This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 dierent parameters: a = 6 , b = 1 , c = 1 and = 0 : 05 . Finally, the initial level of reserves for the exhaustible resource is R = 100 . Write the discrete time optimization problem (corresponding to the con tinuous time problem above) for the social planner and for the monopolist....
View
Full
Document
 Fall '06
 KARP

Click to edit the document details