homework4 - Department of Environmental Economics and...

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Department of Environmental Economics and Policy University of California Economics EEP101/ECON125, Spring 2003 Professor Zilberman Homework Set #4 Due at the Lecture on April 15th, to Yanhong Jin 1 Dynamic System Diminishing Island has a special tree specie. Its population s grows according to the following relationship: g ( s ) = 0 . 8 s - 0 . 00001 s 2 . Cutting down a tree yields a constant marginal benefit of 10 . The total cost of annual harvest depends on the size of its current stock ( s ) and the amount of harvest ( x ), i.e., the total cost is given by T C = 200000 x s . 1. What is the maximum carrying capacity of the stock? 2. What are the sizes of the stock and the annual harvest at the maximum sustainable yield? 3. Discussion on equilibrium outcomes with different management agents (a) The government believes that everyone should be allowed to use forest, and sells licenses for $6 per tree to anyone willing to buy. What are the sizes of stock and the annual harvest at equilibrium? (b) Mr. Greedy runs Diminishing Island, and he cuts down trees and sells in the market to maximize
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