Exercise 6 Consider a simplified version of the Dornbusch model seen in this chapter, described by the following equations:

IS: yt 5 y 1 ηðst 1 p

t 2 ptÞ

LM: mt 2 pt 5 yt 2 it UIP: it 5 i



t 1 Efst11 2 stg MG: mt11 2 mt 5 μ

where yt represents the domestic economy output, pt is the domestic prices level, st is the nominal exchange rate, mt is the supply of money, and it is the nominal interest rate, all 11 For a description of the EMS, see Box 9.1.

Chapter 7 • Macroeconomic Policies and Exchange Rate in the Short Run 193 variables are in logarithm. The variables identified with  represent those in the international economy and they are taken as constant. The parameters, μ, which represents the rate of growth of money supply, η, which represents the elasticity of the aggregate demand with respect to the real exchange rate, and y, which represents the output under full employment, are strictly positive. The operator Etf:g represents the expected value operator, conditional to the set of information available in t. Assume that prices are rigid in the first period ðp1 5 pÞ
and perfectly flexible from the second period forward, a period in which the output is compatible with the level of full employment. All variables in the model are described in logarithmic terms. Derive the nominal and real exchange rate paths in response to the following shocks:

a. There is a permanent increase in the rate of growth of money supply μ.

b. There is a permanent increase in the full employment output level y. Make a distinction between the following cases:
1. η 5 1.
2. η E ð0; 1Þ.
To simplify, now assume that p; p; i  and y are equal to zero. Keeping the same structure presented previously, answer the following items:

c. Assume that y and mt are equal to zero, and that agents expect them to indefinitely remain at these levels. Determine the equilibrium values for yt, pt, and st from the first period and forward.

d. Assume that in period t 5 1 the level of international prices permanently goes up to p 5 1. Determine the equilibrium values for yt, pt, and st from the first period forward.
Does nominal exchange rate st overshooting occur in relation to its long-run level?
Explain your answer.

e. Assume that the level of international prices is once again equal to p 5 0, however, in period t 5 1, the international interest rate goes up permanently to i  5 1. Determine the equilibrium values for yt, pt, and st from the first period forward. Does nominal exchange rate st overshooting occur in relation to its long-run level? Explain your answer.