Question 3- Consider an economy with a shrinking stock of fiat money. Let Nt = N, a constant, and Mt = z Mt-1 for

Question 3- Consider an economy with a shrinking stock of fiat money. Let N; = N, a constant,and M, = z MM for every period t, where z is positive and less than 1. The government taxes each old person 1: goods in each period, payable in fiat money. It destroys the money it collects. . Find and explain the rate of return in a monetary equilibrium. 6. Prove that the monetary equilibrium does not maximize the utility of the futuregenerations. Hint: fillow the steps of the equilibrium with a subsidy, noting that a tax islike a negative subsidy. f. Do the initial old prefer this policy to the policy that maintains a constant stock of fiatmoney? Explain.