Exercise 7 Consider the monetary model seen throughout this chapter, where the behavior of the nominal exchange rate is reproduced by the following equation:

st 5 ðmt 2 m

t Þ 2 ðyt 2 y

t Þ 1 0:5ðEtfst11g 2 stÞ

where st represents the nominal exchange rate, yt represents the product level, and Etfg is the hope operator conditional based on the set of information available for period t. The variables identified with  represent international economy variables. In this model, all variables are expressed in logarithmic terms. Assume that the agents possess a perfect forecast of the future, so that Etfst11g 5 st11. To simplify, assume that m

t 5 y

t 5 0 and it is hoped that these levels are maintained for all future periods. Determine the nominal exchange rate trajectory, before and after the policy changes.

a. Assume that the supply of money growth rate has been 10% to date and that the agents hope that this level will be maintained in the future. Then, the following policy changes occurred:

1. On date t, the central bank announced it would reduce the rate of growth for the supply of money by half from t forward and the agents hope that this new rate will maintain its new level indefinitely.

2. On date t, the central bank announces that it will reduce the money supply growth rate by half from t forward, but the agents believe that, with probability 1, actually the bank will double the supply of money and will remain at this new level indefinitely.

3. On date t, the central bank announces it will reduce the money supply growth rate by half from t forward, but the agents believe this may occur with a probability of only 50%, attributing the remainder of the probability to the scenario where the money supply will not be altered, but remain indefinitely at the initial level.

b. Assume that the money supply has been constant in mj 5 10, until date j # t 2 1. On date t, the central bank established the money supply at mj 5 5, for j $ t. The agents, however, believe that the money supply will be increased to mj 5 20, for the date j $ t.