation expectations by the general public and rescuing the Phillips curve: There is not one Phillips curve, but are many Phillips curves which correspond to different rates of expected inflation. In other words, an expected rate of inflation is a shift variable for the Phillips curve.

In this ‘Expectations-augmented Phillips curves, at the natural rate of unemployment or NAIRU(do you recall what it stands for?), the expected rate of inflation, as the shift variable of a Phillips curve, is the same as the actual rate of inflation on the vertical axis. In other word, when the expected and actual rates of inflation are equal to each other, regardless of what the numerical rates are, the national income is at the full employment level. The idea here is similar to the expectation-augmented aggregate supply curve or Lucas’s aggregate supply curve while the Expectations-augmented Phillips curves are shown in terms of the trade-off between ‘inflation rates’ and unemployment rates and the EAS or Lucas’s AS is described in terms of the negative relationship between ‘the Price Level’ and national income. Thus, we can have a vertical line above the NAIRU which passes through all Phillips curves of different expected-inflation rates (and the corresponding same actual rates

2

1

3


of inflation respectively). Some may call this ‘the Long-run Phillips curve’ in contrast to Expectations-augmented Phillips curves.

(4) Application of Expectation-Augmented Phillips Curves

The application of EAPC is similar to that of EAS.

When government accelerates money creation and thus the rate of inflation goes up, the unemployment rate may or may not come down depending on the inflation expectation of the general public:

When the rate of inflation goes up and if the general public’s expected inflation does not change, the unemployment rate will fall.

However, it is for only short-run until the general public figure out what is happening to inflation rates. Eventually, as they revise their expectations of inflation rates, the Phillips curve shifts up. The unemployment will come back to the NAIRU.

When the rate of inflation goes up and if the general public’s expected inflation change in line with it, the unemployment rate will not change.

We can put this change in a reverse gear:

When government lowers the rate of inflation, the national income may or may not fall. If the people revise their inflation expectation down in line with the government policy, then there will be no changes in national income. However, if the people hold onto their current


inflation expectation, which is higher than the rate of inflation to be realized, recession will take place with a higher rate of unemployment and a lower level of national income at least in the short-run.

When government lowers the rate of money creation and thus the rate of inflation, it may lead to ‘painless’ only when the general public revise their inflation expectation in line with the government policy. This is a successful ‘Disinflation Policy’, which means a lower inflation without a recession and thus an enhanced efficiency of resource allocation for the economy.

(5) In the Short- and Long-run, and the New Keynesian Histeresis.

According to the above theory, in the long-run, as people figure out the reality and revise their expectations in line with reality, there is no trade-off between rates of inflation and rate of unemployment. In the long-run, economy moves along the Long-Run Phillips Curve.

However, some new Keynesians have come up with a different idea from their empirical observation of some European countries of the 1980s.

Suppose that an economy is initially at the full employment level, but with a high rate of inflation.

Suppose that the government decides to have a disinflation policy. When the rate of inflation comes down and if initially people do not revise their expected inflation in line with the actual rate of inflation, the economy should first experience a recession. And then, eventually in the long-run as people revise their expectations, the economy should go back to the full employment level of national income or the NAIRU.

However, if the economy has a ‘memory’ and is ‘path-dependent’, it may not go all the way back to the full employment level. This would be particularly the case if the recession has lasted for a while. This phenomenon is called ‘histeresis’: a supposed short-run increase of unemployment rates becomes permanently embedded in the economy as an additional part of NAIRU. Thus after recession as a result of disinflation, a new NAIRU is now higher than the previous NAIRU. In this case, the Long-Run Phillips Curve is not vertical but slanted. In this case, it will be very difficult to lower the rate of unemployment through a macroeconomic policy. The government may have to break up the hard core part of unemployment, that is, the NAIRU, through labor market policies.


3) Revisiting Milton Friedman: The Optimal Inflation

Whatever the constant rate of money creation might be, say 10% or 1000%, and whatever the constant rate of inflation might be, national income level dose not change as long as it is fully anticipated and thus the PIT holds – Neutrality of Money.

Even anticipated changes in the rates of money creation, acceleration or deceleration, may not alter the national income – Super neutrality of Money.

If so, can we safely afford to be indifferent to the rate of inflation or the rate of money creation? The answer is ‘no’ when the social welfare or social efficiency is taken into account; inflation is resource-wasting and welfare-reducing.

Here we would like to introduce Professor Milton Friedman’s theory of optimal inflation. It is the quintessential Milton Friedman Theory. It tells us what is the optimal economic condition, and has so many lessons and inspiration.

(1) Social Welfare Analysis of Money

First of all, let us examine the proportion that “Inflation creates a wedge between the social optimum and the private optimum in terms of money holdings”:

Social Optimum in the use of money is achieved when the Social Marginal Cost of (producing) money = MB. In fact, SMC = 0. Therefore, money should be held or used up to the point where MB = 0 which is the saturation point of money holdings.


Illustration

1) When , PMC > SMC = 0 Private Optimum falls short of S.O.

2) When , = SMC = 0Private Optimum = S.O.

Private Optimum in the holding of money is achieved when the Private Marginal Cost of (holding) money = MB. In reality, the PMC = nominal interest rate i. Therefore, any positive nominal interest rate prevents the public to hold money up to the saturation point. Only when i = 0, then the Private Marginal Cost of holding money becomes zero (PMC = 0). Then the public will increase money holdings up to the point where the PMC = 0 = MB. The private optimum coincides with the social optimum. This is the saturation point of holding money. At this point, nobody in the economy foolishly wastes any resources including his/her own mental energies on economizing on the holding of money because the holding of money incurs no opportunity cost. Money is a cheap way of having transactions than other means of payment such as gold, silver, and other arrangements. How can the government make the nominal interest rate equal to zero, and therefore induce the general public to hold real balances up to the saturation point? Fisher’s equation says that i = r + . When = -r, i = 0. The optimal rate of inflation is equal to the minus real interest rate. Thus the socially optimal rate of money creation is the one which leads to = -r or i = 0.

The optimal rate of inflation, optimal in the sense that the social welfare is maximized, is equal to minus real interest rate. This is the first best world. In the second best world, among the positive rates of inflation, the lower rate of inflation is better than the higher rate of inflation. As for the above question, we can say that 10% rate of inflation is clearly and far better than 100% rate of inflation from the standpoint of the social welfare. The loss of social welfare is larger with 10% rate of inflation then with 1000% rate of inflation.

(2) Social Welfares for Different Levels of Inflation:

The Social Welfare or the welfare associated with the use of money for a given real money demand is the integral or sum of the marginal benefit over the social marginal cost from the origin to the point of the real money demand or the holding of real cash balances: the area below the marginal benefit above the social marginal cost line (= horizontal line).

Time

i

00 i

01 i

MBMUmd

PMCPrivate Optimum for 0i

Social Optimum

Private Optimum for 1i

SMC = 0PMC = 0

00 i

01 i CPM


The private sector’s welfare for a given real money demand is the integral or sum of the marginal benefit over the private marginal cost from the origin to the point of the holding of real cash balances: the area below the marginal benefit above the private marginal cost line (= the given nominal interest rate).

What is the difference between the two and who gets it? Why the social welfare is larger than the private welfare? The difference between the two is obtained by the government as its revenue from inflation. It is inflation-tax revenue or seigniorage. It is the rectangular =

(and is equal to if real interest r = 0).

The area of the rectangular changes as the rate of inflation changes. When is the area of the rectangular maximized for a given MB or money demand curve? The answer is when the rectangular becomes a square. When inflation rate is at the point corresponding to the midpoint of the money demand function or the MB line, the rectangular has the largest area being a square. This is called the inflation-tax-revenue maximizing the rate of inflation.

Let us compare zero inflation, 10% inflation, and 1000% inflation.

The difference in the social welfare between zero inflation and 10% inflation is the social deadweight welfare loss. The difference is larger between zero and 1000% inflations. This means that the social deadweight loss increases as the rate of inflation increases.

The welfare loss represents resources wasted in efforts to economize on real cash balances. From a slightly different angle, the welfare loss can be described as the sum of shoe-leather and menu costs.

dmi dm

i

0i

consumer surplus

()

S =ocial welfare consumer surplus + producer surplus

(seigniorage) producer surplus

social dead weight loss

i

010 irr DWL

i

11000 ir

DWL


(3) Reality check- Time Inconsistency of Disinflation Policy

Now if the optimal rate of inflation is the negative of real interest rate, why do we in reality observe mostly positive rates of inflation all around the world?

The first answer is found in the political economy surrounding the seigniorage. Many countries rely on the seigniorage for financing government expenditures. This forces them to set the date of money creation above the Friedman’s optimal rate.

The second answer is to be found in the dynamic game of the ‘Time Inconsistency’ of the optimal (low inflation) policy. The monetary authorities know that a low inflation is the optimal policy, but once it is announced and trusted by the general public, they all too often deviate from the professed policy and use ‘money surprises’ as a means of boosting the national income. In other words, the disinflation policy has an innate or built-in incentive for the policy maker to break or to renege on. This kind of policy in general is called ‘Time Inconsistent’: At one point of time, the policy is optimal as it is, but over time, it becomes optimal not to follow the policy.

A bigger problem of a ‘Time Inconsistent’ policy is that the general public will figure this out and will not trust the policy maker. Most likely it will happen over time. As the policy maker announces a target of a lower inflation. People base their wages settlement and so forth on those expectations of inflation. Then, however, the policy maker will generate a larger amount of money supply and a higher rate of inflation. This surprise inflation will lower the real wages for the economy, and thus helps entrepreneurs to expand production and employment. The national income rises. The government may have lied but it will say that it was a necessary evil by quoting, “All is well that ends well”. The problem is that in the mind of the general public it is not the end, and there will be a next time.

The next time when the policy maker announces a certain target rate of inflation, the general public will not trust the announcement. People will form their own expectations of inflation, which will be certainly higher than the publicly announced target rate of inflation. The rest of the course will be ‘self-realizing prophecy’, and the economic system is settled at the rate of inflation higher than the optimal rate. Professors Finn Kydland and Edward Prescott have developed a dynamic theory of ‘Time Inconsistency’ and have got the Nobel Prize in economics.

Time inconsistency of the policy refers to the situation where the optimality of policies is inconsistent over time: first it is optimal to have a certain policy, and later it becomes optimal not to follow the policy. The examples are numerous beside the above disinflation policy:

Example 1) The U.S. government keeps announcing that it will vigorously prosecute illegal immigrants. However, the government is tempted to give ‘general amnesty’ to illegal immigrants as they alleviate the shortage of labor forces particularly in the fields which many American workers shun away from. The potential illegal immigrants are ‘rational’ enough to know this time-inconsistency of the government, and they try to enter the U.S. in any way. So the announced policy against illegal immigration is not credible and has no effects in deterring potential illegal immigrants.

Example 2) The government may announce that it will not render any help to those who are building houses in an area which is constantly flooded. However, once an area is flooded or


keeps being flooded, it is in the best interest of the government to come to its rescue and to help its residents. That is because such an action increases the popularity of the government and enhances the change for re-election. The rational economic agents figure out this ahead of time. They will not regard the announced policy as being credible from the beginning, and will build the houses in the flooded area anyways. The announced government policy has no forces at all.

How can the government resolve this time inconsistency problem? One solution is to eliminate discretion (for a policy change) on the part of the policy-maker so that the policy once made cannot be easily altered. The policy-makers should follow rules as opposed to discretion. It can enhance the credibility by making it difficult to change any policy. Alternatively, the policy-makers can build up their reputation over time.

This theory will be fully covered in the next sequel of this course, that is, Advanced Macroeconomics.

5. Applications to Canada

1) Setting

The Bank of Canada announced the plan to lower the rate of inflation step by step by lowering the rate of money creation: It is planning to lower the rate of money creation over time so that as a consequence to the rate of inflation will be lowered from 7% now to 3% per annum by the end of 1992, and 2.5% by the middle of 1994, and finally to 2% by the end of 1995.

2) Justification of disinflation policy: Anticipated decrease in the rate of inflation

If the policy is carried out in a fully anticipated and credible way, all the economic agents will act upon a lower expected rate of inflation: new labor contracts will be written in advance, and so on. In this situation, there will not be any change in the national income. We have also seen that disinflation will lower the nominal interest only (not the real interest rate) and that does not reduce the real cost of borrowing capital for the Canadian firms. The question is, why should the government bother to lower the rate of inflation?

We have seen that the lower the rate of inflation, the better in terms of social welfare. Fewer resources will be wasted on economizing on the holdings of real cash balances. This gain in efficiency can be redistributed to the constituents of society and make them better-off.

3) Why Gradualism over ‘Cold Turkey’?

The above-announced policy is ‘Gradualism’ as opposed to a ‘cold turkey’ prescription in achieving a lower rate of inflation through several stages.

Of course, if the policy invariance theorem is correct, even without gradualism the disinflation policy would not cause any cost in terms of a reduction in the national income under the following set of conditions:


i) Rational Expectations

The general public should form rational expectations as to money supplies and the price level. This is a reasonable assumption.

On the contrary, if the economic agents form adaptive expectations, there would be a persistent difference between the anticipated monetary policy and the actual one, a systematic forecast error. The worker’s revision of expectations in to a lower one will lag behind the actual disinflation. The downward adjustment of the rate of nominal wage raise, which is based on the worker’s expectations of inflation rates, will lag behind the actual disinflation. As a result, the real wage will be higher than the market-clearing one and there will be unemployment and a decrease in the national income.

ii) a Fully Anticipated Policy

A policy change should be fully anticipated and acted upon by the economic agents, workers and employers alike.

First, the policy should be announced far in advance and in detail, sending a clear signal to the public in general and leaving no room for uncertainty, speculation or misinterpretation.

Second, the policy should be ‘credible’. No credible policy will be believed by the public in the first place, and subsequently will be acted upon. Some policies are not believed as the government has no credibility. In this case the government should build up a ‘reputation’ by demonstrating its will power. Other policies are not credible as they contain an incentive for the policy maker to renege on. Those policies are said to be ‘time inconsistent’.

If the above conditions are all met and thus all monetary policy should be announced and credible, and the economic agent or the general public is rational, then the PIT should hold. The public will be very swift in readjusting their expectations and there will not be any forecast error about the price level or about the money supply even in the short-run, and thus there should not be any change (decrease) in the national income.

iii) The above i) and ii) may hold. However, if the workers are locked-up in a multiple-period and non-indexed labor contract which was set up before this change in government policy, the rational workers cannot react to this new policy during the interim period of the contract. During this period, the policy invariance theorem does not hold and the disinflation policy would take toll on the national income.

The rapid disinflation would cause changes in real wages of those whose nominal wages are fixed by the non-indexed multi-period labor contract: the existing non-indexed multi-period

contract incorporates a previous higher expected rate of inflation ( ). After the disinflation policy comes into effect, the new rate of inflation is lower than the previous one. So under the contract which was signed before the announcement of the new and lower rate of inflation, the predetermined (negotiated and previously set) increase in normal wages will be larger, and so will be the increase in real wages. Thus there will be a decrease in the demand for labor. The level of employment will drop and there will be a decrease in the national income.

te

1-t

t1-t

PW


It is important to give time for the workers to exit the existing contract and to have a new contract which incorporates a lower rate of inflation.

Friedman argues that the most important device for mitigating the side effects is to slow inflation gradually but steadily under the circumstances where workers are locked up in long-term or multi-period and non-indexed contracts: The government should announce the policy in advance so that the public in general can prepare itself for the change and adjust its expectations about the monetary policy and the new inflation. It also should adhere to the policy (should not make a U-turn) so that the policy should be shown to be credible and any uncertainty should be dispelled. This gradualness and advance announcement is to give people time to readjust their arrangements (M. Friedman, Free to Choose, p. 273).

We note that the announced disinflation policy intends to decrease the rate of inflation over next four years in a gradual fashion; the present 7-8% inflation in March 1991 will be lowered to 2% by the end of 1995.

Macroeconomics 229 Ch IX. Open Macroeconomics

Chapter IX. Open Macroeconomics: IS-LM-BP Model

1. Introduction

1) Assumption: Price level (domestic: P; foreign P*) is fixed.

2) Definition:

S denotes exchange rate. It is defined as the price of foreign currency in terms of domestic currency.

If the Canadian dollar price of U.S. $1 is 1.50, we take this as an exchange rate. Note that the news paper uses different exchange rate, that is, how much of foreign currencies a unit of domestic dollar can fetch. For instance, if Cdn $1 can fetch U.S. $0.67, the exchange rate is 0.65. All throughout this course, we will use the first definition, which is convenient and consistent: Just like any other goods such as a hamburger, the price of a unit of foreign currency is the exchange rate.

An increase in exchange rate or S due to market forces under the flexible exchange rate system is called an appreciation of foreign currency and a depreciation of domestic currency.

When government raises exchange rates or S under the fixed exchange rate system, it is called a ‘devaluation’ of domestic currency. The opposite is called an ‘evaluation’.

2. IS Curve

1) Modification of the IS curve in the Open Macroeconomics setting

The IS is derived by equating Y with AE = C + I + G + X-M. Whenever there is a change in AE or its components, the IS curve shifts around. Now the X-M has to be specified.

X-M is the Net exports (NX), which is approximate equal to the Current Account balance: X-M = NX = CA.

So we can rewrite into AE = C + I + G + CA. Whatever affects the components of the AE shifts the IS curve: Now an improving current account will shift the IS to the right, and a deteriorating current account to the left.

2) What determines the Net Exports or Current Account Balance?

X = M*(Y*, SP*/P)

Our exports are the imports by the foreign country. How much the foreign country imports from us depends on their income (foreign country's national income), and the relative price level of the foreign country to our country (SP*/P).

P* is the price level of the foreign country in terms of the foreign currency. S is òur' price of `their' dollar. So the product of S P* is the relative price level of the foreign


country to our (the domestic country) in our currency terms. For instance, suppose that a hamburger in the U.S. is $1.00 in U.S. dollar terms (P*), a Canadian hamburger is $1.30 in Canadian dollar terms (P), and the Canadian dollar price of U.S. $1 is $1.40 (S). The U.S. hamburger costs Canadian $1.40 as S times P* = 1.4 X 1. The Canadian hamburger costs Canadian $1.30. So the relative price level of the foreign to the domestic country is 1.4 to 1.3, that is, 1.076. The foreign price level is 1.076 times as high as the domestic price level. In our model we assume that the price level, domestic and foreign, is fixed. An increase in the exchange rate or S makes the foreign good dearer and more expensive, and raises the foreign price level compared to the domestic price level. This will in turn make consumers, domestic and foreign, switch from foreign to domestic goods: our exports of domestic goods rise and our imports of foreign goods fall. Our current account and the balance of payment will improve: S SP* SP*/P Foreign price level Demand for domestic goods and Demand for foreign goods X and M Net Exports(X-M) (doubly improving) CA.

M = M(Y, SP*/P)

Our imports are an increasing function of our national income, and a decreasing function of the relative price level of the foreign to the domestic country: The more money we have, the more of foreign goods we can afford to import. The higher the foreign price level, the less we would like to import.

Combining the above two as CA = NX = X-M, we get

CA = X(Y*, SP*/P) - M(Y, SP*/P)

Ultimately, the current account is a function of Y, Y*, SP*/P;

CA = f(Y, Y*, SP*/P)

Let's review the impact of each variable on the net exports or current account:

i) Y M NX = CA

ii) Y* X NX = CA

iii) S SP*/P M and X NX = CA

This suggests that the IS curve becomes endogenous under the flexible exchange rate system. A changing exchange rate leads to a change in the AE curve, which in turn shifts the IS curve around.

In short, the IS curve has shift parameters of C, I. G and CA(=X-M), and CA becomes endogenous under the flexbile foreign exchange rate system.


3. LM Curve

LM curve has shift parameters the real money supply (=MS/P) and the random term in the money demand u. The price level is fixed. The only shift parameters are the nominal money supply MS and the random money demand term u.

As the nominal money supply MS changes (increases/decreases), LM shifts around (to the right/left).

As will be seen in details later, under the Fixed Exchange Rate System, government intervention into the foreign exchange market has a side-effect of a changing money supply and thus the nominal money supply becomes endogenous and the LM curve moves around beyond the control of government.

Money supply becomes endogenous, and the LM curve shifts around under the fixed foreign exchange rate system.

4. BP Curve

1) Definition

There are two concepts of the Balance of Payment. The broad sense of the Balance of Payment includes all the external transactions in the private as well as public sectors. The narrow sense of the BP with which we are mainly concerned in economics is the account of the private sector's transactions with other countries. This is called `the Above-the-Line' Balance of Payment, where the line of demarcation divides the transactions of the private sector from those of the public sector or the government:

I. Current Account (CA)Trade Exports Imports

RemittancesTransfers

II. Capital Account of the Private Sector (KA)Capital Flows Inflows Outflows

______________________________________________

III. Capital Account of the Public SectorOfficial Financing Inflows Outflows

The double entry bookkeeping makes the broad sense of the BP, which is the sum of I, II and III, equals zero all the time. So it is rather uninteresting.

Our BP, the narrow sense of BP, or the Above-the-Line BP is the sum of I + II:

BP = X – M = CI – CO = CA + KA.


It can take on any value. When it happens to be equal to zero, it is said, the BP is in equilibrium: BP = 0. Otherwise, the BP is in disequilibrium. We also say that the economy is in the external equilibrium. When BP<0, the BP is in deficits. When BP>0, the BP is in surplus.

The BP curve is the locus of the combinations of the national income and interest rate (y, i) which bring about the BP equilibrium: BP = 0 along this BP curve.

2) Determinants of BP = CA + KA

i) CA

We have already examined the determinants of the current account. Recall that CA = NX (Y, Y*, SP*/P); -when domestic national income rises, CA falls.-when foreign national income rises, CA rises.-when foreign exchange rate rises, foreign currency becomes more expensive in terms of domestic currency, and thus the domestic prices of foreign goods goes up. Therefore, less imports and more exports, and CA rises.

ii) KA = Net Private Capital Inflows = CI - CO

KA = NCI ( r - r*), where r (real) interest rate or real rate of returns on domestic bonds; r-r* is the interest differential between domestic and foreign countries or how higher domestic interest rate is than foreign one. This signifies the relative attractiveness of investment in the domestic country to investment in the foreign country. The larger the interest differential, the larger the capital inflows into the domestic country.

When r-r*, international investors bring foreign currencies to convert into domestic currency: KA, and BP

The above will happen either when domestic interest rate r rises, or when foreign interest rate r* falls.

iii) Now BP is the sum of the current and the capital accounts

BP = CA(Y, Y*, SP*/P) + KA(r-r*)

Therefore, BP = BP(Y, Y*, SP*/P, r-r*)

3) Derivation of BP curve

The BP curve shows different combinations of interest rates and income which all bring about external equilibrium or BP=0. In general the BP curve is upward sloping, meaning that along the external equilibrium BP=0 the interest rate and income are changing in the same direction.


Step 1: Start with a point where BP = 0 (@ a)

Step 2: Now suppose that national income rises. The current account and thus BP will deteriorate:Y rises M CA BP < 0 (@ b)

Step 3: How to restore the external equilibrium BP=0? There should be an improvement of KA by the same amount of the decrease in CA, and then they will cancel each other. In order to have KA improve, the domestic interest rate should be raised:KA by r (@ c). Then BP = CA + KA = 0 again.

Step 4: Link a and c to get `BP = 0 Curve.

Note that the region above or to the left of the BP curve the BP is in surplus and the region below or to the right of the BP curve the BP is in deficits:

Let's suppose that the BP = 0 at point a in the following graph. Point b means less national income and thus less demand for foreign goods: the better current account and thus now the BP


is in surplus: BP= CA () + KA >0. Note that as this point lies at the same height of point a, the interest rate remains unchanged and thus there is no change in the capital account. Point c means more income and thus less CA and BP<0.

Point d lies straight above point a of BP=0, meaning the same national income but a higher domestic interest rate. The better capital account and thus now the BP is in surplus: BP= CA + KA () >0. Point e lies straight below point a, meaning the same national income but a lower domestic interest rate. The capital account at point e is smaller than that at point a, and thus now the BP is in deficits at point e: BP= CA + KA () <0.

4) Different Slopes of BP curve

The slopes of BP curve depend on the Degree of Capital Mobility across countries or the sensitivity of capital flow with respect to interest rate differentials. The principle is that the more mobile the capital (the freer capital flows), the flatter the BP curve.

Illustration

In the above two graphs, the same increase in Y causes the same decrease in CA at b. As BP = CA + KA, in order to get back to BP = 0, the same amount of increase in KA through capital inflows is required.


However, to induce the same increase in KA, Case I requires a more raise of interest rate than Case II: When capital is not so mobile like Case I, a relatively large increase in interest rate is needed to induce the same increase in KA. On the contrary, when capital is very mobile, only a small rise in the interest rate will bring about the same amount of capital inflows and thus the needed KA improvement.

There are four different slopes of the BP curves depending on the degree of mobility of capital:

5) Shift of BP Curve

All determinants of BP = BP(Y, Y*, SP*/P, r-r*) other than r and Y shift the BP curve: Y*, S, and r* are shift parameters. The first two variables which affect the Current Account shift the BP curve horizontally (to the right/left). The last variable r* or the foreign interest rate which primarily affects the Capital Account shifts the BP curve vertically (up/down).

Case I: S BP shifts to the right

Recall that to the left of the BP curve, BP > 0 (surplus); to the right of BP curve, BP < 0 (deficit).

i)Suppose that initially BP =0 at point a

ii) S SP*/P (relative foreign price level) X and M CA

So now point a should have BP>0 at the same interest rate (no change in KA). Point a should lie to the left of the new BP curve BP', which is the BP surplus region in the graph. To restore the external equilibrium BP = 0, the national income should rise to have a deterioration of the current account which offsets the initial improvement in CA. Point a moves to point b. From the viewpoint of the BP curve, we can say that the BP curve shifts to the right.


Case II: Y* BP shifts to the right

Case III: r* BP shifts up

i) Initially BP = 0 at point a

ii) r* Capital Outflows KA ; So now point a should have BP <0 at the same Y (which means no change in CA as there is no change in income). Point a should lie below the new BP.

We note that Cases I and II affect the CA favourably, and shift the BP curve to the right, and Case III affects the KA adversely and shifts the BP curve up. The emerging principle is that whatever affects the CA favourably shifts the BP curve to the right, and whatever affects the KA favourably shifts the BP curve down.

In general cases of an upward sloping BP curve, the rightward shift is virtually the same as the downward shift: all expands the BP surplus region in the graph. However, they are quite different in the following extreme cases:

In the case of perfect capital mobility, an increase in exchange rate or S would not affect the BP curve at all. The horizontal BP curve shifts to the right without any substantive change.

r = i r = i

Y Y


In the case of perfect capital immobility, an increase in foreign interest rate would not affect the BP curve at all. The vertical BP curve shifts up without any substantive change.

r = i r = i

Y Y

5. Exchange Rate

Depending on what exchange rate system the government adopts, either IS-BP or LM may become endogenous.

1) Imbalance of Payment and Pressures on Exchange Rates (SR)

BP > 0(surplus)

Excess Supply of Foreign Currency

Downward Pressure on Foreign Exchange Rate

BP < 0(deficit)

Excess Demand for Foreign Currency

Upward Pressure on Foreign Exchange Rate

BP > 0 means that the Balance of Payment is in surplus. This implies that BP = CA + KA > 0 and that the total receipt of foreign currency (exchange) through exports(X) and capital inflows(CI) exceeds the total payment of foreign currency through imports(M) and capital outflows(CO).

X + CI > M + CO; X-M + CI -CO > 0 ;NX + NCI > 0, where NCI denotes Net Capital Inflows.CA + KA > 0; BP > 0

So the Supply of foreign currency exceeds the Demand for foreign currency. When S>D, there is Excess Supply and there occurs downward pressures on the price of foreign currency, that is, foreign exchange rate. Left alone, foreign exchange rate will fall.

2) Fixed Exchange Rate System:

" Money Supply becomes Endogenous" “LM Curve moves around to restore the balance of payment equilibrium”

The Fixed Exchange Rate System means the government's standing commitment to maintain foreign exchange rate at a fixed level through unlimited sales/purchases of foreign currency.


Under the fixed exchange rate system, government should buy/sell foreign currency whenever there occurs BP surplus/deficit.

In the above example, to diffuse the downward pressure on exchange rate and to fix the exchange rate, government should eliminate the Excess Supply of foreign currency by moping it up. Government should buy excess supply of foreign currency.

Under the fixed exchange rate system, there is a very important side effect to this operation. You may remember whenever government buys anything from the general public, it should make payment in domestic currency from them. As Money flows from the government to the general public, Money Supply increases. The LM curve shifts to the right. Under the fixed exchange rate system, money supply becomes endogenous (meaning that government loses control over MS).

BP Gov't action to fix S Side Effect (LM) (in the LR)

surplus buys foreign currency MS increases()

deficit sells foreign currency MS decreases()

Sterilization Policy Actually there is a way of regaining the control of MS: at least in the short-run;

The government may take a counteraction in the open market operation in order to offset any change in MS due to its purchase of foreign currency.

For instance, in the case of BP surplus under the fixed exchange rate system, the government has to buy foreign exchanges. This will increase the money supply in the private sector. This in turn may put upward pressures on the price level and inflationary trends. If the government would like to reign in the money supply, then it should do something .The government may sell bonds. These sales of bonds or securities are in exchange for domestic money as their payment. Thus all in all, the money supply comes back to the initial level. There will not be any net change in money supply.

This counteraction designed to offset the impact of government intervention in the foreign exchange market is called `Sterilization' policy.


The short-term nature of sterilization is more obvious with the case of BP deficits.

The BP deficits will exert an upward pressure on foreign exchange rates. To diffuse the upward pressures on exchange rates, the government will have to sell foreign currencies. This government action has a side-effect of decreasing the money supply as the private sector’s buyers of the foreign exchanges will make payments with domestic currency. Thus the money supply falls, exerting a contractionary impact on the economy. The sterilization policy in the case dictates that the government may buy bonds or securities. As the government makes payments in domestic currency, money flows from government to private sector. The money supply of the private sector rises. This offsets the initial decrease in money supply which has resulted from the government sales of foreign exchanges. Overall, there will be no net change in the money supply.

Graphically, the BP deficits shift the LM curve to the left in its gravitation to restore the new equilibrium. However, the sterilization policy puts the LM back to the state where the BP takes place. In this way, the sterilization policy perpetuates the BP balance of payment disequilibrium, or BP deficits in this particular case. This forces the government to intervene in the foreign exchange market and the sales of foreign exchanges. The government will continue to do so until it runs out of foreign exchanges. Thus the sterilization is only a short-term measure of gaining the control of money supply.

i LM’ LM i LM

BP BP

IS IS

Without Sterilization With Sterilization


Y Y

3) Flexible Exchange Rate System:

“Exchange rates change”. "IS and BP curves becomes endogenous to restore the balance of payment equilibrium."

BP Exchange Rate Current Account BP Curve (LR)

IS Curve (LR)

surplus S CA to left to left

deficit S CA to right to right

When BP > 0 and government does not do anything to diffuse the downward pressure on exchange rate, the exchange rate will fall (S). The falling exchange rate means a lower relative foreign price level (SP*/P). Exports decrease and imports increases, and thus the net export NX = X-M or current account CA falls. AE = C + I + G + X-M falls and the IS curve shifts to the left.

6. Applications

Let us familiarize ourselves with the terminologies such as the internal (domestic) and external equilibrium: The intersection of the IS and LM curves is called the Ìnternal Equilibrium'. The External Equilibrium is achieved along the BP curve where BP=0. At the `Grand Equilibrium' both the internal and external equilibria are achieved at the same time. Graphically the intersection of the IS and LM curves should be on the BP curve.

Shocks can create a discrepancy between the internal equilibrium (intersection of IS and LM) and the external equilibrium (BP curve): the intersection of IS-LM is no longer on BP curve. BP is in disequilibrium: BP>0 or BP<0. There occurs an adjustment process of internal and external equilibrium converging to each other. Alternative exchange rate systems do have different adjustment processes. After the process is over, the economy restores external and internal equilibrium: BP=0. Under the Fixed Exchange Rate System, the MS changes endogenously, and thus the LM curve shifts to restore the external equilibrium. Under the Flexible Exchange Rate System: S (goes up/down) changes endogenously and thus IS and BP curves shift (to the right/left).

1) Inevitability of Competitive Devaluation in the 1930s

If an economy has unemployment and BP deficits at the same time under the fixed exchange rate system and no capital mobility, it is impossible to resolve any problems, of the domestic and international sector, through fiscal or monetary polices. The two policies will be completely incapable of any solution. The only possible way out is devaluation.


In the above graph, let's suppose that the initial condition of an economy is at point E0 with unemployment (y < yf) and BP deficits (to the right of the BP curve is the BP negative region).

If government raises its expenditures in the hopes of eliminating unemployment, the balance of payment will deteriorate further. The BP deficits require the government sell foreign currencies under the fixed exchange rate system. The side-effect will be a decrease in the money supply and the LM curve will shift to the left. An expansionary monetary policy or the government's attempt to increase money supply and thus to shift the LM to the right will be also futile under the fixed exchange rate system: the BP deficits require the government to sell foreign currencies and thus to reduce money supply. As a result the LM curve continues to shift to the left.

The only solution is to shift the BP curve and the IS curve at the same time so that the intersection of the new IS and LM curves are on the new vertical BP curve. This can be done only when the exchange rate is raised by the government. We may recall that this administered raise in the exchange rate is called `devaluation'.

In the 1920s and 1930s, the prevailing exchange rate system was the fixed one, and the international capital mobility was very limited at least outside economic blocs. Many countries suffered from recession and balance of payment deficits. They tried all kinds of economic policies with no success and finally entered competitive devaluations, which resulted into a total collapse of the international fixed exchange rate system.

2) Impacts of Fiscal and Monetary Policies on BP

An expansionary monetary policy has a clear-cut negative impact on the balance of payment;

The expansionary monetary policy increases the national income Y and decreases interest rate i.

The first leads to a deterioration of the current account balance as an increased national income leads to more imports. The second leads to the deterioration of the capital account as the lower interest rate means capital outflows. The combined impact is clearly negative on the BP.

BP LM LM

Capital is immobile Capital is mobile

BP BP BP

0ELM

IS

LM

IS

LM

IS

i i i

Y YY*Y1Y Fiscal Policy Monetary Policy


BP

IS

As shown in the graph below, an expansionary fiscal policy has an ambiguous impact on the balance of payment;

An expansionary fiscal policy leads to a larger Y and a higher interest rate or i. The first leads to a deterioration of the current account of BP, and the second to the improvement of the capital account of BP. The first negative and the second positive impacts work against each other. The overall impact depends on the relative magnitude of the two effects.

When capital is mobile, the improvement of the capital account may be substantial, and be large enough to more than offset the first negative impact. The net BP will improve.

i IS

BP

LM Mobile Y

When capital is immobile, the improvement of the capital account may be small, and thus be not large enough to offset the BP deterioration resulting from an increasing national income and imports. All in all, the BP will deteriorate on the net basis.

i BP LM

IS

Immobile Y

3) Modified Effectiveness of Fiscal and Monetary Policies

e

BP<0

BP>0

BP<0BP<0

e


We have just seen that, in certain cases with added international dimensions, the IS-LM model developed for a closed economy should be greatly modified.

Effectiveness of fiscal and monetary policies in the open macroeconomics (IS-LM-BP model) will be significantly different from the prediction for the closed economy (IS-LM model).

(1) Effectiveness of Fiscal Policies

Case I. Capital is relatively immobile: The BP curve is steeper than the LM curve.

Expansionary fiscal policy leads to the BP deficit: a rightward shift of the IS curve in the IS-LM setting means a higher equilibrium national income and a higher interest rate. A higher national income means a fall in CA. A higher interest rate means a rise in KA. The assumed capital immobility means that the second is smaller than the first, and thus the net impact on the BP is negative. The BP deficit means the excess demand for foreign currencies (exchanges). There occurs upward pressure on exchange rates.

Under the Fixed exchange rate system, as government diffuses the foreign currency shortage by selling foreign currencies, the payment for them in domestic currency flows into the government and thus the money supply in the private sector decreases. The LM curve shifts to the left, exerting recessionary impacts on the economy and thus partially offsetting the initial expansionary fiscal policy. Here the fiscal policy is being hampered.

(Note: Fixed Forex, Immobile Capital)

Under the Flexible exchange rate system, the exchange rate will rise. As a result the price level of the foreign country expressed in terms of domestic currency rises, which leads to international demand switch from foreign to domestic goods. CA improves. The IS curve will shift further to the right, and the BP curve will shift to the right, too. The resultant equilibrium income is still larger. Here the fiscal policy is reinforced by the international factor.


(Note: Flexible Forex. Capital Relatively Immobile)

Under a relative capital immobility, the fiscal policy and the flexible exchange rate system are a good combination.

Case II. Capital is relatively mobile: The BP curve is flatter than the LM curve.

Expansionary fiscal policies lead to the BP surplus. Why? When the IS curve shifts to the right as a result of the expansionary fiscal policy, two things will happen to affect the BP: an increase in Y* at the new internal equilibrium or the new intersection of the IS-LM leads to more imports and thus a decrease in CA. On the other hand, the interest rate goes up as a result of crowing-out and this rise in the interest rate attracts more international funds into the country, which leads to an increase in KA. The net change in the BP is the difference between the decrease in CA and an increase in KA. The assumption of the highly mobile capital implies that the increase in KA is larger than the decrease in CA: a higher interest rate will attract an avalanche of massive capital inflows which will more than dominate the deteriorating current account due to a higher income.

The BP surplus means an excess supply (`too much of foreign currencies').

Under the Fixed exchange rate system, as government mops up the foreign currency surplus by buying foreign currencies, the payment for them in domestic currency flows from the government to the private sector and thus the money supply in the private sector increases. The LM curve shifts to the right, exerting expansionary impacts on the economy and thus reinforcing the initial expansionary fiscal policy. Here the fiscal policy is being reinforced.


Under the Flexible exchange rate system, the exchange rate will fall. As a result the price level of the foreign country expressed in terms of domestic currency falls, which leads to international demand switch from domestic to foreign goods. CA falls. The IS curve will shift to the left, partially offsetting its initial rightward shift, and the BP curve will shift up too. The resultant equilibrium income is not as large as that in the simple IS-LM setting. Here the fiscal policy is partially offset by the international factor.

Under a relative capital mobility, the fiscal policy and the fixed exchange rate system are a good combination. When international capital flows are quite brisk in and out of a country, and government is now being engaged in fiscal policy, it should not allow the exchange rate to fluctuate. The fluctuation exchange rate will offset the current fiscal policy.

For instance, the capital mobility between Canada and U.S. is very high. Let's suppose that the Canadian government wants to get out of recession by increasing government expenditures. The resultant higher interest rate will attract international funds into Canada (KA) and thus the BP will improve. There occurs a downward pressure on foreign exchange rate (upward pressure on the external value of the Canadian dollar). The point is that if the government wants to boost the economy, it cannot afford to let the exchange rate fall. Because the falling exchange rate will hamper exports and encourage imports. The CA will fall and thus the AE (=C + I + G + CA) will fall. There will be a recessionary impact on the export industry, which nullifies the initial expansionary fiscal policy. If government instead engages itself in fixing the exchange rate (keeping the Canadian dollar artificially low), government ends up selling the Canadian dollars and buying the U.S. dollars. The money supply (Canadian dollars) in the private sector rises. It will exert expansionary impacts on the economy, furthering the initial fiscal policy. The fiscal policy and the fixed exchange rate system is a good combination.

You may think of the opposite case where the Canadian government wants to fight against inflationary pressure by cutting government expenditures. Still the fixed exchange rate system or some attempt to fix the exchange rate at the current level is a better choice than the flexible exchange rate system.

(2) Effectiveness of Monetary Policies


Regardless of the degrees of capital mobility, an expansionary monetary policy invariably leads to a deterioration of the BP: When the LM curve shifts to the right, the equilibrium income rises and equilibrium interest rate falls. a rising income leads to more imports and thus a fall in CA. A falling interest rate leads to a fall in KA. If we start with an initial equilibrium of BP=0, an expansionary monetary policy will lead to the BP deficit or BP <0.

Under the fixed exchange rate system, the BP<0 requires the government sell foreign currencies (simultaneously taking in domestic money as their payments). The money supply in the private sector decreases and thus the LM curve will shift to the left. The initial expansionary monetary policy is now hampered.

Under the flexible exchange rate system, the BP<0 will lead to a rise in the exchange rate. The rising exchange rate will bring about an increase in exports and a decrease in imports: CA The IS as well as the BP curves will shift to the right and meet the already-shifted LM curve.

Regardless of the capital mobility, the monetary policy and the flexible exchange rate system are a good combination.

For instance, when the first priority of the Canadian government is a tight monetary policy, it cannot afford to intervene into the foreign exchange market. It should take its hands off from it, and had better let the exchange rate go freely. If the government makes a wrong choice of the fixed exchange rate system, the BP surplus as a result of the tight monetary policy will require the government to buy foreign currencies, which leads to a self-defeating rise in the money supply.

Let’s illustrate the above points.

An expansionary monetary policy is intended to increase the national income. Depending on the capital mobility of the economy, the initial impact of the expansionary monetary policy is as follows:

Both lead to a balance of payment deficit. This deficit will have a contractionary impact under the fixed exchange rate system. And thus the LM will shift back to the left.


Under Flexible Exchange Rate System:

Under the flexible exchange rate system, the BP deficit leads to an increase in exchange rates, which in turn leads to a CA increase. A rising CA shifts the IS and BP curves to the right. The new equilibrium is now on the BP curve. We can say that the flexible exchange rate system magnifies the initial changes in the national income, and thus reinforces the expansionary monetary policy.

Fixed Exchange Rate System

The balance of payment deficit will lead to a contractionary impact under the fixed exchange rate system. And thus the LM curve will shift back to the left.

You can see that the secondary endogenous movement of the LM curve shifts the equilibrium national income back against the direction to which the initial monetary policy has changed Y. Thus, we can say that the fixed foreign exchange rate system offsets the monetary policy regardless of degrees of capital mobility.

4) Exchange Rate System as an Insulator against Shocks

Exchange rate system could be a built-in stabilizer or an amplifier of economic shocks or disturbances. Under what conditions which exchange rate system becomes a magnifier or a pacifier of troubles? As will see below, it all depends on the degree of capital mobility and the nature of shocks. One thing which clearly emerges from discussion will be that there is no


insulator from foreign monetary shocks at all: no exchange rate system will serve as a buffer from the foreign monetary shocks.

For instance, if the U.S. government raises interest rate, which is a foreign monetary shock, its impact will be inevitable felt on the Canadian economy no matter which exchange rate system Canada adopts. What still matter is that such an impact could be expansionary or contractionary on the Canadian economy depending on the exchange rate system. A higher interest rate will lead to capital outflows from Canada, a KA deterioration and thus a BP deficit in Canada. If the fixed exchange rate system is adopted (the Canadian government tries to depend the external value of the Canadian dollars which are loosing values against the U.S. dollars), the very government's attempt to fix the exchange rate by selling the U.S. dollars in exchange for the Canadian dollars will lead to a decrease in the money supply in Canada. The LM curve shifts to the left, exerting a contractionary impact on the Canadian economy. Alternatively, if the Canadian government simply lets the exchange rate go, the falling exchange rate will lead to the improvement of the CA (recall S and CA move in the same direction all the time). The IS and BP curve will shift to the left, exerting a contractionary impact. One more thing we should keep in mind is that the expansionary impact is not necessarily a better one than the contractionary impact. Which is the better depends on what government wants for now. If government targets at boosting an economy amid recession, yes, the expansionary impact helps. However, if the government's first priority is to restrain the overheated economy, the expansionary impact will hurt.

In order to figure out the correct impact, we have to specify three important things very clearly before plunging into analysis:

(a) The Nature of Initial Shocks; "Do the initial troubles or shocks shift which curve(s)? IS, LM, and/or BP?"

(b) The Degree of Capital Mobility; "Is capital perfectly immobile, relatively immobile, relatively mobile or perfectly mobile?" Alternatively, "Is the BP curve in question vertical, steeper than the LM, flatter than the LM, or horizontal?" In the modern world, the vertical BP is hard to find except for a very few exceptional cases (for instance, between North Korea and any other country), which accordingly are uninteresting. The perfect capital mobility is not general either, yet it shares basic features with the case of a relatively mobile capital with a few minor modifications. The example of perfect capital mobility is between Canada and U.S. in the age of free trades, and the current situation is quite close to it. So we should examine at least the last two possible cases: a relatively mobile capital, and a relatively immobile capital.

(c) The Exchange Rate System; "What exchange rate system the government is adopting?" Alternatively, in the age of dirty floating where government mixes elements of fixed and flexible exchange rate systems as expediency dictates, "Is the government trying to intervene in the foreign exchange market and to influence the exchange rate or to let exchange rates go?"

(1) Internal Goods Market Shocks:

These are ΔC or ΔI which shifts the IS curve around.


Case I. Relatively Immobile Capital

In both graphs, the initial goods market shocks shift the IS to the right as the single-line arrow indicates. The internal equilibrium, which is the intersection of the new IS and LM curve, is now at E1. E1 lies to the right of the steep BP curve, belonging to a BP deficit region:

Under the fixed exchange rate system, the BP deficit leads automatically to a contractionary decrease in the money supply and the leftward shift of the LM curve, which is indicated by the double-line arrow. The new equilibrium E2 is now on the BP curve. Comparing E1 with the initial troubles only and E2 with the working fixed exchange rate system, we can say that the fixed exchange rate system partially offset the initial changes in income. Here clearly the fixed exchange rate system works as a moderator to fluctuations in income, and thus serves as a built-in stabilizer or insulator.

Under the flexible exchange rate system, the BP deficit leads to an increase in exchange rates which in turn leads to a CA increase. A rising CA shifts the IS and BP curves to the right, which are indicated by the double-line arrow. The new equilibrium E2 is now on the BP curve. Comparing E1 with the initial troubles only and E2 with the working fixed exchange rate system, we can say that the flexible exchange rate system magnifies the initial changes in income. Here clearly the flexible exchange rate system works as an amplifier of fluctuations in income.

Case II. Relatively Mobile Capital Suppose that consumption or investment rises: Initially, only IS curve shifts to the right.


(2) Domestic Money Market Shocks:

Δu which shifts the LM curve around

First of all, we should note that the domestic monetary shocks do have unambiguous impact on the BP regardless of capital mobility. This contrasts with the domestic goods market shocks which can lead to either a BP surplus or deficit depending on capital mobility. You may recall because of this difference, in the previous section as to the effective of policies, the analysis of the fiscal policy was a lot more complicated than that of the monetary policy.

We know that a decrease in the money demand due to a random factor (u) shifts the LM curve to the right: md = K y - h i + u.

Fixed Forex

Both lead to a balance of payment deficit. This deficit will have a contractionary impact under the fixed exchange rate system. And thus the LM will shift back to the left.

Flexible Exchange Rate System


Under the flexible exchange rate system, the BP deficit leads to an increase in exchange rates, which in turn leads to a CA increase. A rising CA shifts the IS and BP curves to the right. The new equilibrium is now on the BP curve. We can say that the flexible exchange rate system magnifies the initial changes in income.

Fixed Exchange Rate System

The balance of payment deficit will lead to a contractionary impact under the fixed exchange rate system. And thus the LM curve will shift back to the left.

You can see that the secondary endogenous movement of the LM curve shifts the equilibrium national income back against the direction to which the initial monetary shock has changed Y. Thus, we can say that the fixed foreign exchange rate system offsets the monetary shock regardless of degrees of capital mobility.

(3) External Goods Market Shocks

Good market shocks: ΔCA (resulting from ΔY* and thus ΔX), which shifts the IS and BP curves around.


Suppose X rises, or Exchange rates rises: Initially, not only IS but also BP shift to the right.

We can think of the external goods market shock in the setting of perfect capital mobility. This is simpler to think of as the BP curve is horizontal.

(4) External Monetary Shocks:

Δr* (resulting from MS*) which affects KA only, so that only the BP curve moves around, particularly up or down..

Here again the rise in the foreign interest has unambiguous impact on the BP: A higher interest rate of the foreign country will lead to capital outflows from the domestic country and thus KA and BP deteriorates no matter what the exchange rate system might be. Recall that graphically the rise in foreign interest rate shifts the BP curve up: r* BP. The BP deficit region expands: the area above the BP curve is now smaller after the shift than before. The intersection of IS-LM curves lies below the BP curve, which means that the economy is now with BP deficits.

We will discuss this case in a specific setting of a perfect capital mobility:Cast this issue in the case of Perfect Capital Mobility, or horizontal BP

LM LM BP’

BP BP

IS IS

Flexible Exchange Rate Fixed Exchange Rate

I LM LM

BP>0

BP BP

IS IS

Fixed Exchange Rate Flexible Exchange Rate


For instance, if the U.S. government raises interest rate, which is a foreign monetary shock, its impact will be inevitably felt on the Canadian economy no matter which exchange rate system Canada adopts.

What still matter is that such an impact could be expansionary or contractionary on the Canadian economy depending on the exchange rate system. A higher interest rate will lead to capital outflows from Canada, a KA deterioration and thus a BP deficit in Canada.

If the Canadian government simply lets the exchange rate go, The BP deficits put upward pressure on foreign exchange rates.

The rising exchange rate will lead to the improvement of the CA (recall S and CA move in the same direction all the time). The IS and BP curve will shift to the right, exerting an expansionary impact. The national income rises.

Alternatively, if the fixed exchange rate system is adopted (the Canadian government tries to depend the external value of the Canadian dollars which are losing values against the U.S. dollars), the very government's attempt to fix the exchange rate by selling the U.S. dollars in exchange for the Canadian dollars will lead to a decrease in the money supply in Canada. The LM curve shifts to the left, exerting a contractionary impact on the Canadian economy.

LM LM BP’

BP BP

IS IS

Macroeconomics Lecture Note - instruct.uwo.cainstruct.uwo.ca/economics/220a-570/JD Han - Notes for I… · Web viewMacroeconomics36 Chapter II Appendix. Macroeconomics. 13. Chapter

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