Problem 2: Fishing Effort and the Open Access Equilibrium [3.5 points] Assume that the stock of tuna continues to grow according to the difference equation Xt+1 - X, + F(X:)- He where F(X,) is a function representing the net growth of tuna and H, is the harvest of tuna at time t. Again, suppose that net growth of tuna depends on the size of the fish stock and is given by the function F(X) - X.(1 - X.). 2.A. Suppose that the harvest of tuna in any time period is determined by the amount of fishing "effort" and the biomass of the tuna stock, according to the following rule: Hi(X, Et) - qEt Xe, where q is a parameter measuring how effective effort is at catching fish. i) [0.5 points] Determine the steady-state tuna stock X'ss as function of industry effort E. How does X'ss change as E increases? ii) [0.5 points] Determine the steady-state harvest of tuna Has as function of industry effort E. How does Has change as E increases? Explain what is happening here. 2.B. Now suppose that the tuna fishery is governed by open access. Assume that the fishing industry earns the following profits, a - pH - CE, where p is the price of fish and c is the per-unit cost of effort. i) [0.5 points] Derive an expression for the open access level of effort EnA. What would the price have to be so that there is no effort in the fishery? ii) [0.5 points] Using your answer above, derive an expression for the open access tuna stock Xox. iii) [0.5 points] Plot open access levels of effort Fox and tuna stock biomass Xox as a function of the price of fish p in two different graphs in Excel using the parameter values q - 0.01 and c - 0.01. Is it possible for the steady-state stock of tuna under open access to be extinction? Explain. iv) [0.5 points] In a separate graph, plot the open access supply curve of tuna Hox as a function of the price of fish p with quantity of tuna harvested on the x-axis and price of fish on the y-axis. How does this supply curve under open access differ from normal supply curves? Explain. v) [0.5 points] If you are a benevolent social planner trying to maximize the welfare of society, are you happy with the steady-state outcome under open access? Why and/ or why not