Professor Christina Romer SUGGESTED ANSWERS TO PROBLEM SET 6

Transcription

1 Economics 2 Spring 2017 Professor Christina Romer Professor David Romer SUGGESTED ANSWERS TO PROBLEM SET 6 1.a. The main tool we use to analyze short-run fluctuations in the economy is the Keynesian cross. The two lines in the Keynesian cross diagram are the 45 degree line, Y = PAE, and the expenditure line (PAE), PAE = C + I p + G + NX. The problem says that consumers expectations become permanently less optimistic, and that this causes a fall in autonomous consumption. That is, the intercept of the consumption function, C = C + c (Y T), declines. This means that there will be a downward shift of the expenditure line at a given Y, C is lower than before, and so C + I p + G + NX is PAE Y = PAE PAE 1 PAE 2 lower than before. This is shown as the shift from PAE 1 to PAE 2 in the diagram. (Note that because of Y 2 Y* Y nominal rigidity, inflation does not change in the short run, and so the Fed does not change r.) The downward shift of the expenditure line lowers output (from its initial value, Y 1=Y*, to Y 2). As usual, the change in Y is larger than the amount of the vertical shift of the expenditure line because of the multiplier effect. That is, the decrease in PAE has an additional negative effect on output because consumption depends on Y. As a result, the total fall in C is larger than just the fall in autonomous consumption, C. b. What brings output back to potential is the behavior of inflation and the response of the Federal Reserve to inflation. After the downward shift of the expenditure line, Y is less than Y*. As a result, after a while inflation starts to fall. The Fed, following its reaction function, lowers r. The fall in r raises I p and C at a given Y, and so causes the expenditure line to start to shift back up. After a while, the expenditure line might be the one shown as PAE MR (for medium run ), and so output would be at Y MR above Y 2 but still below Y*. PAE Y = PAE PAE 1,LR PAE MR PAE 2 Y 2 Y MR Y* (Y 1,LR) Y Even though Y MR is above Y 2, it is still below Y*. That is, firms are still operating below their normal, comfortable capacity. As a result, inflation continues to fall, so the Fed continues to lower r. Thus the expenditure line continues to shift up and output continues to rise. The process ends when Y is back at Y*. (That is, we need inflation to have fallen by enough that the Fed has cut r by enough to shift the expenditure line back up to its initial position, so that it again crosses the 45 degree line at Y*. Thus the final expenditure line, PAE LR, is the same as the initial expenditure line, PAE 1.) When Y = Y*, inflation holds steady, and so there is nothing causing things in the economy to change the economy is in long-run equilibrium. The initial level of output, Y 1, and its level when the economy is back in long-run equilibrium, Y LR, are both equal to potential output, Y*.

2 2 c. The tool we use to analyze the determination of the real interest rate and investment in the long run (that is, when output is at potential) is the long-run saving and investment diagram. As described in part (a), the change in consumers expectations permanently reduces consumption (at a given level of disposable income and of the real interest rate), and so increases saving. Thus the long-run supply of saving curve, which shows saving as a function of the real interest rate when output is equal to its potential or long-run value, shifts out (from S 1 to S 2). The long-run effect is that the real interest rate falls (from r 1 to ) and investment rises (from to I 2 ). r 1 S 1 S 2 I 2 S*,I* Notice that the implication of the long-run saving and investment diagram for the behavior of r in the long run is the same as the implication of the analysis of the economy s behavior over time in parts (a) and (b). In parts (a) and (b), we found that r did not change in the short run (because of nominal rigidity and the Fed s reaction function), but then fell gradually as output returned to Y* (because inflation was falling and the Fed was moving down along its reaction function in response). Thus, that analysis implies that when output is back at potential, the real interest rate is lower than it was initially matching what the long-run saving and investment diagram shows. Notice also that it is harder to figure out what happens to consumption in the long run using the analysis in parts (a) and (b) than using the long-run saving and investment diagram. Parts (a) and (b) tell us that consumption falls in the short run, but then rises gradually as the economy returns to potential (because r is falling and Y is rising). Thus if we try to use this approach, the overall change in consumption from the initial long-run equilibrium to when the economy is in the new long-run equilibrium is not obvious. But the long-run saving and investment diagram shows clearly that normal saving (S*) is higher in the long run. Since consumption equals disposable income minus saving, and disposable income (Y T) does not change in the long run, it is clear that consumption is lower in the long run. The case of an open economy. Although the problem did not ask what happens to net capital inflows, net exports, and the exchange rate, we can figure out what happens to those variables. In part a (the short run): Inflation does not change, and so the Fed does not change the real interest rate. As a result, net capital inflows do not change, which tells us that net exports do not change (since NX = KI). Neither the supply nor the demand curve in the market for foreign currency shifts, and so the exchange rate does not change. In part b (the return to potential output): Inflation is falling, and so the Fed is reducing the real interest rate. Thus, assets in the U.S. look less attractive relative to assets abroad. Hence net capital inflows fall. It follows that net exports rise. (Thus the PAE line in part (b) shifts up as r falls not only because C and I p rise, but also because NX rises.) In the market for foreign exchange, the supply curve of dollars shifts to the right (since Americans want to buy more foreign assets), and the demand curve for dollars shifts to the left (since foreigners want to buy fewer foreign assets). Thus the exchange rate falls; that is, the dollar depreciates. It is this depreciation of the dollar that makes foreigners want to buy more American goods and services and Americans want to buy fewer foreign goods and services, and so causes NX to rise.

3 3 In part c (the long run): The tool we use to analyze the determination of the real interest rate, saving, investment, and net capital inflows in the long run is the long-run S+KI and I diagram. The change in consumers expectations reduces consumption at a given level of the real interest rate when output is equal to potential, and so increases saving at a given r. There is no reason for net capital inflows at a given r to change. Thus the long-run S+KI curve, which shows saving plus net capital inflows as a function of the real interest rate when output is equal to its potential or long-run value, shifts out. Because it was the S portion and not the KI portion that shifted, we show the shift as being r 1 I 2 S 1 +K S 2 +K from S 1 +K to S 2 +K. The long-run effect is that the real interest rate falls (from r 1 to ) and investment rises (from to I 2 ). To figure out what happens to KI, e, and NX in the long run, note that the KI function did not shift. Thus, the change in r causes a movement along the KI function: r falls in the long run, so KI falls in the long run. Since NX = KI, net exports rise in the long run. In the market for foreign exchange, the fall in r shifts the supply curve of dollars to the right and the demand curve for dollars to the left, so that the exchange rate falls in the long run. S*,I* 2.a. If American wealthholders lose confidence in European assets, and so decide to buy fewer European stocks and bonds, this means that Americans will desire to trade fewer dollars for euros to buy European assets. Thus, the supply curve of dollars in the foreign exchange market will shift to the left (from S 1 to S 2). Since the problem does not describe any change in the preferences or views of European wealthholders, there is no reason for the demand curve for dollars to shift. As a result, the price of the dollar in terms of euros will rise (from e 1 to e 2). The dollar will appreciate. b. If European countries put tariffs on a number of goods from the United States, this means that at a given exchange rate, American goods are now more expensive for Europeans. As a result, Europeans will want to buy fewer American goods, and so they will demand fewer dollars in the foreign exchange market. That is, the demand curve for dollars shifts to the left. The problem says that the United States does not change its trade policy. Thus the supply curve of dollars does not shift: at a given exchange rate, Americans want to trade the same quantity of dollars for euros as before. The price of the dollar in terms of euros will fall (from e 1 to e 2). The dollar will depreciate. Price of $ in euros e 2 e 1 Price of $ in euros e 1 e 2 S 2 S 1 D 1 Quantity of $ S 1 D 1 D 2 Quantity of $

4 Notice that even though the United States has not imposed tariffs, Americans end up buying fewer European goods: the depreciation of the dollar makes European goods more expensive, and so causes Americans to buy fewer of them. This shows up in the diagram as a movement up along the supply curve of dollars. Likewise, the depreciation of the dollar encourages European purchases of American goods, which offsets some of the effect of the tariffs on Europe s imports from the United States. As discussed in lecture on Thursday, the effects of the exchange rate movement on net exports end up fully offsetting the effects of the tariffs, so that the tariffs do not increase Europe s net exports or decrease the United States s net exports. 4 c. If American real interest rates rise relative to those in Europe, Europeans will want to buy more American assets, and Americans will want to buy fewer European assets. The increase in Europeans desire to buy American assets will cause them to demand more dollars in the foreign exchange market at a given exchange rate. This corresponds to a shift out in the European demand curve for dollars (from D 1 to D 2). Likewise, the decrease in Americans desire to buy European assets will cause them to supply fewer dollars in the foreign exchange market at a given exchange rate, and so shift the supply curve of dollars back (from S 1 to S 2). The result is that the price of dollars will rise (from e 1 to e 2). The dollar will appreciate. Price of $ in euros e 2 e 1 S 2 S 1 D 2 D 1 Quantity of $ 3.a. As we have discussed, the Federal Reserve has no choice about what the real interest rate will be in r the long run: it must equal the real interest rate where saving and investment are equal in the longrun saving-investment diagram. Thus when the Fed chooses its reaction function, it is implicitly deciding what inflation will be in the long run: in the long run, inflation must be at the level that leads the Fed, following its reaction function, to set r =. Thus to raise its inflation target, the Fed needs to shift its reaction function so that the inflation rate it sets when r = is higher than before. As the diagram shows, this requires a shift of the reaction function to the right (or down). The Fed s inflation target (that is, what inflation will be in the long run) rises from π 1 to π 2. function 1 function 2 π 1 π 2 π b. Because of nominal rigidity, inflation does not change in the short run in response to the shift in the Fed s reaction function. Thus in the short run, it is still equal to the Fed s old target, π 1 (recall that the economy started in long-run equilibrium). The Fed now sets the real interest rate according to its new reaction function. Thus it lowers the real interest rate from to. Because of nominal rigidity, the nominal interest rate falls as well: i = r + π, and the fall in r with no change in π means that i falls. r function 1 function 2 π 1 π 2 π

5 5 The way the Fed controls interest rates is by buying and selling bonds in exchange for currency. If it wants to increase the money supply, it buys bonds with currency, thereby putting more currency in circulation. If it wants to decrease the money supply, it sells bonds in exchange for currency, and so reduces the amount of currency in circulation. i i 1 i 2 MS 1 MS 2 The supply and demand diagram of the money MD 1 market shows that for the Fed to lower the nominal interest rate (which, because of nominal rigidity, is what it needs to do to lower the real interest rate in M the short run), it needs to increase the supply of money (for example, from MS 1 to MS 2, lowering the nominal interest rate from i 1 to i 2). To do this, it needs to buy bonds for currency, thereby increasing the amount of currency in the economy. c. The way the change in the reaction function eventually brings about the higher rate of inflation is through the usual process by which the economy gets back to long-run equilibrium. The Fed s reduction in the real interest rate increases consumption (at a given Y T) and planned investment, and so shifts the PAE curve in the Keynesian cross diagram up. As a result, output rises from its initial level of Y 1=Y* (since the economy started in long-run equilibrium). This is shown as the shift up in the PAE line from PAE 1 to PAE 2 (and the resulting rise in output from Y* to Y 2) in the right-hand diagram below. Although inflation does not respond immediately to the change, over time the fact that output is greater than Y* causes inflation to rise. As inflation rises, the Fed, following its new reaction function, raises the real interest rate (see the left-hand diagram below). This starts to shift the PAE line back down. After a while, the PAE line might be in a position like PAE MR (for medium run ), so that output is at Y MR, and inflation and the real interest rate might be at π MR and r MR. Since output is still above Y*, inflation continues to rise. The process continues until inflation has risen to the point where the Fed, following its new reaction function, sets r =. This happens when π = π 2. When that happens, the PAE line is back to its original position, and Y is back at Y*. r function 1 PAE Y = PAE PAE 2 PAE MR function 2 PAE 1,LR r MR π 1 π MR π 2 π Y* Y MR Y 2 Y (Y 1,LR)

6 d. The change will not affect the real interest rate in the long run. The Fed s actions have no effect on the long-run saving and investment diagram, which shows saving and investment as functions of the real S 1,S 2 interest rate when Y = Y*. When the Fed temporarily moves r away from, it moves Y temporarily away from Y*. When Y is not equal to Y*, the long-run saving and investment diagram is not the right tool r 1, to use to understand the behavior of the real interest rate. But when Y is back at Y*, it is; and since the Fed has done nothing to affect long-run investment,i 2 demand or long-run saving supply, is the same as it was originally. This is an example of the general rule that the Fed has no choice about what the real I 1, I 2 S*,I* interest rate will be in the long run; that is, the Fed cannot affect the real interest rate in the long run. The case of an open economy. As with problem 1, although this problem did not ask what happens to net capital inflows, net exports, and the exchange rate, we can figure out what happens to those variables. In part c (the short run and the return to potential): Because of the shift in the Fed s reaction function, the real interest rate falls. This makes U.S. assets less attractive relative to foreign assets, and so net capital inflows fall. Since NX = KI, net exports rise. (Thus the PAE line is shifting up because C, I p, and NX are all rising.) In the foreign currency market, the fall in r shifts the supply curve of dollars to the right and the demand curve of dollars to the left, and so the price of dollars (the exchange rate) falls; that is, the dollar depreciates. The depreciation of the dollar is what causes Americans to want to buy fewer goods and services from aboard and foreigners want to buy more goods and services from the United States. As inflation rises and the Fed increases the real interest rate along its reaction function, everything moves back toward where it started: net capital inflows rise, net exports fall, and the exchange rate rises. In part d (the long run): Nothing has changed I, S, or KI as functions of r when output is at its potential level. Thus in the long run, the real interest rate, net capital inflows, and net exports are all back where they were before the change in the Fed s reaction function. 6