Problem Set 8 Economics 122: Fall 2013
Professor Nordhaus and staff 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 .
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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.
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.
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.
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.
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 2-15, which compares the two scenarios described. Note that the chart refers to the difference between the economy with and without the policy. 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:
Δk=sfk-n+δ+gk=0,
where the tilde denotes efficiency units of capital, K / EL. Given fk=k1/3, it is easy to show that
k*=sn+δ+g3/2,
and with initial s = 0.13, n = 0, and δ+g = 0.115, we have that k*=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.
c. Give one important criticism of the model, and explain it carefully.
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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