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Unformatted text preview: Exam ARE 263 Fall 2003 Answer both questions 1 and 2 and either question 3 or 4. Each question is worth the same number of points. 1) When an agent harvests h t f sh in a period and the current stock is S t , the stock the next period is S t +1 = f ( S t h t ) . The bene f t of harvest in the current period is U ( h t ) and the discount factor is . The growth function f is concave. (a) Write down the optimization problem for the agent who maximizes the present value of the stream of bene f ts of harvest and write down the dynamic programming equation. (b) Use the DPE to obtain the Euler equation. (c) Give an intuitive interpretation of the Euler equation. (d) Write down the steady state Euler equation. How does the steady state stock depend on (i) the discount factor and (ii) the elasticity of marginal utility? [Hint: This question does not require any algebra.] (e) Discuss an algorithm for solving this (discrete stage) control problem numerically....
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- Fall '06