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Unformatted text preview: 1 Endogenous Labor Supply Before we assumed that an agent works “full time” every period and receives an exogenous income y t . We now let an agent choose how much to work. Income is proportional to the number of hours spent at work l t and the wage in period t is w t . We assume that the labor market is competitive. This means that every agent takes wage rate as given. We modify the utility function and include labor choice: ∞ summationdisplay t =0 β t ˜ u ( c, l ) Assumption 1 ′ : a) ˜ u c > , ˜ u l < ; b) ˜ u cc < , ˜ u ll < , u cc u ll − u 2 cl > This is a generalization of assumption 1. It states that working more hours reduces utility and that each additional work hour decreases utility by more. It also insures that the period utility function is strictly concave in ( c, l ). The system of equilibrium conditions is: c t : 0 = β t ˜ u c ( c t , l t ) − λ t (1a) l t : 0 = β t ˜ u l ( c t , l t ) − λ t w t (1b) a t +1 : 0 = λ t +1 R t +2 − λ t (1c) where λ t is as before the Lagrange multiplier on the budget constraint. We continue to assume that borrowing limits are not binding. Combining the first two equations we obtain the labor supply equation: w t = − ˜ u l ( c t , l t ) / ˜ u c ( c t , l t ) . (2) This equation allows solving for the number of hours worked as a function...
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This note was uploaded on 11/10/2011 for the course ECONOMICS 601 taught by Professor Viktortsyrennikov during the Spring '11 term at Cornell University (Engineering School).
 Spring '11
 ViktorTsyrennikov

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