Assume that the relationship between the growth of a fish population and the population size can be expressed as g = 4P - 0.1P2, where g is the growth in tons and P is the size of the population (in thousands of tons). Given a price of $100 a ton, the marginal benefit of smaller population sizes (and hence larger catches) can be computed as 20P - 400.
a. Compute 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?
b. If the marginal cost of additional catches (expressed in terms of the population size) is MC = 2(160 - P), what is the population size that is compatible with the efficient sustainable yield?