14.02: Principles of Macroeconomics, Fall 19992 pagesProblem Set 6Due: Wednesday, October 27.AnswersQuestion 1.a. FALSE. If the budget deficit is zero, a trade deficit could indicate either that investment ishigh OR that saving is low. In addition, a trade deficit could also indicate that private saving (S-I) issmaller than public spending (G-T).b. FALSE. If private saving is sufficiently high, a budget deficit can exist simultaneouslywith a trade surplus, as is the case in Japan.c. FALSE. See the focus box on Belgium versus the United States. Open economies havesmaller multipliers and net exports which are more sensitive to autonomous expenditure than largecountries.d. FALSE. The appreciation need not be painful, as expansionary fiscal or monetary policycan be combined with an apprecation to eliminate a trade surplus without changing equilibriumincome.e. FALSE. If exports and imports respond slowly to changes in relative prices, net exportswill actually improve before the trade balance deteriorates. This is the j-curve.Question 2.a.Y = C + I + G + X ? Q = 30 + 0.8ÂY ? 10Ã + 0.3YD? 0.3YY = 44 + 0.6YDThe multiplier for this economy is 2 when foreign output is fixed. The closed economymultiplier is 5, and it is different from the open economy multiplier because higher income increasesimports, which are a leakage from the economy, and do not bring about higher income.b. Y = YDimplies Y = YD= 110. The multiplier for this economy, taking into account thatforeign income is endogenous, is 3.125. It is higher than the open economy multiplier above becauseit takes into account the impact of higher imports on foreign income, which raises exports. As thedomestic country becomes small relative to the foreign country, this feedback effect goes awaybecause any change in imports will be small relative to foreign output, implying the change inforeign imports (and thus domestic exports) will be small as well. The point here is that smallcountries should probably not think about this channel in considering the consequences of policychanges.c. If Y = 125 then YD= 44 + 0.6 D 125 = 119. Using these two facts and the equationY = 24 + 2G + 0.6YDyields the equation, 125 = 24 + 2G + 0.6 D 119, which implies that G = 14.8.In the domestic country NX = 0.3Â119Ã ? 0.3Â125Ã = ?1.8. In the foreign countryNXD= ?NX = 1.8.d. If Y = YD= 125 then we have the following equation, 125 = 24 + 2G + 0.6Â125Ã,whichimplies G = GD= 13. In both countries, net exports are still zero, but the budget deficit hasincreased by 3.e. In part because of the benefits of doing nothing, as indicated from part c. In this example,there is also little difference in the cost in tax dollars in either strategy, so the foreign country maynot be willing to spend the nine additional units required to raise output from 119 to 125, giving upits favorable trade position as well.Question 3.a. A tax on foreign goods of rate tau affects Q(e(1+tau),Y) but not X(e,Y*). The higher priceof foreign goods to domestic consumers will reduce demand for imports (but not affect demand forexports), which given domestic income increases NX. This shifts the IS curve to the right, increasingdomestic equilibrium income. Higher domestic income will offset some of the initial increase in NX,but the overall effect is still favorable. A second effect of lower foreign income will reduce thiseffect, but does not change the results qualatatively. Intuitively, the government is reducing leakagesfrom the economy, increasing the multiplier.b. The tax has opposite effects in the foreign country, affecting their exports negatively,shifting the IS curve to the left, which reduces equilibrium income. Lower income and higherforeign income mitigates the reduced exports somewhat, but net exports still fall overall.c. Each shift in the IS curve will be reversed, but the overall volume of trade, described byQ+Q* will fall. If agents simply substitute domestic goods for foreign goods, output will remain
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