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review5 - Review 5 EEP101/Econ 125 David Zilberman Fishery...

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Review 5 EEP101/Econ 125 David Zilberman
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Fishery Suppose that the Growth of the fishery is given by . ∆N=N-.01N 2 -X Where N is population size and X is harvesting The harvesting cost is given by C(X,N) = 5X 2 /N A.Suppose fish price is $1, and 12 fish are being caught by Profit Maximizing fishermen- what is the size of the fish population? Is it a sustainable outcome? What are the steady state levels of X and N? B. Suppose the harvesting equipment damages costs damage of $. 5 per fish caught. What is the steady state X and N with a tax? Explain. C. Suppose the cost is C(X,N) = .05X 2 - will it result in a steady state? Suppose regulator limit harvest to Maximum sustainable yield by a quota- what is the price of the quota.
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Fishery (Answer 1) Suppose that the Growth of the fishery is given by . ∆ ∆N=N-.01N 2 -X Where N is population size The harvesting cost is given by C(X,N) = 5X 2 /N A.Suppose fish price is $1, and 12 fish are being caught by Profit Maximizing fishermen- what is the size of the fish population? Is it a sustainable? What are the steady state levels of X and N? Answer- Profit is maximized when 1=10X/N so if X=12 optimal N =120. Not sustainable. Maximum sustainable stock is 100 (X=0). At the equilibrium X=.1N. The steady state 0=N-.01N 2 -.1N. Thus, . 9=.01N, so N=90 at steady state and X=9. B. Suppose the harvesting equipment damages costs damage of $. 5 per fish caught. What is the steady state X and N with a tax? Explain. Answer-The profit maximizing condition is .5=10X/N. At steady state X=.05N. The steady states with profit maximization 0=N-.01N 2 -.05N, yielding . 95=.01N, hence N=95 and X=4.75. Tax reduces harvest.
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Fishery (Answer 2) C. Suppose P=1 and the cost is C(X,N) = .01X 2 - will it result in a steady state? Suppose regulators limit harvest to Maximum sustainable yield by a quota- what is the price of the quota? Answer- Profit maximizing formula is Price =1=Marginal cost=.02X, so profit maximizing harvest is at X=50.
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