Problem Set 3 Econ 122a: Fall 2013 Prof. Nordhaus and Staff Due: In class, Wednesday, September 25 Problem Set 3 Solutions Sebastian is responsible for this answer sheet. If you have any questions about the solutions, please email him at Sebastian.heise@yale.edu. ==================================================================== 1. Various shocks on a small open economy Assume for the purpose of this question that the United States is a small classical open economy (Mankiw 141-142). Use the model in Chapter 6 to predict what would happen to the US trade balance (NX) in response to the following events: a. Wages in developing countries exporting to the U.S. rise sharply. Net exports unchanged. We assume that the U.S. is importing labor-intensive products from developing countries. An increase in foreign wages will make these products more expensive, leading the U.S. to reduce its imports from the developing countries. Since neither domestic savings nor domestic investments change, the S-I schedule stays unchanged and the real exchange rate appreciates to offset the reduced demand for foreign goods. This causes exports to decline, and overall net exports stay unchanged. See diagram. b. Americans decide that they want to reduce their carbon footprint and reduce their consumption sharply. Net exports increase. The reduction in consumption leads to an increase in domestic savings, since S = Y C G. This increases net exports. Intuitively, the country doesn t need to borrow as much from abroad and therefore imports less, or can lend more to foreigners and exports more. The figure illustrates the case where consumption falls so much that net exports become positive. 1
Note also that the real exchange rate depreciates, making domestic goods cheaper relative to foreign goods and supporting the expansion of exports. c. The Congress puts a large tariff on imports from developing countries to punish countries with low wages and to reduce the trade deficit. Net exports unchanged. The tariff reduces imports from foreign countries, since their products are now more expensive. This sets in motion the same mechanism as in part a., and net exports remain unchanged. d. The US Congress cuts federal military purchases to reduce the budget deficit. Net exports increase. The reduction in military purchases leads to a fall in government spending, G, and hence an increase in domestic savings. As illustrated in part b., this implies an increase in net exports. As before, the real exchange rate falls. 2. Lilliputian economics Lilliputia is a small open economy, described by the following set of equations: Y = C + I + G + NX Y = 5000, G = 1000, T = 1000 C = 250 + 0.75 (Y-T) I = 1000 50r NX = 500 500R r = r* = 5% per year In these equations, R is the real exchange rate, and r* is the world interest rate. Suppose that a large number of foreign countries begin to subsidize investment, but Lilliputia does not institute such an investment subsidy. 2
a. Solve for Lilliputia s national saving, investment, the trade balance, and the equilibrium exchange rate before the investment subsidy. We have that C = 250 + 0.75(5000-1000) = 3250. Then national saving is S = Y C G = 5000 3250 1000 = 750. Investment is I = 1000 50*5 = 750. It follows that NX = S I = 0. The real exchange rate is therefore R = 1. b. How will the investment subsidy of the foreign countries influence foreign countries investment demand function (as a function of the interest rate)? What happens to the world interest rate? Draw a hypothetical world supply and demand for savings and investment. The investment subsidy will increase the foreign countries investment at any interest rate. Therefore, the investment curve in the S-I diagram for the world shifts upward. This is illustrated in the diagram. Since the world supply of savings is assumed fixed, the subsidy will just lead to an increase in the world interest rate to r**. Note that r* would also increase if we assumed that savings were not perfectly inelastic (i.e., the savings curve is not vertical, but with finite positive slope). In that case investment and savings expand, and so the rise in r* would not be as large as in the perfectly inelastic case. c. Assume that as a result of the investment subsidies, r* rises to 10%. How is investment in Lilliputia affected by this change in the world interest rate? Investment is now I = 1000 50*10 = 500. Intuitively, investment has declined because firm now have to pay higher interest rates to finance their projects. d. What happens to Lilliputia s trade balance (NX) and the real exchange rate (R) after the investment subsidies? Interpret. Assuming that S did not change, we now have NX = S I = 750 500 = 250. Thus, Lilliputia is now running a trade surplus. Its excess savings are exported (capital exports), and are used to finance other countries imports of Lilliputia s goods. Since the supply of Lilliputia s currency has increased, the real exchange rate depreciates to R = 0.5. 3
3. A large open economy prepares for war (You will need to study the Appendix to Chapter 6 for this question.) We now realistically assume that the US is a large classical open economy. It faces the prospect of military conflict. For each of these events, describe the effect on the US national savings, domestic investment, the trade balance, the US interest rate, and the exchange rate of the dollar. To keep things simple, consider each of the following effects separately. a. Negotiations in the Mideast break down. The US, fearing it may need to engage in prolonged hostilities, increases its purchases of military equipment. Government expenditures G increase. This lowers US national savings since S = Y C G. Reduced savings lead to excess demand in the market for loanable funds and raise the US interest rate to equilibrate supply and demand. Higher interest rates mean that domestic investments fall, and furthermore the net flow of capital to other countries declines. Consequently foreign countries receive less US currency and the dollar appreciates. Net exports fall. See diagram. b. Other countries worry about their own security. As a result, they increase their purchases of high-technology weapons, which are a major export of the United States. Foreign governments increase their expenditures, leading them to reduce government savings. This leads to excess demand for savings abroad and raises the foreign interest rate. The rise in the foreign interest rate increases the net flow of capital, which means that less capital is available domestically. This raises the domestic interest rate. Domestic investment falls, but this fall just mitigates the interest rate rise and is not enough to offset it. Domestic savings are unaffected. The net outflows of capital increase the supply of dollars, which depreciates the real exchange rate. Net exports increase. c. The prospect of war frightens US consumers, and they increase their savings rate in response. 4
The mechanics are just the reverse as in part a. The domestic savings rate increases. This leads to an excess supply of savings and reduces the domestic interest rate. Therefore, domestic investment and the net flow of capital to other countries increase. This reduces the real exchange rate and raises net exports. d. Investors around the world also get frightened and move massive quantities of their financial portfolios into good old safe US Treasury securities. The capital inflows lead to a reduction of the net flow of capital (CF). This increases the supply of capital in the US and depresses the domestic interest rate. Note that while this in turn tends to raise capital outflows again, this is only a partial effect and therefore the net flow of capital still falls. Domestic savings remain unchanged, while the decline in the interest rate raises domestic investment. The reduced level of capital outflows lowers the supply of US dollars and appreciates the foreign exchange rate, which reduces net exports. 5