File 0' (D File me I I .rpsewpu: Edit View History Bookmarks People Tab Window Help l'lllujL, i - are'l757pset34 x /Users/headbandbuckets/Downloads/are175-pset3pdf Assume that the stock of tuna continues to grow according to the difference equation X z+1 : X z + F(X,) 7 11,, where F(Xt) is a function representing the net growth of tuna and He is the harvest of tuna at time it. Again, suppose that net growth of tuna depends on the size of the sh stock and is given by the function F(X,) = X,(1 Xi). 2.A. Suppose that the harvest of tuna in any time period is determined by the amount of shing "effort" and the biomass of the tuna stock, according to the following rule: H,(X, Et) : th X,, where q is a parameter measuring how effective effort is at catching fish. i) [0.5 points] Determine the steady-state tuna stock X" as function of industry effort E. How does X\" change as E increases? ii) [0.5 points] Determine the steady-state harvest of tuna H\" as function of industry effort E. How does HM change as E increases? Explain what is happening here. 2.3. Now suppose that the tuna shery is governed by open access Assume that the shing industry earns the following profim, 7r = 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 EOA. What would the price have to be so that there is no effort in the shery? ii) [0.5 points] Using your answer above, derive an expression for the open access tuna stock XOA. iii) [05 points] Plot open access levels of effort EDA and tuna stock biomass XOA as a flmction of the price of sh 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 extinch'on? Explain. iv) [0.5 points] In a separate graph, plot the open access supply curve of tuna HOA as a function of the price of fish 17 with quantity of tuna harvested on the xaxis 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