4. Let Ht denote the harvest in year t. Let Et denote the level of effort devoted to harvesting that year. For this fishery, the harvest equation is H, =0.1E,S, Denote the steady state stock by S*, the steady state harvest by H* and the steady-state effort by E* . Assume the growth equation given above in question 1.~ (a) In a steady state, the steady-state stock S* depends on the level of steady-state effort, [*. What is the mathematical relationship between S* and E* in this case (i.e., the equation giving S* as a function of E*)? (b) Suppose the steady stock S* were set equal to the stock associated with the MSY. What steady state level of effort would correspond to this steady-state stock?~ (c) Suppose the price of fish is $2,000 per unit of harvest, and the cost of harvesting is $1,000 per unit of effort. What level of steady-state effort maximizes steady-state profit from harvesting the fish? (d) How does the answer to part (c) compare with the level of effort in your answer to part (b)? Explain why do the two answers differ in the way that they do.~ (e) What is the level of effort that would be expected to occur in a steady state when the fishery is unregulated and there is open access to the fishery? Describe the general rule that characterizes an open-access steady state equilibrium. Then calculate numerically the open- access, steady-state level of effort in this particular case.~ (f) At the level of effort in part (e) will the stock of fish be biologically over-exploited (i.e., will the stock be at a level below the level consistent with production of MSY)? Explain the intuition underlying your answer.~ 5. What role is played by the discount rate in the analysis you performed in Question 4? What is the economic explanation