Suppose you are a cherry stone clam fisheries manager who owns the sole rights to an area of ocean bottom where the annual clam growth model is F(X) = 0.5X 0.001X2 where X = stock in bushels. Suppose the price of clams is $6 per bushel. Your interest rate, r, is zero.

1. Bionomics: What is the stock size and harvest level corresponding to the MSY? What is the unharvested equilibrium level?

2. Suppose there is a cost of harvest, H, such that TC = 40H/X. What is the stock and harvest level that corresponds to the maximum economic rent for your ocean bottom?

3. What would happen to the harvest level and rent if the government made it an open access fishery (assume that the cost function is the same)?

4. Suppose you started with a stock equal to 500 bushels. What path over time would you likely follow as a rent-maximizing plan? Provide a qualitative answer.