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Consider an economy with a shrinking stock of fiat money. Let N = nNt-1 a constant, and Mt = =Mt_1 for every period t , where z is positive and less than 1. The government taxes each old person 7 goods in each period, payable in flat money. It destroys the money it collects. 1. Find and explain the rate of return in a monetary equilibrium (5 points) 2. Prove that the monetary equilibrium does not maximize the utility of the future generations. (10 points) [Hint: Follow the steps of the equilibrium with a subsidy, noting that a tax is like a negative subsidy.] 3. Do the initial old prefer this policy to the policy that maintains a constant stock of fiat money? Explain (10 points)