Consider an economy with a shrinking stock of fiat money. Let Nt=N. a constant, and Mt=zMt-1 for every period t, where z is positive and less than 1. The government taxes each old person t 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.

c) Do the initial old prefer this policy to the policy that maintains a constant stock of ifat money.