ECON 100 Tutorial: Week 18 [email protected] office hours: 3:00PM to 4:45PM tuesdays LUMS C85.

ECON 100 Tutorial: Week 18

www.lancaster.ac.uk/postgrad/murphys4/[email protected]

office hours: 3:00PM to 4:45PM tuesdays LUMS C85

Mad Minute

• You have one minute to do as many problems as you can.

• Whoever gets the most points wins a prize…

Mad Minute Solutions

Mad Minute – You have one minute to complete as many problems as you can on the following worksheet. When I call time, stop writing, turn your paper over and give it to the person sitting to your right to mark. Whoever gets the highest mark gets a prize.

I’ve got a couple more worksheets posted to my website; see if you can beat your score!

IS-LM ModelThe IS-LM model describes equilibrium in two markets and together determines general equilibrium in the economy. (See pgs. 713-723 in Mankiw 2nd Ed.)

IS stands for Investment and Savings.The IS curve shows the relationship between the interest rate (r) and level of income (Y) in the goods market. This relationship is an inverse relationship, so the IS curve is downward sloping.Shifts in the IS curve are due to changes in fiscal policy (i.e. it will shift to the right if Government expenditure increases, Taxes decrease, Investment increases (sometimes we could say business outlook becomes more optimistic, that is something that leads to an increase in I), and increases in autonomous Consumption, and vice versa).

LM stands for Liquidity and Money.The LM curve shows all points where the money market is in equilibrium (MD = MS) given a combination of the rate of interest and national income. The LM curve is upward-sloping, showing that an increase in income is associated with an increase in interest rate, and vice-versa. Shifts in the LM curve are due to changes in monetary policy (i.e. increase in M S shifts LM to the right, and vice versa).

Question 3(a)You are given the following information about an economy: autonomous consumption is £100 billion; autonomous investment is £500 billion; the marginal propensity to consume is 0.75; the coefficient on interest in the marginal efficiency of investment function is 10; the demand for money function takes the form: MD = 0.5Y – 15r, where Y is the economy's real output and r is the interest rate expressed as a percentage; and the real money supply is £850 billion.

Find the equations of i) the IS curve and ii) the LM curve.

The IS curve

The LM curve

Question 3(a)You are given the following information about an economy: autonomous consumption is £100 billion; autonomous investment is £500 billion; the marginal propensity to consume is 0.75; the coefficient on interest in the marginal efficiency of investment function is 10; the demand for money function takes the form: MD = 0.5Y – 15r, where Y is the economy's real output and r is the interest rate expressed as a percentage; and the real money supply is £850 billion.

Find the equations of the IS curveIn the product market, equilibrium occurs when Y = C + I and so:

C = 100 + 0.75YI = 500 -10r

We can plug these in to Y = C + I Y = 100 + 0.75Y + 500 – 10r 0.25Y = 600 -10r

Y = 2400 – 40r This is equation of the IS curve.

Question 3(a)You are given the following information about an economy: autonomous consumption is £100 billion; autonomous investment is £500 billion; the marginal propensity to consume is 0.75; the coefficient on interest in the marginal efficiency of investment function is 10; the demand for money function takes the form: MD = 0.5Y – 15r, where Y is the economy's real output and r is the interest rate expressed as a percentage; the real money supply is £850 billion.

Find the equations of the LM curve.In the money market, equilibrium occurs when MD = MS and so:

MD = MS

0.5Y – 15r = 850 0.5Y = 850 + 15r

Y = 1700 + 30r This is the equation of the LM curve.

Question 3(b)In part (a) we found:

IS: Y = 2400 – 40r LM: Y =1700 + 30r

What are the equilibrium income and rate of interest in the economy given the information above?To find the equilibrium, set IS equal to LM:

IS = LM 2400 – 40r = 1700 + 30r 70r = 700

r = 10% This is the equilibrium interest rate.

To find the equilibrium income, we can plug this value of r into either expression for Y and obtain Y = £2,000 billion.

Question 3(c)If autonomous investment increases by £35 billion, what will be the new equilibrium income and interest rate? What will be consumption and investment? What is the value of the multiplier?Autonomous investment is now £535 billion, so I = 535 – 10r.

This is just like part (a). First, we’ll find the equations of the IS curveIn the product market, equilibrium occurs when Y = C + I and so:

C = 100 + 0.75YI = 535 -10r

We can plug these in to Y = C + I Y = 100 + 0.75Y + 535 – 10r 0.25Y = 635 -10r

Y = 2540 – 40r This is equation of the IS curve. (note: it shifts to the right from before)

What happens when the IS curve shifts to the right?

IS curve shifts right increases Y and i

Question 3(c)If autonomous investment increases by £35 billion, what will be the new equilibrium income and interest rate? What will be consumption and investment?

The LM curve is still the same as in part(a):LM: Y =1700 + 30r

So setting the new IS curve = LM, we get:2540 – 40r = 1700 + 30r

Solving we get:70r = 840

So, r = 12% and Y = £2,060 billionTo find consumption and investment, we can plug in r and Y into our equations for C and I:

C = 100 + 0.75Y I = 535 -10r C = 100 + 0.75*(2060 billion) I = 535 -10*12C = £1,645 billion I = £415 billion

Question 3(c)If autonomous investment increases by £35 billion, what is the value of the multiplier?

The multiplier is: Multiplier = (change in Y)/(change in I) = (2,060-2000)/35 = 60/35

= 1.714 (4sf)

This multiplier, which takes account of the effect of the interest rate change associated with the extra investment, is sometimes called the interest-variable multiplier.

Question 3(d)Suppose the interest rate had not changed when autonomous investment increased, what would consumption, investment, and planned expenditure have been? What is the value of the multiplier in this case?

If r remained at 10% then I = 535 – 10*(10) = £435 billion

Y = £2,140 billion from the IS equation.C = £1,705 billion

The value of the multiplier is now 140/35 = 4.

This multiplier is the interest-constant multiplier. When we previously derived values for the multiplier it was this we obtained. Note that 1/(1 – MPC) in the economy equals 4, which confirms the value calculated using changes in Y and I. Introducing the money markets into the model, as the answers to c) and d) show, reduces the value of the multiplier. This is another complication to add to those caused by permanent income and life-cycle considerations. It is not easy being an economic policy-maker.

Question 3(d)How is it possible for IS to shift and the interest rate (r) to remain constant?

LM would need to shift right as well.This can occur due to a shift in money supply:

Ms = Md = (0.5Y) – 15r Ms = Md = (0.5*2140) – (15*10) = 1070 - 150 = 920 i.e. an increase of 70.

This will lead to a further change in Y.LM1

Question 3(e)Compare your answers to c) and d) to derive the crowding out effect.

Crowding out usually refers to how government investment sometimes is in projects that individuals would have invested in if the government hadn’t made the investment.

In our problem, we have an increase in autonomous investment , which shifts the IS curve out, causing an increase in interest rate. Because total investment is a function of both of these things, I does not increase as much as it would have if r could have been held constant:

I = autonomous investment – 15r

From this, we can see the effect from how a rise in interest rates due to increasing autonomous investment has a smaller negative effect on investment, cutting off some of the increase in investment (and income) that would have occurred if the interest rate had not increased.

In this case, the answer to d) tells us that income would have been £2,140 billion if the interest rate had not risen to the 12% rate established in c). Instead, with this higher interest rate income is £2,060 billion. The size of the crowding out effect is the difference between the two income figures, that is £80 billion.

IS Curve is Equilibrium in the Goods MarketTo solve for the IS curve set Output (Y) equal to Expenditure (C+I+G). I is usually a function of interest rate (r). To the up and right of the IS-curve, output is greater than Expenditure, while to the bottom and left of the IS-Curve, Output is less than Expenditure.

To shift the IS curve to the right, we need to increase Expenditure (usually, I or G).

Likewise, to shift IS to the left, we would need to decrease Expenditure.

LM Curve is Equilibrium in the Money MarketTo solve for the LM-curve set Money Supply (Ms) equal to Money Demand (Md). Money Supply is usually constant and Money Demand is usually a function increasing in output (Y) and decreasing in interest rates (r).

To shift the LM curve to the right, we need to increase Money Supply or decrease Money Demand (this could be done through increasing interest rates).

Likewise, to shift LM to the left, we would need to decrease Money Supply or increase Money Demand (again, by using interest rates).

Question 2(a)

The economy is in disequilibrium at points A and B in the diagram above. For each point, what are the prevailing conditions in i) the money market, and ii) the product market?At A, In the money market: the demand for money is greater than the supplyIn the product market: planned expenditure is less than planned output

(or planned injections are less than planned withdrawals)At B, In the money market: the demand for money is less than the supply In the product market: planned expenditure is less than planned output, same as A

Question 7

In which segment in the diagram above is the supply of money greater than the demand for money in the money market and aggregate demand greater than planned output in the product market?

a) 1b) 2c) 3d) 4

Question 2(b)

For each point, were income to remain unchanged, what would happen to the interest rate?This question is just asking, what would happen in the money market at Point A, and at point B?

In A:In the money market: MD > MS r↑

In the product market: planned expenditure < than planned output inventories ↑ investment ↓ Y↓

For B:In the money market: MD < MS r ↓

In the product market: planned expenditure < than planned output inventories ↑ investment ↓ Y↓

Question 2(c)

For each point, why is it likely that income will, in fact, change?Here, we are being asked at each point, due to the disequilibrium, what happens in the goods market?

In A:In the money market: MD > MS r↑

In the product market: planned expenditure < than planned output inventories ↑ investment ↓ Y↓

For B:In the money market: MD < MS r ↓

In the product market: planned expenditure < than planned output inventories ↑ investment ↓ Y↓

Coskeran’s solution:At both A and B conditions in the product market mean that unplanned investment is rising in firms. They will respond to this by cutting output which will cause income to fall.

Question 2(d)

For each point, what must happen to r and Y to bring the economy back into equilibrium?

From A, r will rise and Y will fall. From B, both r and Y will fall.

Question 4A rise in interest rates will increase: a) the speculative demand for moneyb) the precautionary demand for moneyc) the transactions demand for moneyd) none of the above

Question 5The demand for money represents the idea that there is: a) a negative relationship between the interest rate and the

quantity of money demanded.b) a negative relationship between the price level and the

quantity of money demanded.c) a positive relationship between the interest rate and the

quantity of money demanded.d) a negative relationship between the level of aggregate

output and the quantity of money demanded.

Question 6Aggregate demand in an economy is determined by the following equations:

C = 4 + 0.8Y and I = 180 – 10r where C is consumption expenditure (in billions of pounds), Y is income (in billions of pounds), I is investment expenditure (in billions of pounds), and r is the interest rate expressed as a percentage. Equilibrium income when r is 10% is:

a) £400 billionb) £420 billionc) £180 billiond) Cannot be calculated from the information provided

Question 7

In which segment in the diagram above is the supply of money greater than the demand for money in the money market and aggregate demand greater than planned output in the product market?

a) 1b) 2c) 3d) 4

Short-Answer Exam on Friday• Check Moodle for your exam time and

location• Bring a pencil, eraser, calculator, and anything

you need for drawing diagrams.• Bring your library card number• Do worksheets on website– www.lancaster.ac.uk/postgrad/murphys4/

Good luck!