Individual trading quotas in a fishery: A fishery is characterized by the following growth rate: g(S)=100S-S 2 , where S is the stock of fish (in tons). The market price of fish is P=1. The amount of fish caught per unit of effort is proportional to the size of the fish population. That is, q=kS, where q is the quantity caught per unit of effort, and k is a constant equal to 1. Note that the catch is equal to Q=qE, where E is the effort. There are 2 fishermen in this fishery with different marginal costs (MC). MCa=Ea/2 and MCb=Eb/6.

a. What is the industry-wide marginal cost (MCtot)? Draw a figure with MCa, MCb, MCtot. (Hint: you must horizontally add the MC curves from both producers to get MCtot).

b. What is the optimal sustainable catch for this fishery, E*? [Note: you already have the MB from the previous question; the solution is not a round number]

c. What is the efficient level of the catch Q*? [Note: the answer is not a round number]

d. Say that the fishery is initially under open-access. Policy-makers -following the advice of their resource economic advisers- set fishing quotas approximately equal Q*, say 2,400.

The government allocates 1,200 quotas to each fisherman. Will the fishermen trade quotas? Who will be the seller? The buyer? Explain.