Consider an economy with a shrinking stock of fiat money. Let Nt= N, a constant, and Mt= zMt−1for every period t, where z is positive and less than The governmenttaxes each old person τ goods in each period, payable in fiat money. It destroys themoney it collects. a. Find and explain the rate of return in a monetary equilibrium.
b. Prove that the monetary equilibrium does not maximize the utility of the futuregenerations. Hint: Follow the steps of the equilibrium with a subsidy, noting that atax is like a negative subsidy.
c. Do the initial old prefer this policy to the policy that maintains a constant stock offiat money? Explain.