Fei2123PS3_soln

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Problem Set 3 *Solution*

Macroeconomics, ECON 2123

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Part I: True/False/Uncertain Please justify your answer with a short argument for each question and

draw a diagram if necessary.

1. Suppose that workers in the Republic of Communia are highly unionized, while workers in the

Republic of Individuela are not. In all other respects, the two countries are exactly the same. Then

Communia is likely to have a higher natural level of output than Individuela.

False. In our model of the labor market, the level of unionization is captured by the

Communia is likely to have a higher natural rate of unemployment than Individuela. Hence Communia is

likely to have a lower natural level of output than Individuela.

2. Suppose there is a decrease in the price level from P to P’. Given the stock of nominal money, M, this

leads to an increase in the real money stock, M/P, which shifts the LM curve down. This implies that the

AD curve shifts to the right.

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3. When output is below the natural level of output, the actual price level is lower than the expected price

level.

True. The actual price level equals the expected price level when output is equal to the natural level of

output. Because the AS curve is upward-sloping, if output is below its natural level, the actual price level

is lower than expected. See diagram:

4. In terms of changing output, monetary policy is relatively more effective when the AS curve is

relatively flat, while fiscal policy is more effective when the AS curve is relatively steep.

False. Monetary and fiscal policies affect the AD curve, not the AS curve. Monetary and fiscal policies

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are both more effective in changing output when the AS curve is flatter and less effective when the AS

curve is steeper. In the extreme case, when the AS curve is vertical, neither policy has any effect on

output (the only effect of monetary and fiscal policy in this case is a change in the price level).

5. The aggregate demand relation slopes down because at a higher price level, consumers wish to

purchase fewer goods.

False. The AD curve slopes down because an increase in P leads to a fall in M/P, so the nominal interest

rate increases, and investment I and output Y fall.

Part II: The Labor Market (Chapter 6)

1. The existence of unemployment

(a) Suppose previously the unemployment rate was relatively high. But now things change: the

unemployment rate becomes very low this year. What change happens in terms of the relative bargaining

power of workers and firms when the unemployment rate becomes very low? What do your answers

imply about what happens to the wage as the unemployment rate gets very low, given expected price and

actual price constant?

(When the unemployment rate is very low, it is very difficult for firms to find workers to hire and very

easy for workers to find jobs. As a result,) the bargaining power of workers is very high relative to firms

when the unemployment rate is very low. Therefore, the wage gets very high as the unemployment rate

gets very low.

(b) Given your answer to part (a), why is there unemployment in the economy? (What would happen to

real wages if the unemployment rate approached zero? Suppose expected price and actual price remain

constant.)

Presumably, the real wage would grow without bound as the unemployment rate approached zero since

the wage is a decreasing function of unemployment rate. (Since a worker could always find a job if the

unemployment rate equaled zero, there would be nothing to constrain aggressive wage bargaining.) At

any positive rate of unemployment, however, there is some constraint on workers' bargaining power, so

the real wage cannot grow without bound. (You can also show this using the wage-setting relation curve

in the diagram).

Part III: The IS-LM Model and the AS-AD Model (Chapter 5 and Chapter 7)

1. The Republic of Keynesia is a closed economy and obeys our short-run IS-LM model. Assume it starts

out in equilibrium in both the goods market and the money market. Keynesia’s economy is described by

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the following set of equations:

Goods market:

C = c0 + c1 (1-t)Y, where C is consumption; Y is income; t represents a proportional tax; and c0 and

c1 are positive constants

I = b0 – b1 i, where I is investment; i is the interest rate; and b0 and b1 are positive constants

G = G , where G is a positive constant

Money market:

Md

= P (m0 + m1Y – m2 i), where Md

is nominal money demand; P is the price level; m0 (a positive

constant) represents exogenous changes to Md

; and m1 and m2 are also positive constants

Let Ms represent nominal money supply

(a) Derive the IS relation and the LM relation equations.

IS:

LM: Ms = Md

Ms/P = m0 + m1 Y - m2 i

(b) Now suppose 1/[1-c1(1-t)]=λ for simplicity. Derive the expression for aggregate demand using

your answer to part (a). (Hint: To derive the AD curve, just substitute in for i into the IS equation

from the LM equation. You will obtain an equation of Y as a function of P.)

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(c) Now let:

c0=200 c1=0.5 b0=300 b1=0.4

m0=400 m1=1 m2=0.8 Ms=200

G=100 t=0 Yn=550

Derive the AD equation using these figures. (All figures are in millions of HK dollars.)

(d) Use the same condition in part (c). Suppose the aggregate supply takes the following form:

P = Pe + (1/50)( Y − Yn ) and P=1. Assume we are in the short-run for now. What is the equilibrium

output, Y*? What is the expected price level, Pe? Draw and label the AS-AD diagram for this case

and denote the equilibrium in this economy as point A. Also denote the natural level of output in the

diagram.

First, use the AD equation from part (c), substitute P=1, you will obtain the equilibrium Y*=500.

Then, use the AS equation, obtain Pe=2.

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(e) If Y happened to be equal to the natural level of output Yn, what is the relation between P and Pe?

When Y=Y n , P= Pe

(f) The Keynesian government is up for reelection soon, and so it wants to achieve the natural level of

output. (We are still in the short run.) Propose two different policy options that would do the job.

For each policy option, draw the AS-AD and the IS-LM diagrams, and show how the two diagrams

are related to each other. Calculate by how much the government must increase/decrease

government spending to achieve the natural level of output. For monetary policy, you don’t need to

do any calculations. What is the difference between the effects of the two policy options?

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(g) The Keynesian government decides not to listen to you, and raises government spending by more

than would be required to achieve the natural level of output. Its argument is that higher output is

better. The voters apparently think so too, and the government gets reelected. What happens as time

passes and we get to the “medium run”? (You do not have to do any calculations, just draw

diagrams and give some intuition/explanation.)

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2. Closed Economy AS-AD (33 marks)

Price Setting Relation: W = Pe F (u, z)

Wage Setting Relation: P = (1 + μ) W

Goods Market: Y = C(Y, T) + I(Y, i) + G

Financial Market: Ms

/P = Md

(Y, i)

(a) Find the aggregate supply relation. Describe the channel through which the AS curve slopes up/down.

(3 marks)

(b) Assume that the economy is at a point such that the unemployment rate is equal to the natural rate of

unemployment. What does this imply about the price level and output? Explain. (2 marks)

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(c) If the Fed carries out a monetary contraction, what happens in the short-run (SR) and the

medium-run (MR)? Start from point A where P = Pe. Label the following: all curves including

(IS0, ISSR , ISMR , LM0, LMSR , LMMR , ADSR , ADMR , ASSR , ASMR , where the subscript 0 denotes

initial status), the short-run equilibrium as point B, the medium-run equilibrium as point C, and

output associated with natural rate of unemployment. (10 points)

See in-class notes.

(d) What does neutrality of money imply about the effectiveness of contractionary monetary policy in

affecting output and interest rate in the short- and medium-run? (2 marks)

(e) If the price of oil increases sharply, what happens in the short-run (SR) and the medium-run (MR)?

Start from point A where P = Pe. Label the following: all curves including (IS0, ISSR , ISMR , LM0,

LMSR , LMMR , ADSR , ADMR , ASSR , ASMR , where the subscript 0 denotes initial status), the short-run

equilibrium as point B, the medium-run equilibrium as point C, and output associated with natural

rate of unemployment. (10 marks)

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(f) Indicate whether these variables increase, decrease or remain the same when the price of oil rises

sharply. (You may use arrows.) (6 marks)

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