2.19. Stationary monetary equilibria in the Samuelson overlapping-generations model. (Again this follows Samuelson, 1958.) Consider the setup described in Problem 2.18. Assume that x < 1 + n. Suppose that the old individuals in period 0, in addition to being endowed with Z units of the good, are each endowed with M units of a storable, divisible commodity, which we will call money. Money is not a source of utility.

(a) Consider an individual born at t. Suppose the price of the good in units of money is Pt in t and Pt +1 in t + 1. Thus the individual can sell units of endowment for Pt units of money and then use that money to buy Pt/Pt +1 units of the next generation’s endowment the following period. What is the individual’s behavior as a function of Pt/Pt +1?

(b) Show that there is an equilibrium with Pt +1 = Pt/(1 + n) for all t ≥ 0 and no storage, and thus that the presence of “money” allows the economy to reach the golden-rule level of storage