Exercise 1 Let there be two economies: domestic and foreign. The money market equilibrium is given by the two following equations:

mt 2 pt 5 φyt 2 λit m

t 2 p

t 5 φy

t 2 λi



t where yt, pt, mt, and it represent the product, price index, nominal money supply, and nominal interest rate, respectively. All variables are in logarithm, and the  superscript refers to the foreign economy. The parameters φ . 0 and λ . 0 represent demand elasticity per money in relation to income and interest, respectively. The international capital market equilibrium is given by the uncovered interest rate parity condition:

it 2 i



t 5 Etðst11Þ 2 st;

where st represents the nominal exchange rate and Et represents the operator of conditional hope to the set of available information in t. In this model, time is defined in discreet terms.

The relationship between price levels and the nominal exchange rate is given by the following purchasing power parity relationship:

st 5 pt 2 p

t :

Define the variable ft 5 ðmt 2 m

t Þ 2 φðyt 2 y

t Þ as the fundamentals of the economy.

a. Derive the equation that governs the nominal exchange rate behavior, where the exchange rate is a function of the fundamentals as previously defined. Interpret this equation.

b. Present and justify, with economic arguments, the hypothesis of absence of speculative bubbles. Find a solution to the equation in the previous item under this hypothesis.

c. Denote Δft 5 ft 2 ft21 and assume that the economic fundamentals follow the following stochastic process: Δft 5 ρΔft21 1 zt, where zt is a shock with mean zero and ρAð0:1Þ.

Using your answer to item ðbÞ, calculate the equilibrium exchange rate when the fundamentals follow this process.

d. Show that this model is able to explain the following stylized fact for the exchange rate:

varðstÞ . varðΔftÞ, where varðÞ represents the variance operator. Interpret the result.

e. Assume the government establishes a fixed exchange rate policy, simultaneous with an expansionist credit policy. What does the government need to do to maintain the fixed exchange rate? What happens when the government no longer has international reserves?

Chapter 6 • Money and Exchange Rate in the Long Run 163