hw02 - Econ 4721: Money and Banking, Fall 2009 Homework 2...

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Econ 4721: Money and Banking, Fall 2009 Homework 2 Wednesday, October 14, at the beginning of class. Problem 1. Inflation Consider an overlapping generations model in which consumers live for two periods. The number of people born in each generation grows in each period, according to N t = nN t - 1 , where n = 1 . 2. In each period, young consumers are endowed with y = 60 and old consumers are endowed with 0 units of the single consumption good. Each member of the generations born in period 1 and later have the following utility function: u ( c 1 ,t ,c 2 ,t +1 ) = log c 1 ,t + β log c 2 ,t +1 (1) with β = 0 . 5. Members of the initial old generation only live for one period and have utility u ( c 0 , 1 ) = log c 0 , 1 . The government expands the money supply by a factor of z each period, M t = zM t - 1 . Assume that z = 1 . 5. The money created each period is used to finance a lump-sum subsidy of a t +1 goods to each old person. (a) Solve for the (stationary) Pareto efficient allocation. The answer should be two num- bers ( c PO 1 ,c PO 2 ) . (b) Write the government’s budget constraint in period t + 1. (c) Define a competitive equilibrium with money for this economy. (d) Solve for the rate of return of money ( v t +1 /v t ) and the growth rate of the price level ( p t +1 /p t ) in a stationary equilibrium. The answer should be two numbers. (e) Solve for the consumption allocation ( c * 1 ,c * 2 ) and a lump-sum subsidy a * in a stationary equilibrium. The answer should be three numbers. 1
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(f) Verify that agents prefer the Pareto Optimal allocation to the competitive equilibrium allocation with inflation. (g) Illustrate the Pareto Optimal allocation ( c PO 1 ,c PO 2 ) and the competitive equilibrium allocation ( c * 1 ,c * 2 ) on the ( c 1 ,c 2 ) plane. Your graph should also include the feasibility line, the life-time budget constraint, and their indifference curves. Problem 2. Financing Government Expenses
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hw02 - Econ 4721: Money and Banking, Fall 2009 Homework 2...

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