3. (18 marks) The marginal benefit of reduction is given by MB = 20-x and the marginal cost of reduction is given by MC =10+ x, where x is the number of units. a. (2 marks) Calculate the efficient amount and price of reduction. b. (2 marks) Calculate the total surplus under the efficient amount of reduction. The regulator is imperfectly informed about the market and sets a price for reduction that happens to be twenty percent less than the efficient price of reduction. c. (2 marks) Calculate the price and amount of reduction achieved in response to the regulator's price policy. d. (2 marks) Calculate the total surplus in response to the regulator's price policy. e. (2 marks) Calculate the reduction in total surplus in response to the regulator's price policy.2. (16 marks) In the text, we looked at the simplest bioeconomic model for renewable resource growth, the logistic growth function. That function, S,,, = S, + gS, 1-2 , defines the stock of the renewable resource at time t +1, S,, , as a function of the stock of the renewable resource at time t, S, , the intrinsic growth rate of the renewable resource, g, and the natural carrying capacity, K. For this question, let the renewable resource be the number of lobsters off the shore of Corduroy Island. a. (2 marks) Briefly explain the relationship between S, and S,,, that indicates a "sustainable" lobster population. b. (2 marks) If the lobster population is sustainable, determine how many, if any, can be sustainably "harvested" (ie, caught) in any given year. Use the variable H to represent this amount and describe it in terms of g, S and K. Assume that the harvest, H, is a function of the fisher's effort, e, and how easy it is to catch lobsters, 0 (this is known as the "catchability coefficient"). In other words, assume that H = deS. c. (2 marks) Use this information, along with your result in part (b) to calculate the sustainable stock of lobsters, S", as a function of g, K, e and 0.d. (2 marks) Briey explain how the sustainable stock depends on g, K, e and B. (No math is required here nor is getting the correct answer in part (c), just common sense.) e. (2 marks) Substitute the sustainable stock of lobsters found in part (c) into the harvest function H = 9.95 to calculate the sustainable harvest as a function of g, K, e and 6. If the lobster sher increases her effort by one unit, it costs her 0, but the additional number of lobsters 23 she catches is given by ME. = 91([1 . Each additional lobster can be sold at a price of p. g f. (2 marks) Calculate her efcient effort level (ie, the effort level that balances the marginal benefit to her against the marginal cost to her) as a function of g, K, e, 9 , p and c. g. (2 marks) Briey explain how the efficient effort level depends on g, K, 6' , p and c. (No math is required here nor is getting the correct answer in part (f), just common sense.) h. (2 marks) Assuming that 3, K and E} are functions of nature and not within our control, briey explain how changes in p and 6 could lead to a collapse in the lobster shery. (No math is required here, just common sense.) Instead of the tax, the regulator sets a quantity for reduction that happens to be twenty percent less than the efficient quantity of reduction. f. (2 marks) Calculate the amount of reduction and price achieved in response to the regulator's quantity policy. g. (2 marks) Calculate the total surplus in response to the regulator's quantity policy. h. (2 marks) Calculate the reduction in total surplus in response to the regulator's price policy. i. (2 marks) If the regulator is concerned about efficiency, briefly explain whether the regulator should set a price that is twenty percent below the efficient level or set a quantity that is twenty percent below the efficient level. 13