Chapter 5 A Closed- Economy One-Period Macroeconomic Model Copyright © 2010 Pearson Education Canada.

Chapter 5

A Closed-Economy

One-Period Macroeconomic Model

Copyright © 2010 Pearson Education Canada

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 5-2

Chapter 5 Topics

• Construct closed-economy one-period macroeconomic model, which has: (i) representative consumer; (ii) representative firm; (iii) government.

• Introduce the government.• Economic efficiency and Pareto

optimality.• Experiments: Increases in government

spending and total factor productivity.• Consider a distorting tax on wage income

and study the Laffer curve.Copyright © 2010 Pearson Education Canada


Closed-Economy One-Period Macroeconomic Model

There are three different actors in this economy:

• the representative consumer who stands in for the many consumers in the economy who sell labour and buy consumption goods.

• the representative firm that stands in for the many firms in the economy that buy labour and sell consumption goods.

• the government

• Competitive Equilibrium

• Experiments: What does the model tell us are the effects of changes in government spending and in total factor productivity?


The Government

• In this one-period closed economy model the behaviour of the government is quite simple.

• In this model, the government wants to purchase a given quantity of consumption goods, G, and finances these purchases by taxing the representative consumer, which is denoted by T.

• In practice, governments provide many different goods and services, including roads and bridges, national defence, air traffic control, and education.

The Government

• Which goods and services the government should provide is subject to both political and economic debate.

• But economists generally agree that the government has a special role to play in providing public goods, which have two special charactristics: nonrivalness in consumption and nonexcludability in the benefits of consumption, that are difficult or impossible for the private sector to provide.

• Example of a public good: National defence

The Government

• To keep things simple, for now in the model we will not be specific about the public-ggods nature of government expenditures.

• What we want to capture here is that government spending uses up resources, and we will model this by assuming that government spending simply involves taking goods from the private sector.

• Output is produced, and the government purchases an exogenous amount G of this output, with the remainder consumed by the representative consumer.

The Government• An exogenous variable is determined outside the model,

while an endogenous variable is determined by the model itself.

• Government spending is exogenous in our model, as we are assuming that government spending is independent of what happens in the rest of the economy.

• The government must abide by the government budget constraint, which we write as

G = T,or government purchases (G) equal to taxes (T), in real terms.

The Government – Fiscal Policy

• Introducing the government in this way allows us to study some basic effects of fiscal policy.

• In general, fiscal policy refers to the government’s choices over its expenditures, taxes, transfers, and borrowing.

• In the current one-period model, the government cannot borrow to finance government expenditures, since there is no future in which to repay its debt.

The Government – Fiscal Policy

• The government does not tax more than it spends, as this would imply that the government would foolishly throw goods away.

• The government budget deficit, which is G – T here, is always zero.

• Thus, only elements of fiscal policy we will study in Chapter 5 are the setting of government purchases, G, and the macroeconomic effects of changing G.

• In Chapter 8, we will explore what happens when the government run deficits and surpluses.

Competitive Equilibrium

• We have to now understand how consistency is obtained in the actions of all three economic agents.

• Mathematically, a macroeconomic model takes the exogenous variables and determines values for the endogenous variables, as outlined in Figure 5.1.


A Model Takes Exogenous Variables and Determines Endogenous Variables (Figure 5.1)



• Exogenous variables in the model: G, z and K.• Endogenous variables: C, Ns, Nd, T, Y and w



• Representative consumer optimizes given market prices.

• Representative firm optimizes given market prices.

• The labor market clears.

• The government budget constraint is satisfied, or G = T.



Income-Expenditure Identitity

In a competitive equilibrium, the income-expenditure identity is satisfied, so

Y = C + G


The Production Function

• We will work with the this simple macroeconomic model in graphical form.

• Start with representing the production function in graphical form.

• In a competitive equilibrium, Nd = Ns = N and we will refer to N as employment.

• Production function: Y=zF(K,N) (5.4)• We graph the production function in Figure

5.2(a) for a given capital stock K.

The Production Function• The maximum output that could be produced in this

economy is Y* in Figure 5.2(a).• In equilibrium, N = h – l.• Substituting for N in the production function (5.4),

we getY = zF(K, h-l), (5.5)

which is relationship between output Y and leisure l, given exogenous variables z and K.

• This relationship is graphed in Figure 5.2(b) and we get a mirror image of the production function in Figure 5.2(a).


The Production Function and the Production Possibilities Frontier (Figure 5.2)


The Production Function• Note that since the slope of the production function in Figure

5.2(a) is MPN, the marginal product of labour, the slope of the relationship in Figure 5.2(b) is – MPN, since this relationship is just the mirror image of the production function.

• Since in equilibrium C = Y – G, from the income-expenditure identity, from (5.5) we get

C = zF(K, h-l) – G,which is a relationship between C and l, given the exogenous variables z, K and G.

• This relationship, graphed in Figure 5.2(c), is just the relationship in Figure 5.2(b) shifted down by the amount of G.

Production Possibilities Frontier (PPF)

• The relationship in Figure 5.2(c) is called a production possibilities frontier (PPF).

• It describes what technological possibilities are for the economy as a whole, in terms of the production of consumption goods and leisure.

• All of the points in the shaded area inside the PPF and on the PPF in Figure 5.2(c) are technologically possible in this economy.


• The PPF captures the tradeoff between leisure and consumption that the available production technology makes available to the representative consumer in the economy.

• Note that the points on the PPF on line AB are not feasible for this economy, as consumption is negative.

• Only the points on the PPF on line DB are feasible.


• As in Figure 5.2(b), the slope of the PPF in Figure 5.2(c) is –MPN.

• The negative of the slope of the PPF is called the marginal rate of transformation.

• The marginal rate of transformation is the rate at which one good can be converted technologically into another; in this case, the marginal rate of transformation is the rate at which leisure can be converted in the economy into consumption goods through work.

• MRTl,c = MPN = -(slope of the PPF)





Key Properties of a Competitive Equilibrium



Pareto Optimality



Key Properties of a Pareto Optimum

• In this model, the competitive equilibrium and the Pareto optimum are identical, as the marginal rate of substitution is equal to the marginal rate of transformation.



First and Second Welfare Theorems

• These theorems apply to any macroeconomic model

• First Welfare Theorem: Under certain conditions, a competitive equilibrium is Pareto optimal.

• Second Welfare Theorem: Under certain conditions, a Pareto optimum is a competitive equilibrium.


Sources of Social Inefficiencies

• There are three reasons why a competitive equilibrium could fail to be Pareto-optimal.

1. Externalities2. Distorting taxes3. Monopoly Power


Using the Second Welfare Theorem to Determine a Competitive Equilibrium



Effects of an Increase in G

• Essentially a pure income effect

• C decreases, l decreases, Y increases, w falls



Equilibrium Effects of an Increase in Government Spending



World War II Increase in G

• Very large increase in G

• Y increases, C decreases by a small amount



GDP, Consumption, and Government Expenditures



Effects of an Increase in z (or an increase in K)

• PPF shifts out, and becomes steeper – income and substitution effects are involved.

• C increases, l may increase or decrease, Y increases, w increases



Increase in Total Factor Productivity



Competitive Equilibrium Effects of an Increase in Total Factor Productivity



Income and Substitution Effects of an Increase in Total Factor Productivity



Deviations from Trend in Real GDP and the Solow Residual



The Relative Price of Energy and the Solow Residual



A Simplified Model with a Proportional Income Tax

• Use the model to study the incentive effects of the income tax, and to derive the “Laffer curve.”



Production function without capital

• Labor is the only input, but there is still constant returns to scale (linear production function).

Y = zNd



Production Possibilities Frontier



Consumer’s budget constraint



Profits for the firm



The consumer’s budget constraint in equilibrium



The Production Possibilities Frontier in the Simplified Model



The Labor Demand Curve in the Simplified Model



Competitive Equilibrium in the Simplified Model with a Proportional Tax on Labor Income


Revenue for the government given the tax rate t

• REV = tz[h-l(t)] (5.12)• G = tz[h-l(t)]


A Laffer Curve



There Can Be Two Competitive Equilibria


Chapter 5 A Closed- Economy One-Period Macroeconomic Model Copyright © 2010 Pearson Education Canada.

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