Consider the random-relocation economy developed in this chapter. Each person receives an endowment of 500 goods when young and nothing when old. People only want to consume when old. Let M_t = 1.1M_t for every period t. The net rate of return on capital is 15 percent.
a. Write down the contract that a competitive bank would offer to a mover.
b. Write down the contract that a competitive bank would offer to a nonmover.
c. Does this represent perfect risk sharing? Briefly explain your answer.
d. What would the growth rate of the money supply have to be in order to achieve perfect risk sharing? Is the monetary policy associated with perfect risk sharing the optimal policy setting?