Consider two identical countries in our standard overlapping generations model. In each country, the population of every generation is 100 and each young person wants money balances worth 18 goods. Each member of the initial old starts with $3 of country α money and £3 of country b money, regardless of citizenship. The exchange rate is fixed at 2: $1 is worth £2. There are no foreign currency controls.
a. Find the value (measured in goods) of a unit of each country's money in a stationary equilibrium with unchanging money stocks. (Use the world money market-clearing condition [Equation 5.13].) What is the consumption of each old person? (Remember that each old person owns currency from both countries.)
b. Suppose each member of the initial old of both countries decides to cut his real balances of country α money by one-third (to 8 goods). He turns in $1 to the monetary authority of country α in order to acquire more country b money. Assume that the monetary authority of country b has agreed to cooperate by printing as much of its currency as is demanded. What will the total nominal stock of each country's money be? What will the value of a unit of each country's money be?
c. Suppose each member of the initial old turns in $1 to the monetary authority of country α in order to acquire more country b money at the fixed exchange rate, but the monetary authority of country b refuses to cooperate. Assume that the government of country α decides to honor its pledge through an equal tax on every old citizen. What is the value of a unit of each country's money? How many goods must each old citizen of α be taxed? Who prefers this policy to the policy in part b? Who does not?
d. Suppose each member of the initial old decides to cut his real balances of country α money by one-third (to 8 goods), and the government decides not to intervene to fix the exchange rate. What is the new exchange rate? What is the consumption of each old person? Why doesn't the exchange rate change hurt anyone? Who prefers this policy to the policy in part c? Who does not?