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Intermediate Macroeconomics

Spring 2013 Problem Set 4 Due in 6.6 in class

1. Chapter 10: 2

An economy begins in long-run equilibrium,and then a change in government regulationsallows banks to start paying interest onchecking accounts. Recall that the moneystock is the sum of currency and demanddeposits, including checking accounts, so thisregulatory change makes holding moneymore attractive.

a. How does this change affect the demand formoney? b. What happens to the velocity of money?

c. If the Fed keeps the money supply constant,what will happen to output and prices in theshort run and in the long run?

d. If the goal of the Fed is to stabilize theprice level, should the Fed keep themoney supply constant in response to thisregulatory change? If not, what should itdo? Why?

e. If the goal of the Fed is to stabilize output,how would your answer to part (d) change?

2. Chapter 11: 2

Although our development of the Keynesiancross in this chapter assumes that taxes are afixed amount, in many countries (including theUnited States) taxes depend on income. Let’srepresent the tax system by writing taxrevenue as

where

and t are parameters of the tax code.The parameter t is the marginal tax rate: ifincome

rises by $1, taxes rise by t ×$1.

a. How does this tax system change the wayconsumption responds to changes in GDP?

b. In the Keynesian cross, how does thistax system alter the government-purchasesmultiplier? c. In the IS–LM model, how does this tax systemalter the slope of the IS curve?

3.Chapter 11:5

The following equations describe an economy.

C=120+0.5(Y-T).I=100-10t.G=50.T=40.(M/P)d=Y-20t.M=600.P=2.a. Identify each of the variables and briefly explain their meaning.

b. From the above list, use the relevant set of equations to derive the IS curve. Graph the IS

curve on an appropriately labeled graph.

c. From the above list, use the relevant set of equations to derive the LM curve. Graph the LM

curve on the same graph you used in part (b).

d. What are the equilibrium level of income and equilibrium interest rate?

4. Chapter 12: 3

Consider the economy of Hicksonia.

a. The consumption function is given byC = 200 + 0.75(Y ?T ).The investment function isI = 200

?25r.Government purchases and taxes are both100. For this economy, graph the IS curve forr ranging from 0 to 8.

b. The money demand function in Hicksonia is(M/P)d= Y ?100r.The money supply M is 1,000

and the pricelevel P is 2. For this economy, graph the LMcurve for r ranging from 0 to 8. c. Find the equilibrium interest rate r and theequilibrium level of income Y.

d. Suppose that government purchases are raisedfrom 100 to 150. How much does the IScurve

shift? What are the new equilibriuminterest rate and level of income?

e. Suppose instead that the money supply israised from 1,000 to 1,200. How much doesthe

LM curve shift? What are the new equilibriuminterest rate and level of income?

f. With the initial values for monetary andfiscal policy, suppose that the price level risesfrom 2

to 4. What happens? What are thenew equilibrium interest rate and level ofincome?

5. Chapter 12: 8

This problem asks you to analyze the IS–LMmodel algebraically. Suppose consumption is a

linear function of disposable income:C(Y – T) = a + b(Y ?T),where a >0 and 0 0 and d >0.

a. Solve for Y as a function of r, the exogenousvariables G and T, and the model’s parametersa,

b, c, and d.

b. How does the slope of the IS curve dependon the parameter d, the interest rate sensitivityof

investment? Refer to your answer topart (a), and explain the intuition.

c. Which will cause a bigger horizontal shift inthe IS curve, a $100 tax cut or a $100 increasein

government spending? Refer to youranswer to part (a), and explain the intuition.

Now suppose demand for real money balances isa linear function of income and the interest rate:L(r, Y) = eY ? fr,where e > 0 and f > 0.

d. Solve for r as a function of Y, M, and P andthe parameters e and f.

e. Using your answer to part (d), determinewhether the LM curve is steeper for large orsmall

values of f, and explain the intuition.

f. How does the size of the shift in the LMcurve resulting from a $100 increase in Mdepend on i. the value of the parameter e, the incomesensitivity of money demand? ii. the value of the parameter f, the interestsensitivity of money demand?

g. Use your answers to parts (a) and (d) toderive an expression for the aggregatedemand curve.

Your expression should showY as a function of P; of exogenous policyvariables M, G, and T; and of the model’sparameters. This expression should notcontain r.

h. Use your answer to part (g) to prove thatthe aggregate demand curve has a negativeslope. i. Use your answer to part (g) to prove thatincreases in G and M, and decreases in T,shift the aggregate demand curve to the right.How does this result change if the parameterf, the interest sensitivity of money demand,equals zero? Explain the intuition for your result.

6. Chapter 12: 9

The Fed is considering two alternative monetarypolicies:

? holding the money supply constant andletting the interest rate adjust, or ? adjusting the money supply to hold the interestrate constant.

In the IS–LM model, which policy will betterstabilize output under the following conditions? a. All shocks to the economy arise from exogenouschanges in the demand for goods andservices. b. All shocks to the economy arise from exogenouschanges in the demand for money.

7. Chapter 14: 1

Assume that people have rational expectationsand that the economy is described by thesticky-price model. Explain why each of the followingpropositions is true.

a. Only unanticipated changes in the moneysupply affect real GDP. Changes in themoney

supply that were anticipatedwhen prices were set do not have anyreal effects.

b. If the Fed chooses the money supply at thesame time as people are setting prices, sothat

everyone has the same informationabout the state of the economy, then monetarypolicy cannot be used systematically tostabilize output. Hence, a policy of keepingthe money supply constant will have thesame real effects as a policy of adjusting themoney supply in response to the state of theeconomy. (This is called the policy irrelevanceproposition.)

c. If the Fed sets the money supply wellafter people have set prices, so that theFed has

collected more information aboutthe state of the economy, then monetarypolicy can be used systematically to stabilizeoutput.

8. Chapter 14: 6

Some economists believe that taxes have animportant effect on the labor supply. Theyargue that higher taxes cause people to wantto work less and that lower taxes cause themto want to work more. Consider how thiseffect alters the macroeconomic analysis oftax changes. a. If this view is correct, how does a tax cutaffect the natural level of output?

b. How does a tax cut affect the aggregatedemand curve? The long-run aggregate supplycurve?

The short-run aggregate supplycurve?

c. What is the short-run impact of a tax cut onoutput and the price level? How does

youranswer differ from the case without the laborsupplyeffect?

d. What is the long-run impact of a tax cut onoutput and the price level? How does

youranswer differ from the case without the laborsupplyeffect?

9. Chapter 14: 7

Suppose that an economy has the Phillipscurve

and that the natural rate of unemployment isgiven by an average of the past two years’unemployment:

a. Why might the natural rate of unemploymentdepend on recent unemployment (as

isassumed in the preceding equation)

b. Suppose that the Fed follows a policy toreduce permanently the inflation rate by1

percentage point. What effect willpolicy have on the unemployment rateover time? c. What is the sacrifice ratio in this economy?Explain.

d. What do these equations imply aboutshort-run and long-run tradeoffs betweeninflation and

unemployment?