prob_set7

prob_set7 - Problem Set 7 The purpose of this problem set...

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Problem Set 7 The purpose of this problem set is to be sure that you can solve a linear- quadratic control problem, and to be sure that you know what the Principle of Certainty Equivalence says, and when it holds. 1. (Hoel and Karp 2001, Taxes versus Quotas for a Stock Pollutant) Equa- tion 16 in Appendix A is the Dynamic Programming equation for a linear-quadratic problem with additive errors. Using the sketch below this equation, solve the dynamic programming equation. The solution requires that you …nd the control rule and the unknown parameters ½ 0 ; ½ 1 ; ½ 2 . The paper contains the expressions for ½ 0 and ½ 2 so you need only con…rm these equations and …nd the expression for ½ 1 , and …g- ure out the relation between these coe¢cients and the optimal control rule. (The optimal control rule is a linear function of the state. The coe¢cients of this linear function depend on ½ i .) Note that the control rule is independent of the variance of the stochas- tic term; in other words, we would obtain the same control rule if we
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prob_set7 - Problem Set 7 The purpose of this problem set...

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