Exercise 6 Consider a version of the monetary model seen throughout this chapter, composed by the following equations:

LM: mt 2 pt 5 y 2 αit UIP: it 5 i



t 1 Efst11 2 stg PPP: st 5 pt 2 p

t MG: mt11 2 mt 5 μ

where pt is the level of domestic prices, st is the nominal exchange rate, mt is the nominal money supply, and it is the nominal interest rate. The variables identified with  represent variables analogous to the international economy and are taken as constant. The parameters μ, which represents the rate of growth of money supply, and y, which represents full employment, are strictly positive. The operator Etfg represents the hope conditional for the set of available information in t. To simplify, assume that i

; y; p, and mt are equal to zero. In this model, all variables are expressed in logarithmic terms.

a. Assume that in t 5 1 the government fixes the money supply growth rate at μ 5 0:2 and that the agents expect this policy to be maintained indefinitely. Obtain the equilibrium trajectory of st and of pt for t $ 1.

b. Assume that in the period t 5 1 the government announces that it will freeze the exchange rate at s 5 2 from the period t 5 2 forward. The government also announces that it will adjust the money supply for the period t 5 2 and forward in order to maintain the fixed exchange rate established. Assume that the agents believe the government announcement and that the government in fact will implement the referred measures.

Obtain the equilibrium trajectory of st and of pt for t $ 1 and the equilibrium trajectory of the money supply of period t 5 2 forward.

166 PRINCIPLES OF INTERNATIONAL FINANCE AND OPEN ECONOMY MACROECONOMICS