Consider an overlapping generation economy with the following characteristics: each gen- eration is composed of 1000 individuals. The fiat money supply changes according to Me = 2M,-1. The initial old own a total of 10, 000 units of fiat money (Mo = $10, 000). Each period, the newly printed money is given to the old of that period as a lump-sum transfer (subsidy). Each person is endowed with 20 units of the consumption good when born and nothing when old. Preferences are: U(ci,c) = (of + }{)1/e.1. Find the stationary Competitive Equilibrium in this economy as a function of p. 2. If p = -1. What is the gross real rate of return on fiat money? How many goods does an individual receive as a subsidy? What is the price of the consumption good in period 1, p1, in dollars? 3. Find the social Planner's optimal allocation for p = -1. 4. We have shown in class that the social planners allocation is the same as the one in an equilibrium with constant money stock. Does the old agent consume more with a growing money stock and transfers than in the equilibrium without money stock growth and transfers? In words, explain the intuition of this result