Assume the relationship between the growth of a fish population and the population size can be expressed as g = 4P-0.1P^2, where g is the growth in tons of fish and P is the size of the fish population (in thousands of tons). Given a price of $100 per ton, the marginal benefit of smaller population sizes is MB = 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 (in terms of population size) isMC = 2(160-P), what is the population size that is compatible with the efficient sustainable yield?