Problem 3: Regulating the Fishery [3 points] As above, let's assume that a tuna stock at the beginning of time i, denoted by the variable X\" grows according to the difference equation XH 1 = X; + F0573) HE, where the net-growth function is PDQ) = XBH Xi) and the harvest of tuna If, is determined by fIt(X1,E3) = thXE, where E; is the amount of industry shing effort. Also assume that fishermen are price-takers in the market for tuna, and thus receive the market price 3r) per unit of tuna. The cost of harvesting tuna is C(Et} = riEt. Au 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 11..., from the fishery. i) [(1.5 points] Write down the objective function for the sole-owner's steady-state profit maximization problem. ii] [0.15 points] Determine the level of effort E' that maximizes steady-state profits 71-\"... Be sure to explain how you found 13*. iii)I [0.5 points] How does the optimal amount of effort E\" compare to the steady-state open access level of effort 130A 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 fishermen have to pay a tax of I. for every imit of tima that they catch. HOW would you choose the tax level If\" to maximize the tuna fishery rents? Find a value for l.' if c = q = Dill and 11:3. ii] [0.5 points] Explain the practical limitations of managing the tuna fishery using a harvest tax