Consider an overlapping generations mode with the following characteristics: Each generation is composed of 1,000 individuals. The fiat money supply changes according to M_t = 2M_t-1. The initial old own a total of 10,000 units of fiat money (M_o = $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 such that individuals wish to save 10 units when young at the equilibrium rate of return on fiat money.
a. What is the gross real rate of return on fiat money in this economy?
b. How many goods does an individual receive as a subsidy?
c. What is the price of the consumption good in period 1, P₁, in dollars?