Homework 2 2009
DUE: July 20th Monday
Total points: 47 points
1. Consider an economy described by the following equations:
5,000
1,000
1,000
250 0.75 1,000 50 500 500
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a. In this economy, solve for national saving, investment, the trade balance, and the
equilibrium exchange rate. (4 points)
750
1000 505 750
0
, thus 500 500 0, 1 .
b. Now suppose that rises to 1,250. Solve for national saving, investment, the trade
balance, and the equilibrium exchange rate. Explain what you find. (4 points)
500
1000 505 750
250
, thus 500 500 250, 1.5 .
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Homework 2 2009
c. Now suppose the world interest rate rises from 5 to 10. (G is again 1,000). Solve for
national saving, investment, the trade balance, and the equilibrium exchange rate.
Explain what you find. (4 points)
750
1000 5010 500
250
, thus 500 500 250, 0.5 .
2. The country of Leverett is a small open economy. Suddenly, a change in world
fashions makes the exports of Leverett unpopular.
a. What happens in Leverett to saving, investment, net exports, the interest rate, and
the exchange rate? (4 points)
When Leverett’s exports become less popular, its domestic saving does not
change. This is because we assume that output is determined by the labor resources
available. And thus there is no change in the national income and consumption.
Investment also does not change since investment depends on the interest rate, and
Leverett is a small open economy that takes the world interest rate as given. Because
neither saving nor investment changes, net exports which is equal to , do not
change either.
The decreased popularity of Leverett’s exports leads to a shift inward of the net exports
curve. At the new equilibrium, net exports are unchanged but the goods produced in
Leverett become cheaper relative to the foreign goods.
Even though Leverett’s exports are less popular, its trade balance has remained the
same. The reason for this is that the decrease in the price of domestic goods provides a
stimulus to net exports, which overcomes the unpopularity of its exports by making
them cheaper.
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Homework 2 2009
Real Exchange Rate
%
&
% & NX Net Exports
% &
b. The fiscal policy makers of Leverett want to adjust taxes to maintain the exchange
rate at its previous level. What should they do? If they do this, what are the overall
effects on saving, investment, net exports, and the interest rate? (6 points)
If the government reduces taxes, and then disposable income and consumption rises.
Private saving rises as well but public saving will fall to a larger extent. Hence national
saving will decrease so that net exports also fall. This fall in net exports puts upward
pressure on the exchange rate that offsets the decreased world demand. Investment
and the interest rate would be unaffected by this policy since Leverett takes the world
interest rate as given.
3. What will happen to the trade balance and the real exchange rate of a small open
economy when government purchases increase, such as during a war? Does your
answer depend on whether this is a local war or a world war? (5 points)
The increase in government spending decreases government saving and, thus decreases
national saving; this shifts the saving schedule to the left. Given the world interest rate,
the decrease in domestic saving causes the trade balance to fall and the real exchange
rate to rise.
The answer to this question does depend on whether this is a local war or a world war.
A world war causes many governments to increase spending; this increases the world
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Homework 2 2009
interest rate. The effect on the trade balance depends on the size of the change in the
world interest rate relative to the size of the decrease in saving.
4. Country A and country B both have the production function
' (), * )+/- *+/a. Does this production function have constant returns to scale? Explain. (2 points)
Yes. . 2/, 20 2/ %/& 0%/& 2
b. What is the per-worker production function, 1 23? (2 points)
4 56 √6
c. Assume that neither country experiences population growth nor technological
progress and that 5 percent of capital depreciates each year. Assume further that
country A saves 10 percent of output each year and country B saves 20 percent of
output each year. Using your answer from part (b) and the stead-state condition that
investment equals depreciation, find the steady-state level of capital per worker for
each country. Then find the steady-state levels of income per worker and
consumption per worker. (6 points)
The steady state condition: 8√6 96
Saving Rate
Depreciation Rate
Steady State capital per
worker
Steady State consumption
per worker
Steady State output per
worker
Country A
0.1
0.05
4
Country B
0.2
0.05
16
2
4
1.8
3.2
d. Suppose that both countries start off with a capital stock per-worker of 2. Explain
how the capital stock per-worker, consumption per-worker, and output per-worker
evolve over time for each country. (6 points)
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Homework 2 2009
For this problem, one thing we know is that no matter at which point the economy
starts it will converge to the steady state.
5. Describe the difference between frictional unemployment and structural
unemployment. And give some explanation why the real wage may remain above the
level that equilibrates labor supply and labor demand. (4 points)
The frictional unemployment is the unemployment caused by the time it takes to match
workers and jobs. Finding an appropriate job takes time because the flow of information
about job candidates and job vacancies is not instantaneous. Because different jobs
require different skills and pay different wages, unemployed workers may not accept
the first job offer they receive.
In contrast, structural unemployment is the unemployment resulting from wage rigidity
and job rationing. These workers are unemployed not because they are actively
searching for a job that best suits their skills, but because at the prevailing real wage the
supply of labor exceeds the demand. If the wage does not adjust to clear the labor
market, then these workers must wait for jobs to become available.
One possible explanation for the fact that the real wage may remain above the level
that equilibrates labor supply and labor demand is the minimum wage laws.
Click the link below to read an article on the recent change in the minimum wage law.
http://money.cnn.com/2009/07/06/news/economy/minimum_wage/index.htm?sectio
n=money_mostpopular
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