14.02: Principles of Macroeconomics, Fall 2000

Problem Set 5

Due October 25, 2000

- If a
country depreciates its currency, it will normally experience an immediate
*decrease*in net exports. - If a government reduces its budget deficit, it will also reduce the nation’s trade deficit.
- If a country has an interest rate of zero, foreigners will be unwilling to hold its bonds.
- If a country joins a system of fixed exchange rates, it no longer engages in open market operations.
- The increasing productivity and output of another country is a threat to the prosperity of the US.

Consider the following
open economy where foreign variables are starred. Assume both countries use the same currency and prices are fixed,
so that the real exchange rate *e* is
constant, normalized to one.

C = 20 + 0.6(Y - T)^{}

I = 16^{}

G = 10^{}

T = 10^{}

Q = 0.1Y^{}

X = 0.1Y^{*}

a. Solve for equilibrium income in the
domestic economy, given a fixed level of foreign output. What is the multiplier
in this economy? What is the closed economy multiplier? Why are they different?

b. Assume
the foreign economy has the same equations as the domestic economy. Use this to
solve for the equilibrium output of each country. What is the multiplier for
each country now? Why is it different than the open economy multiplier
above? In general, if the domestic
country is relatively small, what do you think its effect on the foreign
economy will be? Explain how this
influences the outcome.

c. Assume
both countries have a target level of output of 125. What is the increase in G
necessary in either of these countries, assuming the other country does not
change G, to achieve target output? Solve for net exports and the budget
deficit in each country.

d. Suppose
they agree to increase their government spending. What level of G = G^{*} is necessary to achieve the
desired outcome?

e. Why is fiscal coordination (such as the common increase in G in part d) difficult to achieve in practice?

Consider the following economy:

Z = C + I + G

C = 10 + .6(Y – T)

I = 10 – 20i + 0.2Y

G = 10

T = 10

M^{d} = PY/(10*i)

M^{s} = 50

P = 1

- Find the IS and LM curves for this economy. What’s the equilibrium level of the interest rate and output?

Then suppose the economy opens to trade with another country.

Z = C + I + G + NX

C, I, G, T, and P are the same

NX (Y^{*}, Y, E) = .2Y^{*} - .2Y – (20/E)

Y^{*} = 100

i^{*} = .4

E^{e} = 1

P^{*} = 1

- Find the IS and LM curves for this economy. What are the levels of the equilibrium interest rate, exchange rate, and output?
- The government decides to increase G to 20. What is the effect on the economy?
- The central bank decides to increase the money supply to 100. What is the effect on the economy?
- Suppose the fiscal expansion in part (c) had been done under a system of fixed exchange rates. What action would the central bank have to take? (You can do this graphically/intuitively. You do not need to do the math.) What does this show you about the impact of fiscal policy changes in a fixed exchange rate country?