14.02 Principles of Macroeconomics

Problem Set 5

Posted: Wednesday, March 21, 2001

Due: Wednesday, April 4, 2001

Please remember to write your TA’s name and section time on the front page or your problem set.

Part 1: True/False Questions: Decide whether each statement is true or false and justify your answer with a short argument. (2 points each, 18 points total)

1.      A country cannot reduce its trade deficit through a depreciation. Examining the equality NX= Sp + Sg – I shows that the trade deficit is solely determined through local private saving, government saving and investment, and none of these are affected by the exchange rate.

2.      An expansionary fiscal policy will eventually reduce the trade deficit.

3.      A real depreciation would lead to an immediate improvement in the nominal trade balance.

4.      Due to the nominal appreciation of the US Dollar, I was able to do more things during my trip to Israel.

5.      Technology improvement shifts the AS curve, and leads to a lower prices and higher GNP.

6.      Under perfect capital mobility, when a country joins a system of fixed exchange rates, it gives up the freedom to choose its interest rate.

7.        The increasing productivity and output of another country is a threat to the prosperity of the US.

8.        The twin deficits refer to the government's budget deficit and the international trade deficit.

9.      Similar to consumption, changes in the growth rate of capital spending are smoother than changes in the growth rate of GNP.

Part 2: Open Economy IS-LM (6 points each, 36 points total)

Consider the following open economy:

C=20+0.8*(Y-T)

I=30+0.3*Y-20*i

G=T=10

NX (Net Exports)=40-0.3*Y-30/E

MD=Y-50*i

MS=295

P=P*=1, where P is the domestic and P* is the foreign price level

Expected exchange rates, Ee , =1, the foreign interest rate, i* , = 0.1, and the exchange rate is flexible.

1.      Write down and graph the LM relation. Explain what it represents and whether there are any differences relative to the closed economy.

2.      Write down and interpret in words the equilibrium condition of the goods market. Are there any differences relative to the closed economy?

3.      Derive and graph the open economy IS curve (in the Y-i space). Interpret, and explain any differences relative to the closed economy IS curve.

4.      Explain the effects of a fiscal expansion using words and graphs (no algebra): what happens to output, the interest rate and the exchange rate? What happens to investment and net exports? Answer the same questions for a monetary expansion as well.

5.      How can the government decrease interest rates without changing output? What will happen to the exchange rate and net exports?

6.      Can the government achieve lower interest rates without changing output and net exports in our model? In reality?

Part 3: Exchange Rates And Expectations (8 points each, 24 points total)

Consider an open IS-LM economy with fixed exchange rates E = 1, and the domestic interest rate (i) and the foreign interest rate (i*) given below:

i=0.15, i*=0.6.

1.      What's the exchange rate people expect (Ee) in this market?

2.      What will happen if people are right and the Central Bank devalues the currency to the level people think is correct? In particular, what happens to interest rates and output?

3.      How does your answer change if, after the devaluation, people start thinking that the Central Bank is 'weak' and believe that it will start printing lots of money?

Part 4: Volatility of Investment (8 points each, 24 points total)

Consider an economy with N firms, each of them composed of one entrepreneur and capital. All firms have the same production function: yn,t = At kn,td  (no labor is used).

The real interest rate (r) and the depreciation rate (d) are given as constant. Firms can adjust (either up or down) their stock every period.

1.      What are the:

(a)    GNP of the economy (Y);

(b)   Per-period profit function;

(c)    Optimal capital of the economy (K*);

(d)   Capital/Output ratio (K/Y).

2.      If At = At-1, find gross and net investment at time t (IN).

3.      Assume d=0.6, r=4%, d=10%, A1=A2=A3=1.0, A4=A5=A6=1.2, K0=K1*, IN0=0.Find and plot the path of GNP, K and I.