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Economics 215 Intermediate Macroeconomics Homework 4 Assigned: Thursday, May 5, 2005 Due: Thursday, May 11, 2005 1. Fundamental Exchange Rate. Assume that the exchange rate of the Japanese yen for the US dollar 10 years in the future can be defined as the long run fundamental exchange rate: et+T = eLR. Further, assume we can estimate the market’s assessment of future interest rates over the next 10 years by looking at the interest rate on 10 year bonds. Define 1+i10 as the interest rate on a 10 year bond. 1 i 10 t 10 1 it 1 it 1 1 it 2 1 it 3 ..... 1 it 9 The following table contains information on the interest rate for 10 year bonds for Japan (the domestic economy) and the US (the foreign economy) as well as the spot Yen-Dollar exchange for the period 1998 to 2004. Assume that uncovered interest parity holds. Calculate the markets expectation of the long-term fundamental level of the exchange rate, eLR. 10 Year Bond Rate Japan USA i10 1998 1.97 1999 1.645 2000 1.64 2001 1.365 2002 0.9 2003 1.36 2004 1.435 i10 Yen-Dollar Rate e 4.65 115.2 6.28 102.08 5.24 114.9 5.09 131.47 4.03 119.37 4.27 106.97 4.23 103.78 2. Investment. A firm has a Cobb-Douglas production function. Q L Yt Kt Qt Lt MPKt 1 1 t 1 t 1 2 Kt 1 The real interest rate is 5% (r = .05) and the depreciation rate of capital is 7.5% (d=.05). a. Calculate the average productivity of capital when the firm is at its optimal capital stock. Calculate the capital-labor ratio when technology next period is equal to Q = 1. b. Calculate the optimal capital stock when Qt+1 = 1 and Lt+1 = 4. Calculate the output level at the optimal capital stock. If the current capital stock is equal to Kt =100, how much investment will you need to set next period’s capital stock equal to the optimal level if Kt+1 = (1-d)Kt. + It. c. Now assume that the technology level goes up by 1%, so Qt+1 = 1.01. Calculate the optimal capital stock at the new technology level. Calculate the new level of output at the new technology level. What is the percentage increase in the optimal capital stock compared to the answer in b. How much investment will you need to do to set next period’s capital stock equal to the optimal level? How much of an increase in investment, in percentage terms, will a 1% increase in technology lead to? 3. Sustainable Current Account. The Bureau of Census and Statistics (http://www.info.gov.hk/censtatd/eng/hkstat/index.html) has information on the net international investment position of Hong Kong’s GDP. For 2003, calculate the NIIP to GDP ratio. Obtain the end of year, international investment position, NIIPt here (http://www.info.gov.hk/censtatd/eng/hkstat/fas/bop/iip1_index.html) Find the GDP level for 2003 here (http://www.info.gov.hk/censtatd/eng/hkstat/fas/nat_account/gdp/gdp2_index.htm ) . Assume the real interest rate is 4% (r = .04). Calculate the sustainable trade deficit to GDP ratio for HK if the growth rate of GDP is 6% (gY = .06) and if (gY = .02). 4. Third Generation Crisis Business Cycle Model.of Exchange Rates, (Geometry). In an open economy, consumption is a linear function of disposable income, Ct 100 .5 (Y T ) ; investment is a linear function of output, the government bond interest rate, it, and a risk premium paid by corporate borrowers, rpt: It 35 .1 Yt 100 it rpt ; the treasury runs a balanced budget, Gt = Tt = 50; net exports are a linear function of income and the exchange rate NX t 50 20 (et 1) .2Yt ; and demand is the sum of absorption Yt = Ct + It+ Gt+ NXt. The central bank sets a fixed exchange rate, et = eFIX = 1. Foreign exchange market conditions are given by the linear equation it = it$ + eLR – et + rpt a. Let it$ = .1, eLR = 1, and rp = 0. Solve for equilibrium output, interest rate, consumption, investment and net exports. b. Assume that rp = 0. Let forex markets believe that the exchange rate loses credibility and the fundamental exchange rate changes to eLR = 1.2.. Solve for equilibrium output, interest rate, consumption, investment and net exports if the central bank maintains a fixed exchange rate et = eFIX = 1. Solve for equilibrium output, interest rate, consumption, investment and net exports if the central bank devalues the currency et = 1.2. c. Assume that domestic firms have a great deal of foreign currency debt, so a devaluation reduces their credit worthiness and increases the risk premium. rpt = 1.5∙(et – 1) Let forex markets believe that the exchange rate loses credibility and the fundamental exchange rate changes to eLR = 1.2.. Solve for equilibrium output, interest rate, consumption, investment and net exports if the central bank maintains a fixed exchange rate et = eFIX = 1. Solve for equilibrium output, interest rate, consumption, investment and net exports if the central bank devalues the currency et = 1.2.