In that simple random-relocation model, each person is endowed with 50 goods when young and nothing when old. The money stock is constant and equal to $1,000,000. Each island has a constant population, with 500 people born in each period t. Suppose the fraction of movers takes on either of two values. In the small-fraction event, with probability of .5, 5 percent of the population must move to the other island. In the high-fraction event, with probability of .5, 20 percent of the population must move.
a. Calculate the total currency needed by movers in the event that the small fraction of movers is realized.
b. Calculate the total currency needed by movers in the event that the high fraction of movers is realized.
Suppose the bank holds 15 percent of the deposits in the form of currency. In other words, γ^* = 0.15. Will the bank have enough in currency to meet the needs of the movers in the high-fraction event?
c. Describe how an elastic currency regime would address the answer to part b.