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Unformatted text preview: Department of Economics University of California, Berkeley Fall 2007 ECON 182 Suggested solutions to PS 6 1 Equilibrium of Aggregate Demand and Supply a. Consider the following economy: Output: Y Consumption spending: C = 8000 + 0 . 8 Y d Disposable income: Y d = Y T Net income taxes: T = 0 . 2 Y Investment: I = 10000 Government expenditure: G = 6000 Exports: EX = 2000 + 4300 EP * P Imports: IM = 0 . 05( Y T ) + 2300 EP * P Assume P and P * are fixed in the short run and P * /P = 2. Derive the expression for the DD curve, where output is a function of the nominal exchange rate E . Y = C + I + G + EX IM = 8000 + . 8( Y . 2 Y ) + 10000 + 6000 + 2000 + (4300 2300) 2 E . 05( Y . 2 Y ) = 26000 + 0 . 6 Y + 4000 E = 65000 + 10000 E. b. Consider the following foreign exchange and money markets: Foreign interest rate: i * = 5% Expected future exchange rate: E e = 1 . 7 Real money supply: M s /P = 10000 Money demand: L ( i,Y ) = Y 10 i Derive the expression for the AA curve, where output is also a function of the nominal exchange rate E . UIP: i = i * + E e E E i = 5% + 1 . 7 E 1 = . 95 + 1 . 7 E Last modified 7:46pm, 10/18/2007 1 Department of Economics University of California, Berkeley Fall 2007 ECON 182 Money market: M s /P = L ( i,Y ) 10000 = Y 10 i Y = 100000 i Then we have Y = 95000 + 170000 E c. Calculate the equilibrium output and spot exchange rate. 65000 + 10000 E = 95000 + 170000 E E = 1 and Y = 75000 . 2 DD-AA Diagram and J-curve It is sometimes observed that a countrys current account worsens immediately after a real currency depreciation and begins to improve only some months later, contrary to the assumption we made in deriving the DD curve. If the current account initially worsens after a depreciation, its time path has an initial segment reminiscent of a J and therefore is called the J-curve . For details, see the textbook Chapter 16. When the current accounts response to the exchange rate follows a J-curve, the DD curve might be negatively sloped in the short run, though the absolute value of its slope would probably exceed that of AA . Use this modified diagram to examine the short-run effects of both temporary and permanent a. monetary expansion; A temporary monetary expansion, while depreciating the currency, would reduce output in the very short run. This is shown by a shift in the AA curve to AA and a movement in the equilibrium point from 1 to 2. The output would decline because real depreciation now hasequilibrium point from 1 to 2....
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