Exercise 4 In the monetary model to determine the exchange rate studied throughout this chapter, the nominal exchange rate trajectory is given by the equation:

sðtÞ 5 f ðtÞ 1 ηEt dsðtÞ

dt

;

where sðtÞ is the nominal exchange rate, f ðtÞ represents the economic fundamentals trajectory, η . 0 is a sensitivity parameter, and Etfg is the hope operator conditional for the set of information available in t. In this model, time is considered in continuous terms and the variables are expressed in logarithmic terms.

a. What are the basic hypotheses of this model? Explain the economic intuition of these hypotheses and their influence on the results of the model.

b. Assume that the economic fundamentals follow the following path:

ft 5 ift , f θ

f ðtÞ 5 θt if t , f

θ

θt 1 J otherwise 8

><

>:

where f . 0 and J . 0. Draw a graph with the fundamentals path. Give an economic interpretation for this path.

c. Assume that the fundamentals path in the previous item is common knowledge and there are credibility problems. Derive the exchange rate path. Compare the exchange rate path with that of the fundamentals. Represent them on a graph and present an economic interpretation. (Tip: The general solution for an equation of the type yðxÞ 5 x 1 a dyðxÞ

dx is given by yðxÞ 5 x 1 a 1 C e x

a, for a value of C.)