1. There are n fishermen that participate in the Gulf of Mexico Red Snapper fishery. In a given period, each fisher has a harvest (production) function given by yi=qX^0.5Ei^0.5 where X is the fish stock and Ei is the quantity of effort applied. Output can be sold at a price p per unit. Half of the fishermen have unit cost of effort, c_i=c₁ while the other half have c_i=c₂ and c₁>c₂ . Suppose that the fishery is regulated with individual transferable quotas and that there are M quotas issued in total. Each of the n fishers gets an equal number of quotas that they can keep or trade. They must, however, have one quota for each fish that they harvest. Let b be the market price of a quota, and D_i the number of quotas initially distributed to firm i .

1. Set up the objective function for an individual fisherman and interpret each component (I recommend doing this in terms of yi , which requires that you eliminate Ei ).

2. What is harvest level for firm i as a function of exogenous variables and the quota price?

3. Use the market clearing condition that the quantity of quota demanded equals the quantity supplied to solve for the equilibrium market price (b) of a transferable quota as a function of only parameters (assuming X is a parameter in this case).

4. Qualitatively what is the impact of M, p, and c₁ on the market price for quota? Show the appropriate comparative statics and interpret in words.

5. What is the expression for the number of quotas sold by a firm with c_i=c₁ as a function of only parameters (again assuming X is a parameter)?