Assume the relationship between the growth of a fish population and the population size can be represented as g= 8S – 0.2S2, where g is the growth in tons and S is the size of the population (in thousands of tons) a. Given a price of $100 a ton of fish, what is the marginal benefit of smaller population sizes? b. Estimate the population size that is compatible with the maximum sustainable yield. What would be the size of the annual catch if the population were to be sustained at this level? c. If the marginal cost of additional catches (represented in terms of the population size) is MC= 3(120-S), what is the population size that is compatible with the efficient sustainable yield? d. Is there a difference between the maximum sustainable yield you calculated in part (b) and the efficient sustainable yield in part (c)? Why or why not? Explain briefly (in 1 paragraph or less)
Assume the relationship between the growth of a fish population and the population size can be represented as g= 8S – 0.2S2, where g is the growth in tons and S is the size of the population (in thousands of tons)
a. Given a price of $100 a ton of fish, what is the marginal benefit of smaller population sizes?
b. Estimate the population size that is compatible with the maximum sustainable yield. What would be the size of the annual catch if the population were to be sustained at this level?
c. If the marginal cost of additional catches (represented in terms of the population size) is MC= 3(120-S), what is the population size that is compatible with the efficient sustainable yield?
d. Is there a difference between the maximum sustainable yield you calculated in part (b) and the efficient sustainable yield in part (c)? Why or why not? Explain briefly (in 1 paragraph or less)
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