Problem 3: Regulating the Fishery ARE 175 - you can find the question in the attachment.

Problem 3: Regulating the Fishery [3 points] As above, let's assume that a tuna stock at the beginning of time t, denoted by the variable Xi, grows according to the difference equation Xt+1 = Xi + F (XQ Ht, where the net-growth function is F (Xi) = Xt(1 Xt) and the harvest of tuna Ht is determined by Ht(Xt, Et) = thXt, where Et is the amount of industry shing effort. Also assume that shermen are price-takers in the market for tuna, and thus receive the market price p per unit of tha. The cost of harvesting tuna is 003;) = cEt. A. Suppose that you are the sole owner of the tuna stock and your goal is to choose a level of effort that maximizes steady-state profits 7r\" from the fishery. i) [0.5 points] Write down the objective function for the sole-owner's steady-state prot maximization problem. ii) [0.75 points] Determine the level of effort E * that maximizes steady-state profits 7T\". Be sure to explain how you found 19*. iii) [0.5 points] How does the optimal amount of effort E* compare to the steady-state open access level of effort BOA that you found in Problem 2? Why are they different? B. Now suppose you are the manager of an open access tuna shery and you have the option to impose a harvest tax on tuna. i) [0.75 points] Suppose shermen have to pay a tax of t for every unit of tuna that they catch. How would you choose the tax level 15* to maximize the tuna shery rents? Find a value for t* if c = q = 0.01 and p=3. ii) [0.5 points] Explain the practical limitations of managing the tuna shery using a harvest tax