Question 3- Consider an economy with a shrinking stock of at 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 at 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. Hint: follow the steps of the equilibrium with a subsidy, noting that a tax is like a negative subsidy. 0. Do the initial old prefer this policy to the policy that maintains a constant stock of at money? Explain