Problems 1. The change in preferences cannot change the terms of trade for a small open economy. Therefore, production of each good is unchanged. The shift in preferences implies increased consumption of good a, and reduced consumption of good b. If good a is originally imported, then imports and exports both increase. If good a is originally exported, then imports and exports both decrease. 2. If the marginal rate of transformation increases for every quantity of good a, then there is a shift in the production possibilities frontier. In particular, there is no change in the maximum amount of good b that can be produced, so there is no change in the horizontal intercept. The rest of the PPP becomes steeper and lies everywhere else above the original PPP. Production of good b increases, but production of good a may either rise or fall. If the increase in the marginal rate of substitution rotated the original PPP around the original production point, then production of good a would decrease. The outward shift in the PPP produces a positive income effect. However, because there can be no change in the terms of trade, there can be no substitution effect in consumption. Consumption of goods a and b both increase. Suppose that, as a first approximation, that production of good a is unchanged. If good b is originally exported, then exports of good b increase along with imports of good a. If good b is originally imported, then imports of good b decrease along with exports of good a. 3. Suppose that the economy starts out as in the figure below. The economy produces a 1 units of good a and b 1 units of good b. Consumers consume a 2 units of good a and b 2 units of good b. The economy therefore exports good b and imports good a. Now assume that a quota is placed on imports of good a, and that this quota is, in fact, a binding constraint. Denote the size of the quota as b 3 < b 2. The budget line now becomes vertical at b. 3 The new budget line is depicted in the figure below. The economy continues to produce at point ( a1, b 1). Consumption is at point ( a3, b 3). Therefore, less of good a is imported and less of good b is exported. Consumers are definitely worse off. They are no longer able to consume at a point on indifference curve, I. 1 They are forced to the less desirable indifference curve, I. 2
Chapter 13 International Trade in Goods and Assets 129
Chapter 13 International Trade in Goods and Assets 130 4. Government spending with perfect-complements preferences. (a) The net amount of income available from domestic production net of government spending in the first period is equal to 100 15 = 85, and the net amount of income available from domestic production net of government spending in the second period is equal to 120 20 = 100. The budget constraint is given by: C 100 C + = 85 + 1.1 1.1 Setting first-period and second-period consumption equal, we find that consumption in both periods is equal to 92.14. The current account surplus is equal to domestic income, 100 minus consumption, 92.14, minus government spending, 15, so the current account is equal to 7.14, a deficit. The endowment point, E, and the consumption point, F, are depicted in the first figure below.
Chapter 13 International Trade in Goods and Assets 131 (b) Net first-period income now falls to 75. The budget constraint is given by: C 100 C + = 75 + 1.1 1.1 Setting first-period and second-period consumption equal, we find that consumption in both periods is equal to 87.86. The current account surplus is equal to domestic income, 100 minus consumption, 87.86, minus government spending, 25, so the current account is equal to 12.86, a larger deficit. The endowment point, E, and the consumption point, F, are depicted in the second figure above. (c) In this problem, the increase in government spending leads to a larger current account deficit. The representative consumer increases her borrowing so that first-period consumption need not fall as much as the temporary increase in government spending. 5. Different borrowing and lending rates. (a) For levels of first-period consumption less than Y T, the consumer lends his private savings, and earns the world real rate of interest, r. For levels of first-period consumption greater than Y T, the consumer must borrow at the higher real rate of interest, r*. The representative consumer s budget line is bowed out, away from the origin. A change in r* steepens the part of the budget line where C > Y T. If the consumer was originally a saver, the change in r* has no effect on consumption or the current account surplus. If the consumer was originally a borrower, the budget relevant portion of the line rotates through the point ( Y T, Y' T' ). The substitution effect of the change in r* implies lower first-period consumption and higher second-period consumption. The income effect of the change in r* decreases both first-period and second-period consumption. Since first-period consumption unambiguously decreases, the current account surplus must increase. (b) A tax cut financed by government borrowing pushes the kink in the budget constraint to the right. If the representative consumer is a lender, there is no effect. If the representative consumer is a borrower, this represents a pure income effect. Both first-period and second-period consumption increase. If the current account is initially in balance, then the current account goes into deficit. The representative consumer is able to get to a higher indifference curve, so welfare increases. The government is able to pass along the ability to lend at the world real interest rate, so the additional costs of borrowing are eliminated. 6. Current account deficit policies. (a) If Ricardian equivalence holds, then the level of lump-sum taxation has no effect on the current account. The first group of advisors would therefore be wrong. A tax on investment shifts the investment demand schedule to the left. The output supply curve is unchanged. The output demand curve continues to pass through the original equilibrium position at the given world real interest rate. Because investment has decreased, absorption decreases, so the current account deficit declines. Therefore, the best advice to take would be to adopt the investment tax. (b) The concern with the current account deficit is misguided in this instance. The deficit is being used to finance investment spending. Over time, the increase in investment leads to a larger stock of capital, the output supply curve shifts to the right, and the current account deficit eventually disappears. If the policy is implemented, the stated objective could be met, but welfare would be lower, and the policy would continue to be needed, because it would be difficult for the economy to grow its way out of the situation that caused the deficit.
Chapter 13 International Trade in Goods and Assets 132 7. The expected future increase in government spending decreases lifetime wealth. The output supply schedule shifts to the right. At the unchanged real interest rate, investment is unchanged and both current and future consumption decrease. Absorption decreases and output increases, so the current account must increase. 8. A persistent increase in total factor productivity would shift both the output supply curve and the output demand curve to the right. The supply curve shifts due to higher employment and higher productivity. Investment demand increases due to the increase in expected future productivity. Consumption increases due to the increases in current and future income. The analysis of Chapter 11 argued that the shift in the supply curve would be larger than the combined effects of the changes in investment and consumption, so the current account balance would also increase. At the given world real interest rate, investment increases. At the given world real interest rate, the increase in domestic income increases consumption. These predictions are in line with the typical business cycle. However, this scenario is inconsistent with Figure 13.10 in the text. In the data, the current account is negatively correlated with output. In this example, output and the current account move in the same direction. 9. The increase in future government spending reduces the present value of lifetime income. Labor supply increases, so the output supply curve shifts to the right, and so output increases. Consumption spending decreases due the decrease in lifetime wealth. Investment is unchanged. Therefore, the current account surplus increases.