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Unformatted text preview: Problem Set 6: Exhaustible Resource ARE 261 November 7, 2001 Question 1 The point of this question is to show you how to use GAMS to solve a control problem. Consider a mining industry that faces a linear inverse demand curve given by p = a ¡ bq (1) where p is price, q is the amount of ore demanded (also the control) and a and b are parameters. Furthermore, assume that a > b > . The discount rate is denoted by ± . The equation of motion for the exhaustible resource, R (also the state), is given by _ R = ¡ q (2) Extraction costs are quadratic and are given by C = c 2 q 2 (3) where c is a parameter greater than 0. The following are values for the di¤erent parameters: a = 6 , b = 1 , c = 1 and ± = 0 : 05 . Finally, the initial level of reserves for the exhaustible resource is R = 100 . ² Write the discrete time optimization problem (corresponding to the con tinuous time problem above) for the social planner and for the monopolist....
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 Fall '06
 KARP
 Numerical Analysis, Optimization, GAMS, continuous time problem

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