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Homework Assignment #3 Economics 215 Intermediate Macroeconomics Assigned: Tuesday, April 25, 2000 Due: Thursday, May 4, 2000 1. The Cost of Money Holding. Consider a two period model of the economy. a. In period 1, the price of goods, P1 = 1. In period 2, the price level is P2 = 1.25. Calculate the net inflation rate P̂2 in period 2. If the real interest rate is r = 0, what is the nominal interest rate. ˆ P2 .25 1 i 1.25 b. Consider a consumer who lives during period 1 and period 2. The consumer pays no taxes. The consumer will earn income in each period by selling Q1 = 200 goods in period 1 and Q2 = 100 goods in period 2. Thus, the income from selling goods in period 1 is P1Q1 = 200. The income from selling goods in period 2 is P2Q2 = 1.25100=125. At the end of period 1, the consumer will store any income not spent on consumption in the form of money M that pays no interest or bonds that pay interest, 1+i. This wealth plus second period income can be spent on consumption in period 2. This implies that the budget constraints of the consumer are: M B P1Q1 P1C1 P2 C 2 P2 Q2 M (1 i) B Use the prices in section a to show that these two equations imply that i M1 C1 C2 300 1 i P1 M M B B M B P1Q1 P1C1 1 Q1 C1 Q1 C1 1 P1 P1 P1 P1 P2 C 2 P2 Q2 M (1 i ) B P2 C 2 PQ P2 1 M (1 i ) B 1 2 2 , 1 i P1 1 i P1 1 i P1 1 i P1 1 r 1 i P1 C2 Q2 1 M B 1 r 1 r 1 i P1 P1 C2 Q2 M 1 M Q1 C1 1 ,1 r 1 1 r 1 r 1 i P1 P1 1 M i M C1 C 2 Q1 Q2 1 C1 C 2 300 1 i P1 1 i P1 c. Assume that the consumer smoothes consumption perfectly C C1 C 2 . Solve for consumption, C in each period under the following circumstances, M1 0 , C1 = C2 = 150 P1 M ii. Money holdings are proportional to real output 1 f (Q1 ) .5 Q1 P1 i .2 C1+C2 = 300 - .2*.5*200=280C1 + C2 = 140 1 i i. The consumer holds zero money: 2. Money Creation and the Price Level a. In Korea, the currency supply is 500 won (i.e. CU = 500). The currency to demand deposit ratio is cd = .2 and the reserve to deposit ratio is .2. Solve for reserves, R; demand deposits, D; high-powered money, Mh; and M1 = CU+D. D=2500, M1 = 3000, R = 500, Mh = 1000. b. In Korea, the money demand curve is a function of the output level and MD Q the interest rate. f (Q, i) .5 . If Q = 500 and money supply is P i equal to M1 from the previous section, what is the price level that sets money supply equal to money demand when i = .1. What is the price level that sets money supply equal to money demand when i = .25. Explain with 1 paragraph and 1 graph why the price level is higher in the second case (when i = .25). i = .1 P = 1.2, i = .25P = 3. The purpose for holding money is that it is a useful and convenient tool for conducting transactions. An increase in the nominal interest rate will increase the opportunity cost of holding wealth in the form of money rather than bonds. A higher interest rate will provide incentives to households to undertake more inconvenience (in the form of more frequent trips to the bank) in order to avoid holding money. Thus, the given stock of money will circulate more quickly increasing the speed with which money chases goods. Given a stock of goods, this will increase the price level. At the higher price level, nominal GDP will be greater making people willing to hold the supply of money at the higher interest rate. See Figure 1 at end for graph. c. Assume that an increase in financial technology allows banks to hold fewer reserves, so that rd falls from .2 to .1. Holding the level of highpowered money constant, solve for the new supply of M1. Using the money demand curve in section b, solve for the price level when i = .25. Explain in 1 paragraph and using 1 graph why a drop in reserve ratios increases the price level. The money multiplier at the original reserve ratio was (1.2/.4) = 3. The money multiplier at the new reserve ratio is (1.2/.3) = 4. Holding high powered money constant at 1000, the new money supply is 4000. The new price level is 4. As the fraction of deposits banks must hold in the form of reserves falls, they may make that money money available in the form of loans. Thus, this extra money which had formerly been locked up in the banks vault would be available for spending on goods. This would increase the supply of money available for purchasing goods and will lead to a jump in prices. See Figure 2 for graph. 3. Depreciation Rate. Two countries, Albania and Zimbabwe, have money demand functions such that the demand for money is the ratio of nominal GDP to velocity GDP P Q M V V Recall that the growth rate of a ratio is the difference between the growth rate of the numerator and denominator so the growth rate of money is the growth rate of GDP divided by the growth rate of velocity: gM = gGDP – gV. Recall, also that the growth rate of a product of two variables is the sum of the growth rates of the two variables so the growth rate of GDP is gGDP = gQ + P̂ . a. Assume that velocity is the constant in both countries (gV = 0) and that the money growth rate in both countries is always 10% (i.e. gM = .1). The growth rate of output in Albania is always 2% (gQ = .02) while the growth rate of output in Zimbabwe is 4%. Solve for the inflation rate in both countries. Albania’s inflation rate is gM – gQ = 8% while the inflation in Zimbabwe is 6% b. The nominal interest rate in Albania is 20% (1+iA= 1.2). Assume that purchasing power parity holds and that uncovered interest parity holds. Treating Albania as the home country, solve for the growth rate of the exchange rate, the nominal interest rate in Zimbabwe, and the real interest rate in Albania. The real interest rate in Albania is 1.12%. The nominal interest rate in Zimbabwe is 1.18%. The depreciation rate is 2%. MD’ FIGURE 1 P MS MD M FIGURE 2 P MS MD M