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# hw4 - Homework 4 ECON 4721H Money and Banking Fall 2011 Due...

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Unformatted text preview: Homework 4 ECON 4721H: Money and Banking, Fall 2011 Due Wednesday, November 9, at the beginning of class Problem 1. OLG with Money (25pts) Consider an overlapping generations model in which consumers live for two periods. In each period, young consumers are endowed with y 1 = 60 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: ln( c 1 ,t ) + β ln( c 2 ,t +1 ) with β = 0 . 5 . Members of the initial old generation only live for one period and have utility, ln ( c 2 , 1 ) . 1) Consider a competitive equilibrium without money for this economy. Solve for the equi- librium outcome of individual allocation, ( c 1 ,t ,c 2 ,t +1 ) . Will there be any trades between individuals in the economy? Explain. 2) Now suppose that each member of the initial old generation is endowed with ¯ m units of at money. (Therefore, the stock of at money in the economy M = N × ¯ m. ) Consider a competitive equilibrium with money. Write the budget constraint for the young....
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