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**Unformatted text preview: **Final Exam Solutions Econ 600, Summer 2011 Leland Crane 1. (10 points) A consumer lives forever in discrete time. They choose consumption c t , assets a t +! , and labor supply l t . The interest rate is constant, but wages may uctuate deterministically over time. The consumer's Lagrangian is max a t +1 ,c t ,l t ∞ X t =0 β t [ U ( c t ,l t ) + λ t ( R ( a t + w t l t- c t )- a t +1 )] (1) where w t is the wage and R is the gross interest rate. (a) Write down the Bellman equation for this problem. For this part only, you may assume wages are constant over time. What are the state and control variables? ANSWER: V ( a t ) = max c t ,l t U ( c t ,l t ) + βV ( R ( a t + wl t- c t )) (2) The endogenous state variable is assets a t . c t and l t are control variables. If wages are not constant then calendar time t must be included as a state variable. Using any method you like, solve for the following. Eliminate any Lagrange multipliers from the nal expressions: (b) An intertemporal Euler equation relating U c ( c t ,l t ) to U c ( c t +1...

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- Fall '09
- Economics, Thermodynamics, Utility, Leland Crane