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final 2009 - ECON 7240 Spring 2009 Final Each question...

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ECON 7240 Spring 2009 Final 4/27/09 Each question should be answered with a clear and concise explanation. Yes-no questions should be answered with a supportive argument or counterexample. Please write legibly. 2 hours 1) Consider the following overlapping generations model. In each period, a continuum of households of population L t = (1 + n ) t is born and lives for two periods, where n > - 1. Let C ti be the consumption of a household at time t in its i th period for i = 1,2. The household maximizes , ln 1 1 ln 2 , 1 1 + + + t t C C ρ where ρ > - 1. A household in its first period is born without capital and sells one unit of labor, earning the wage W t . The household can consume this income or invest it in capital. Capital invested at t earns the gross return R t +1 (net of depreciation) at t + 1. The economy also has a continuum of competitive firms with the production function F ( K , L ) = K α L 1 - α . In equilibrium, capital K is the capital invested by young households in the previous period and labor L is L t .
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