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# ans2 - Department of Economics University of California...

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Department of Economics University of California, Berkeley Spring 2006 Economics 182 Suggested Solutions to Problem Set 2 Problem 1 First note that r e = R - π e , that is, the real interest rate equals the nominal interest rate minus the expected inflation rate. When we studied the effect of an unexpected permanent increase in the money supply we concluded that (i) the increase in the money supply M s lowers the interest rate R since the price level P is fixed, (ii) by the neutrality of money we know that an increase in M s will ultimately produce an increase in P , that is, there is a positive expected inflation rate π e . Hence, we know that the real interest rate r will decrease even more than what the nominal interest rate does because of the expectation of inflation. This is depicted in Figure 1. Then, once prices start to increase, the nominal interest rate increases. Moreover, as prices increase some of the expected inflation becomes realized inflation and hence less inflation is expected in the future. This causes the initial gap between the nominal and the real interest rate to shrink. Finally, in the long run, prices have fully adjusted and hence there are no more expectations of future inflation and the nominal and real interest rates equalize. The real interest rate can become negative if the increase in M s is large enough as to produce a large drop in the nominal interest rate and a large increase in future expected inflation. In Figure 2 we see such case. Problem 2 The economy starts with long-run levels of M 0 , P 0 , R 0 , and E 0 . A permanent decrease in the money supply makes E e fall because people expect the dollar to appreciate in the future. The real money supply falls from M 0 /P 0 to M 1 /P 0 as Figure 3 shows. Since the level of prices is fixed at P 0 in the short run, the interest rate increases from R 0 to R 1 to put the money market back in equilibrium. In the foreign exchange market we see that the return on dollar deposits exceeds the return on euro deposits (measured in dollars) and hence the dollar appreciates today to E 1 . Also, the decrease in E e makes the arbitrage curve to shift down and hence the exchange rate appreciates even further to E 2 . As time goes by, the price level begins to fall towards it’s long-run level at P 1 . Hence, the real money supply increases until M 0 /P 0 = M 1 /P 1 . This causes the interest rate to go down back to R 0 and thus the exchange rate depreciates to its long-run value E 3 . 1

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Regarding the time paths, we see that the exchange rate undershoots its long-run value ( E 2 < E 3 ), the interest rate moves back to its original value and prices drop as much as the money supply decrease to make real money balances remain unchanged. Problem 3 (a) When prices are fully flexible, an increase in M s produces an immediate increase in prices in the same proportion. Hence, the real money balances M/P remain unchanged and the interest rate remains at its initial level. In the foreign exchange market, the increase in the money supply produces an increase in the expected exchange rate E e
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