Exercise 10 Consider a small, open economy that satisfies absolute purchase power parity, assuming, for simplification, that lnðP

t Þ 5 0; where P

t is the international price index. The loss function for the central planner in this economy is given by L 5 ðyt2y~tÞ

2 1 χπ2 t 1 CðπtÞ, where yt represents the logarithm of output, y~t is the logarithm of optimum output level, Cð:Þ is a function that measures the cost to abandon the fixed exchange rate regime, and χ . 0 is a constant parameter. Assume that the output is given by yt 5 yt 1 ðπt 2 πe t Þ 2 zt, where yt is the natural output (in logarithm) and zt is a supply shock with zero mean and variance σ2. Assume that y~t 2 yt 5 κ . 0 and remember that inflation is defined as πt 5 lnðPtÞ 2 lnðPt21Þ.

a. The above-described model can be used to analyze which generation of currency crises models? Explain the main ideas associated with this family of models. Would this type of speculative attack model explains attacks that have occurred in economies that have had low unemployment and growing exports? Explain your answer.

b. Obtain the loss function for the social planner as a function of variables πe t , πt, and zt, only.

c. Initially not considering the cost function, Cð:Þ, and given that the government minimizes its loss function after knowing the values of πe t and zt, determine the optimum level of inflation π

t . What happens to the exchange rate in this case? Determine the loss function for optimum inflation L

fl.

d. What is the exchange rate regime when inflation is zero? What is the value of the loss function L

fx in this case?

e. How does the supply shock affect the difference between L

fl and L

fx? Explain your answer.