Problem Set 8
Professor Nordhaus and staff
Economics 122: Fall 2013
Due: Wednesday, December 4 in class
Problem Set 8 solutions
Sebastian is responsible for this answer sheet. If you have any questions about the solutions,
please email him at Sebastian.heise@yale.edu.
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1. Some puzzlers.
(To answer this question, you need to read Chapter 13 in Mankiw. The material on
a small open economy is slightly different from what we did in class.)
Use the Mundell-Fleming model for a small open economy to predict what would
happen to short-run aggregate output, the exchange rate, and net exports for each
of the following shocks:
a. Congress unexpectedly declares that all government spending should be
cut by 10%, with a flexible exchange rate.
First, we construct the MP-curve in the small open economy. The diagram below shows that
this curve is vertical, just as the LM-curve in the book. As usual the MP-curve is upward
sloping with respect to the interest rate. But since in a small open economy r = r*, there is no
independent monetary policy and hence the MP*-curve is independent of the exchange rate.
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We now consider the effect of the spending cut. This leads to a reduction in G. In the IS-LM*
diagram the IS-curve shifts to the left. In a closed economy, the central bank would now lower
the interest rate, based on the MP-equation. In the small open economy, however, the
downward pressure on the interest rates leads to capital outflows and a depreciation of the
exchange rate. This raises net exports exactly to compensate for the fall in G, and aggregate
income is unchanged. Net exports increase. See diagram.
b. A sharp decline in housing prices (such as in 2007-09) leads to a decline in
consumer wealth, with flexible exchange rates.
Assuming that the life cycle model of consumption holds, we know that a reduction in
consumer lifetime wealth will lead the consumer to reduce consumption today. The effect is the
same as in a. The drop in C shifts the IS-curve to the left, which causes a drop in the exchange
rate. Aggregate output remains unchanged, while net exports rise.
c. American consumers fall in love with European clothing, with a flexible
exchange rate.
American consumers’ love for European clothing increases imports from Europe. This reduces
net exports and shifts the IS curve to the left. As before, this depreciates the real exchange rate
and increases net exports back to their initial level. Overall, aggregate income and net exports
remain unchanged.
2. Trilemmas around the world. Be brief on each of the following.
a. Define the trilemma of international finance in your own words in one
sentence.
The trilemma states that a country cannot achieve at the same time a fixed exchange rate, free
capital flows, and retain monetary policy, but can achieve only two of the three.
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b. Give an example of something that is impossible according to the IT. Be specific
(i.e., pick a country and an impossible set of policies).
An example is China: the country has retained its monetary policy and controls its exchange
rate. It would be impossible for China to allow free capital flows. This is easiest to see in the
long-run open economy diagram below. Since China has retained its monetary policy, this
means that it can adjust rd relative to rw freely. If capital were allowed to flow freely, this would
shift the CF curve around, which would imply a fluctuating exchange rate. Since China wants
to keep its exchange rate fixed, it has to constrain capital flows to prevent the CF-curve from
shifting.
c. You are the chief economist of Belgium, which is part of the Eurozone. Prime
Minister Looser is running for reelection. The PM is committed to stay in the
Eurozone and to continue with open financial markets. The PM’s political
advisers have decided that they will advocate a radical new idea for Belgium:
to use monetary policy to stabilize the economy. Analyze briefly this proposal
and make a recommendation to the PM whether to adopt this idea from the
political advisers.
The PM should not adopt this idea because it is impossible to implement. Since he is in the
Eurozone, he has a fixed exchange rate relative to the other Euro countries. He also wants to
keep free capital flows. Then the PM cannot have monetary policy as well, as the figure in part
b. illustrates. Monetary policy would imply that Belgium could set different interest rates from
other countries in the Eurozone. This would lead to capital flows between Belgium and these
other countries caused by interest rate differentials, which would only stop once the exchange
rate between those countries were allowed to adjust. But this would mean leaving the
Eurozone.
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3. Krugmanomics
Paul Krugman (who won the Nobel Prize in Economics for his work on
international trade and globalization) has been a harsh critic of Chinese exchange
rate policy. He has argued that the Chinese policy of pegging the Chinese currency
to the U.S. dollar at an artificially low exchange rate has the effect of raising U.S.
unemployment. Do you agree? Explain. Assume for your answer that the U.S. and
China are the only two countries in the world.
We should agree with Krugman, at least in the short run (after all, he is a Nobel Prize winner).
The artificially weak Chinese currency against the dollar raises R for the U.S. trade with
China. The higher R lowers U.S. net exports to China. In the short-run, in a large open
economy framework, this reduces aggregate output Y. We have seen in class that this is
correlated with an increase in unemployment via Okun’s Law.
In the long-run, presumably relative prices will adjust so that the real exchange rate will not be
artificially low. U.S. unemployment will be at its natural level in the long-run.
4. The strange macroeconomics of quotas
The US current account has had a large trade deficit in recent years. There have
been proposals to put tariffs or quotas on imports. (A quota is a quantitative limit
on imports, such as a limit of 2 million automobiles per year.)
a. Show the impact of an import quota on GDP and the trade balance under
flexible exchange rates for a small open economy.
We again use the small open economy framework for this question. The import quota leads to
an increase in net exports, which shifts the IS-curve to the right. As seen in question 1.,
however, the resulting pressure to increase interest rates leads to capital inflows which
appreciate the exchange rate. This reduces net exports again. Overall, aggregate output and net
exports remain unchanged. See diagram.
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b. Answer the question for a large open economy.
In the large open economy, the central bank is actually able to set interest rates that differ from
the world interest rate. As before, the import quota raises net exports, shifting the IS-curve to
the right. The decrease in imports means that the country also requires less capital inflows to
pay for them, which shifts the CF curve to the right. This leads to the shift from point A to
point B in the diagram below. However, this is not yet an equilibrium. In response to the
increased output, the central bank raises the interest rate according to its Taylor rule, which in
turn again raises capital flows into the country. With a flexible exchange rate, the exchange
rate appreciates, reducing net exports slightly, although not enough to offset the initial effect.
This is the shift from B to C in the diagram. Overall, the import quota raises net exports and
aggregate output.
5. Debt and growth
a. Read the interesting analysis of the President’s Council of Economic
Advisers (CEA) on the impact of deficits on economic growth (see below),
primarily pp. 85-87 but you should skim the rest. This shows how our
economic growth models are actually used in economic policy.
b. Show an economic model that will explain the CEA’s reasoning. Use
algebra and/or a spreadsheet to replicate the results, in particular chart 215, which compares the two scenarios described. Note that the chart refers
to the difference between the economy with and without the policy.
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Assume that the rate of population growth is 0%, and that technological
change is exogenous.
This question asks us to compare the baseline scenario of no change in the savings rate to a
policy scenario with increased savings. Since only the relative change matters, I assume that
initial L = 1 and E = 1. I cannot assume a capital level: since we start out in steady state, the
correct capital level must be derived from the steady state condition. Hence:
Δ𝑘̃ = 𝑠𝑓̃(𝑘̃) − (𝑛 + 𝛿 + 𝑔)𝑘̃ = 0,
where the tilde denotes efficiency units of capital, K / EL. Given 𝑓̃(𝑘̃) = 𝑘̃ 1/3, it is easy to show
that
3/2
𝑠
𝑘̃ ∗ = (
) ,
𝑛+𝛿+𝑔
and with initial s = 0.13, n = 0, and δ+g = 0.115, we have that 𝑘̃ ∗ = 1.202. So the initial K =
1.202.
We can use the spreadsheet we used on one of the previous problem sets on growth to compute
the evolution of aggregate variables over time under the baseline and under the policy. In each
period, we can compute
𝑀𝑃𝐾 = 𝛼𝑌/𝐾
and
𝑀𝑃𝐿 = (1 − 𝛼)𝑌/𝐿.
The diagram below shows the percentage differences between the variables in the two scenarios.
12%
10%
8%
6%
4%
Capital diff
2%
MPL diff
0%
-2% 0
5
10
15
20
25
30
35
40
45
50
MPK diff
-4%
-6%
-8%
-10%
c. Give one important criticism of the model, and explain it carefully.
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One criticism of the model is that it assumes a closed economy with no spillovers from abroad.
This is clearly unrealistic. Capital inflows or outflows can influence investments and hence the
change in the capital stock over time significantly. The policy decision to reduce the deficit
could have an effect on capital flows and might therefore influence the difference between the
two scenarios.
* http://www.econ.yale.edu/~nordhaus/homepage/documents/ERP94.pdf
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