Suppose there are two islands. The total population on the two islands is 500 people. The initial stock of fiat money is $500. The money stock increases according to M_t = 1.1M_t-1. The probability that a person is on Island 1 is 1/4 and the probability that a person is on Island 2 is 3/4. Let l (pⁱ_t) = 4 (so that labor supply does not depend on price).
a. Write down the money market-clearing condition for each island.
b. Solve for the equilibrium price level in date 1.
c. Write down the per-person transfer that the government gives to each old person.
d. Compute the value of the transfer.