ECON 352 Intermediate Macroeconomics

Problem Set 4

Spring 2017

1. Short-Run Phillips Curve Assume that an economy is governed by the Phillips curve:

? = E? ? 0.5(u ? 0.06),

where ? is the inflation rate, E? is the expected inflation rate, and the natural rate of

unemployment is 6%. Also, note from Okun’s law that 1 percentage point of unemployment

translates into 2 percentage points of lost output.

Suppose that today, ? = 0.05 and E? = 0.05. The government wants to lower inflation to

2%.

Assume that people have adaptive expectations.

(a) (1 point) How much cyclical unemployment does the economy have to experience to

have inflation rate of 2%?

(b) (1 point) What is the sacrifice ratio?

Assume that the government announced its plans to lower inflation before the

workers and firms form their expectations. The workers and firms form their

expected inflation by the following rule:

E? = ??a + (1 ? ?)??1 ,

where ??1 is the inflation rate in the previous period, ?a is the announced inflation,

and ? ? [0, 1] is the weight workers and firms put on the announcement (credibility

of the government).

(c) (1 point) Suppose that households and firms fully trust the government, and thus ? = 1.

How much cyclical unemployment does the economy have to experience to have inflation

rate of 2%?

(d) (1 point) Suppose ? = 0.5. How much cyclical unemployment does the economy have

to experience to have inflation rate of 2%? What is the sacrifice ratio?

(e) (1 point) How does ? affect the sacrifice ratio?

1 2. Short-Run Phillips Curve (1 point) How does an adverse supply shock change the shortrun tradeoff between inflation and unemployment? Illustrate how Phillips curve shifts with

an adverse supply shock.

3. Small Open Economy Consider a small open 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

N X = 500 ? 500?

r = r? = 5

(a) (1 point) In this economy, solve for national saving, investment, the trade balance, and

the equilibrium exchange rate.

(b) (1 point) Suppose now that G rises to 1250. Solve for national saving, investment, the

trade balance, and the equilibrium exchange rate. Explain what you find.

(c) (1 point) Now suppose that the world interest rate rises from 5 to 10 percent (with G

1000). Solve for national saving, investment, the trade balance, and the equilibrium

exchange rate. Explain what you find.

4. Mundell-Fleming Suppose that the price level relevant for money demand includes the

price of imported goods, which in turn depends on the exchange rate. That is, the money

market is described by

M

= L(r, Y ),

P

where

P = ?Pd + (1 ? ?) Pf

.

e Here, Pd is the price of domestic goods in domestic currency and Pf is the price of foreign

Pf

goods in foreign currency. Thus,

is the price of foreign goods in domestic currency. The

e

parameter ? ? (0, 1] is the share of domestic goods in the price index P . Assume the Pd and

Pf are sticky in the short-run.

(a) (2 points) Graph the LM ? curve on Y ? e plane.

(b) (2 points) What is the effect of expansionary fiscal policy under floating exchange rates

in this model? How is it different from the benchmark Mundell-Fleming model discussed

in class?

2 (c) (2 points) Suppose that political instability increases the country risk premium ? so that

r = r? + ?. What is the effect on the equilibrium exchange rate and aggregate income in

this model? How is it different from the benchmark Mundell-Fleming model discussed

in class?

5. Intertemporal Choice Consider a consumer whose preferences over consumption today and

consumption tomorrow are represented by the utility function

U (c1 , c2 ) = ln c1 + ? ln c2 ,

where c1 and c2 and consumption today and tomorrow, respectively, and ? is the discounting

factor. The consumer earns income y1 in the first period, and y2 in the second period. The

interest rate in this economy is r, and both borrowers and savers face the same interest rate.

(a) (1 point) Write down the intertemporal budget constraint of this consumer.

(b) (1 point) Write down the optimization problem of the consumer.

(c) (3 points) Solve for the optimal consumption in period 1 and period 2, i.e. c?1 and c?2 as

a function of y1 , y2 , r, and ?. 3