There are two markets in the Dornbusch model of exchange rate overshooting: an asset market in...

    

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There are two markets in the Dornbusch model of exchange rate overshooting: an asset market in which the exchange rate, e, is determined and a goods market in which the domestic price level, p, is determined. In the asset market, the demand for money is given by: m = -ar + by where r is the domestic interest rate, y is the domestic level of output, which is assumed to be constant and a and b are constant positive coefficients of the money demand function. The real supply of money is given by m-0.5p, where m is the exogenous nominal supply of money. Since the economy is open to trade international capital movements will force the domestic interest rate to equal the world interest rate, r", plus an interest rate differential equal to the expected rate of depreciation of the home currency, de de" In the goods market, domestic prices adjust sluggishly in response to excess dp demand. The rate of change of prices is given by: = a(y-ys), a > 0, where y dt and ys are aggregate quantity demanded and supplied respectively and a is the speed of adjustment coefficient. Under the assumption that supply is fixed at y and demand is given by yu+ v(e-p) where e-p is the relative price of domestic goods and u and v are positive coefficients of the demand function. (i) Derive a system of differential equation to represent the rate of change of the exchange rate and the price level. (5 marks) (ii) Given a = 1, v = 1,a=,b=,= 3.4, m = 3,r* = 0.1 and u = 4, solve the system for e(0) = 1 and p(0) = 4. (10 marks) There are two markets in the Dornbusch model of exchange rate overshooting: an asset market in which the exchange rate, e, is determined and a goods market in which the domestic price level, p, is determined. In the asset market, the demand for money is given by: m = -ar + by where r is the domestic interest rate, y is the domestic level of output, which is assumed to be constant and a and b are constant positive coefficients of the money demand function. The real supply of money is given by m-0.5p, where m is the exogenous nominal supply of money. Since the economy is open to trade international capital movements will force the domestic interest rate to equal the world interest rate, r", plus an interest rate differential equal to the expected rate of depreciation of the home currency, de de" In the goods market, domestic prices adjust sluggishly in response to excess dp demand. The rate of change of prices is given by: = a(y-ys), a > 0, where y dt and ys are aggregate quantity demanded and supplied respectively and a is the speed of adjustment coefficient. Under the assumption that supply is fixed at y and demand is given by yu+ v(e-p) where e-p is the relative price of domestic goods and u and v are positive coefficients of the demand function. (i) Derive a system of differential equation to represent the rate of change of the exchange rate and the price level. (5 marks) (ii) Given a = 1, v = 1,a=,b=,= 3.4, m = 3,r* = 0.1 and u = 4, solve the system for e(0) = 1 and p(0) = 4. (10 marks)