Consider an economy with a shrinking stock of fiat money. Let N_t = N, a constant, and M_t = zM_t-1 for every period t, where z is positive and less than 1. The government taxes each old person τ goods in each period, payable in fiat money. It destroys the money 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 future generations. Follow the steps of the equilibrium with a subsidy, noting that a tax is like a negative subsidy.
c. Do the initial old prefer this policy to the policy that maintains a constant stock of fiat money? Explain.