Macroeconomics

Problem Set 2

Sherif Khalifa

1. Suppose an economy has the following Phillips curve:

π = Eπ − 0.5 (u− 0.06)

= π−1 − 0.5 (u− 0.06)

(a) The natural rate of unemployment =

(b) How much cyclical unemployment is necessary to decrease inflation by 5%:

(c) Assume that a change of 1% unemployment translates into a change of 2% in GDP.

The sacrifice ratio =

2. Assume that the sacrifice ratio for an economy is 4. If the Fed wishes to decrease

inflation by 5%. This will cost the economy what percent of GDP:

1

3. Suppose the economy is at its long run equilibrium. Explain the short run and longrun changes that are caused by a monetary expansion using the following diagrams for the

AS-AD model, and the Phillips curve:

SRAS

Y

P LRAS

AD

P1

YN

SRPCUnemployment

Rate

Inflation Rate LRPC

2

4. Suppose you win the lottery. You have a choice between receiving $100,000 a year for20 years or an immediate payment of $1,200,000. If the interest rate is 3%:

(a) Which choice would you make?

(b) For what range of interest rates should you take the immediate payment?

5. Suppose a bond has a maturity of 3 years, annual coupon payments of $5, and a facevalue of $100:

(a) If the interest rate is 4%, the bond price=

(b) If the interest rate is 6%, the bond price=

6. Consider two bonds. Each has a face value of $100 and matures in 10 years. The firsthas no coupon payments, and the second pays $10 per year:

(a) If the interest rate is 3%, the price of the first bond =

(b) If the interest rate is 3%, the price of the second bond =

7. Suppose a bond has a face value of $100, annual coupon payments of $4, a maturity of5 years and a price of $90.

(a) Write an equation that defines the yield to maturity on this bond:

(b) If the price of the bond falls from $90 to $85, the bond’s rate of return over the year

=

3

8. Consider an economy described by the following equations:

Y = C + I +G+NX

Y = 5000

G = 1000

T = 1000

C = 250 + 0.75 (Y − T )

I = 1000− 50r

NX = 500− 500ε

r = r∗ = 5

(a) National saving=

(b) National Investment=

(c) Trade Balance=

(d) Exchange Rate=

9. (a) In a small open economy, if exports = $20 billion, imports = $30 billion, and

domestic national saving =$25 billion, net capital outflow =

(b) If domestic saving=$50 billion, and domestic investment=$50 billion, net capital out-

flow=

10. (a) If 5 Swiss Francs =$1, the U.S. price =$1 per good, and the Swiss price=2 Francs

per good, then the real exchange rate is:

(b) Assume purchasing power parity holds. If a Big Mac costs $2 in the U.S., and if 10

Mexican pesos trade for $1, then the price of a Big Mac in Mexico=

4

11. Use the small open economy model to illustrate graphically the impact of the followingevents on the trade balance:

(a) Governments around the world begin to engage in expansionary fiscal policy in order

to stimulate economic activity in their countries after the financial crisis.

S

I,S

r

r1

I(r)

(b) If corporate downsizing and lack of job security during the financial crisis cause con-

sumers to spend less and save more.

S

I,S

r

r1

I(r)

5

12. Consider the large open economy model. Suppose that, due to economic uncertainty,American investors decide to invest more in Canada. What happens to the real interest rate,

the exchange rate, the net capital ouflow, and the net exports in Canada and in the United

States?

r

L

r

NCOe

$

S(S)

D(I+NCO) NCO

S(NCO)

D(NX)

e1

r1

L1

13. Consider the large open economy model to examine the effect of a contractionary

fiscal policy on the interest rate, the exchange rate, net exports, and net capital outflow:

r

Y

r

NCOe

$

LM

IS NCO

S(NCO)

D(NX)

e1

r1

Y1

6

14. (a) Consider the small open economy model to examine the effect of a policy to cutgovernment spending to balance the budget in a floating exchange rate regime:

LM*

Y1Y

e

e1

IS*

(b) Consider the following small open economy model to examine the effect of a policy to

cut government spending to balance the budget in a fixed exchange rate regime:

LM*

Y1Y

e

e1

IS*

7

15. Assume a large open economy is defined by the following equations:

Y = C + I +G+NX

C = 0.5 (Y − T )

I = 1500− 250r

T = 1000

G = 1500

NX = 1000− 250e

NCO = 500− 250r

NX = NCO

M

P= 0.5Y − 500r

M = 1000, P = 10

(a) Y=

(b) r=

(c) C=

(d) I=

(e) NCO=

(f) NX=

(g) e=

8