Economics of environmental protection

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?