File 0' (D File are175~pse13.pdf Edit View History Bookmarks People Tab Window Help l'm mu ~ '1 HM , - a; ,1 are1757pse134 x /Users/headbandbuckets/Downloads/arel75-pset3pdf 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 X\" grows according to the difference equation X,\" = X; + F(X.) Ht, where the net-growth funch'on is F(X) = X,(1 Xi) and the harvest of tuna H. is determined by Hi(X.,E.) = qE,X,, where E. 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 tuna, The cost of harvesting tuna is C (Eg) = LE\" 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 prots 1r\" from the shery i) [0.5 points] Write down the objective function for the sole-owner's steady-state profit maximization problem. ii) [0.75 points] Determine the level of effort E' that maximizes steady-state profits 7!\". Be sure to explain how you found E'. iii) [0.5 points] How does the optimal amount of effort E' compare to the steadystate open access level of effort EDA that you found in Problem 2? Why are they different? B. Now suppose you are the manager of an open access tuna fishery and you have the option to impose a harvest tax on tunar i) [0.75 points] Suppose fishermen have to pay a tax of t for every unit of tuna that they catch. How would you choose the tax level t' to maximize the tuna fishery rents? Find a value for t' if c = q = 0.01 and 11:3. ii) [05 points] Explain the practical limitations of managing the tuna shery using a harvest taxi