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Econ 154a Problem Set 10 Solution

Econ 154a Problem Set 10 Solution - Economics 154a Fall...

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Economics 154a Fall 2005 Bj¨orn Br¨ugemann Problem Set 10 Solution Problem 1 (Inflation Expectations and the Cost of Reducing Inflation) 1. The initial situation is illustrated in Figure 1. Firms expect the money supply to be M 1 , which would give rise to the aggregate demand curve AD ( P | M 1 , . . . ). Thus the price level they expect is P e 1 , which is the expected price level for which the ag- gregate supply curve AS ( P | P e 1 ) goes through the intersection of the AD ( P | M 1 , . . . ) curve with the ¯ Y -line. Since the firms don’t believe the central bank’s announce- ment, they don’t revise their expectations and the AS curve does not change. 2. By construction, if the AS curve is AS ( P | P e 1 ), then the economy attains full em- ployment if and only if the central bank confirms the firms’ expectations and sets the money supply equal to M 1 . 3. If the central bank follows through and implements M 2 , this is an unanticipated monetary contraction. Output and employment fall below the full employment level. This is illustrated in Figure 2. 4. Let P e 2 be the price expected by firms if they fully believe the announcement by the central bank. This expected price level would give rise to the AS curve AS ( P | P e 2 ) illustrated in Figure 3. Clearly, if firms believe the central bank’s announcement, then the economy ends up in point E c 2 , so the economy attains full employment and prices (and thus inflation from period 0 to period 1) will be very low. If the announcement is not fully credible, then the short run equilibrium of the economy will be a point on the AD ( P | M 2 , . . . ) curve between the points E 2 and E c 2 . The more credibility the central bank has, the closer the short run equilibrium will be to E c 2 . Thus higher credibility implies that the central bank is more successful at reducing the price level and is able to achieve this with a smaller drop of output below full employment. In this sense bringing down inflation is easier for a central bank with a lot of credibility. Problem 2 (Problems of Money-Growth Targeting) 1. In class we obtained the formula M = cu + 1 cu + res BASE (1)

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Figure 1: AD - AS diagram Y P ¯ Y AD ( P | M 1 , . . . ) P e 1 AS ( P | P e 1 ) E 1 Multiplying both sides by cu + res cu +1 and switching sides yields BASE = cu + res cu + 1 M. Thus to achieve the target M T , the central bank must set the base equal to BASE T = cu + res cu + 1 M T . (2) 2. Since all deposits are now in saving accounts, M1 now only consists of currency in circulation, which is unaffected by the “financial innovation”. How can we compute the amount of currency in circulation? As a first step, notice that the ratio of currency in circulation and reserves can be written as RES CU = RES DEP CU DEP = res cu where in the first step both the numerator and the denominator were divided by deposits, and the second step uses the definition of res and cu. Multiplying through by RES yields RES = res cu CU . (3) Next recall the definition of the monetary base BASE = RES + CU 2
Figure 2: Unanticipated Monetary Contraction Y P ¯ Y AD ( P | M 1 , . . . ) P e 1 AS ( P | P e 1 ) E 1 AD ( P | M 2 , . . . ) E 2

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