4721_HW1 - Econ 4721: Money and Banking, Fall 2008 Homework...

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Unformatted text preview: Econ 4721: Money and Banking, Fall 2008 Homework 1 Due Friday, September 26, at the beginning of class. 1 Problem 1. OLG Consider an overlapping generations model in which consumers live for two periods. The number of people born in each generation is constant, N t = N t +1 = N . In each period, young consumers are endowed with y 1 = 30 and old consumers are endowed with y 2 = 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 ) = ln[ c 1 ,t ] + ln[ c 2 ,t +1 ] , with = 0 . 5. Members of the initial old generation only live for one period and have utility u ( c , 1 ) = ln[ c , 1 ]. They have no endowment. (a) Define a feasible consumption allocation for this economy. Illustrate the set of feasible allocations on a graph. (b) Define a Pareto efficient stationary allocation for this economy. (c) Solve for the Pareto efficient stationary allocation. (d) Define a competitive equilibrium without money for this economy. Will there be any trades between individuals in the economy? Explain....
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4721_HW1 - Econ 4721: Money and Banking, Fall 2008 Homework...

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