**14.02 Principles of Macroeconomics**

**Problem Set 5**

**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

M^{D}=Y-50*i

M^{S}=295

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

Expected exchange rates, E^{e
}, =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 (E^{e}) 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: y_{n,t} = A_{t} k_{n,t}^{d}^{
} (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
A_{t} = A_{t-1}, find gross and net investment at time t (I_{N}).

3.
Assume
d=0.6, r=4%, d=10%, A_{1}=A_{2}=A_{3}=1.0,
A_{4}=A_{5}=A_{6}=1.2, K_{0}=K_{1}*, I_{N0}=0.Find
and plot the path of GNP, K and I.