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Consider the market for copper, where demand is given by the equation P(QD) = 500 - 1/2Q and market supply is given by P(Qs) = 50 + Q. The discount rate is r=10% and there is a fixed supply of 400 total units of copper. a. If there is just one period in this model, what would be the equilibrium market price and quantity sold? Show your work. Is the resource exhausted? b. Suppose instead that there are two periods, and that demand and supply are the same in both periods. Derive an expression for the marginal net benefit (MNB) of the resource in each period. c. Find the optimal allocation of copper between the two periods, and using the demand curves, find the price that would prevail in each period. d. How do your answers in part (c) change if the discount rate increases to 25%?

Consider the market for copper, where demand is given by the equation P(QD) = 500 - 1/2Q and market supply is given by P(Qs) = 50 + Q. The discount rate is r=10% and there is a fixed supply of 400 total units of copper. a. If there is just one period in this model, what would be the equilibrium market price and quantity sold? Show your work. Is the resource exhausted? b. Suppose instead that there are two periods, and that demand and supply are the same in both periods. Derive an expression for the marginal net benefit (MNB) of the resource in each period. c. Find the optimal allocation of copper between the two periods, and using the demand curves, find the price that would prevail in each period. d. How do your answers in part (c) change if the discount rate increases to 25%?

Microeconomics: Private and Public Choice (MindTap Course List)
Microeconomics: Private and Public Choice (MindTap Course List)
16th Edition
ISBN:9781305506893
Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
Publisher:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
ChapterST10: The Question Of Resource Exhaustion
Section: Chapter Questions
Problem 1CQ
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Consider the market for copper, where demand is given by the equation P(QD) = 500 - 1/2Q and market supply is given by P(Qs) = 50 + Q. The discount rate is r=10% and there is a fixed supply of 400 total units of copper. a. If there is just one period in this model, what would be the equilibrium market price and quantity sold? Show your work. Is the resource exhausted? b. Suppose instead that there are two periods, and that demand and supply are the same in both periods. Derive an expression for the marginal net benefit (MNB) of the resource in each period. c. Find the optimal allocation of copper between the two periods, and using the demand curves, find the price that would prevail in each period. d. How do your answers in part (c) change if the discount rate increases to 25%?
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