1. Pricing Restrictions versus Quantity Restrictions: 40 points Consider two nightclubs in Pawnee, called the Snakehole Lounge and the Bulge. They both have the same constant (private) marginal cost of production c. The market demand for nightlife in Pawnee is D (p) , where p is the price of entry and demand is decreasing in p. The rms engage in price competition: The demand for the Snakehole Lounge is 0 p5 > 3113 Us (P5493) = %D (P5) P5 = P3 ; D (P5) P5 c or PB 2 p5 > c. (3 points) Unfortunately, both clubs cause noise pollutiona negative production externality that they do not internalize. Fortunately, there is a technology that the clubs can adopt to help reduce the noise pollution (sound absorbing panels). The cost of adopting this technology is different for each club. For the Snakehole Lounge, the cost or reducing 2 units of noise pollution is at c; (z) = zz On the other hand, the cost for the Bulge is _ E 2 CB (2) 22 . It is harder for the Snakehole Lounge to adopt the technology, so ex > B. b. Argue why none of the firms will adopt the pollution reduction technology in the equilibrium in one sentence. (3 points) Suppose that the damage the noise pollution causes the environment is linear in the total units of harmful noise. Hence, the benet of noise reduction is H(zs +23) = 25 +133, where 25 and zB are the total reduction of the Snakehole Lounge and the Bulge respec- tively. c. What is the socially optimal amount of reduction? Underline your answer. Hint: The social benet of reduction is 25 + 1:3 and the social cost of reduction is as (135) + C3 (25) . (4 points) Leslie Knope at the Parks and Recreation Department of Pawnee is considering whether to impose subsidies or quantity restrictions to curb the noise pollution of their environ- ment. The subsidies, (T5, T3) , would be Pigouvian subsidy on the marginal unit of noise reduction that each club emits. The quantity restriction, (25,23) , would be a lower bound. on the amount of noise reduction for each club. For example, the Snakehole Lounge must reduce noise pollution by at least 25. d. What is the optimal Pigouvian subside on the Snakehole Lounge, T5, and the Bulge, T3, to achieve the social optimum? Underline your answer. Hint: With subsidy, the Snakehole Lounge solves maximizes rszs cs (25). (4 points) e. What is the optimal quantity restriction on the Snakehole Lounge, 25, and the Bulge, 25, to achieve the social optimum? Underline your answer. (4 points) f. Do optimal Pigouvian tax policies achieve the same noise reduction as the optimal quantity restrictions in this setting? Please explain why in one sentence. (6 points) Suppose Leslie Knope lcnows that one of the clubs has cost zz and the other has 22, but she does not know which club has the high cost and which one has the low cost. Hence, she can only impose the same Pigouvian tax, 15 = \"[3, and quantity restriction, 25=ZB=%(%+%). g. Are Pigouvian taxes equivalent to quantity restrictions in this case? Which policy is preferred? Please show your work. (6 points) Suppose Ron Swanson suggests to Leslie Knope that she should consider the trading of noise emission permits along with the quantity restrictions. In essence, it initially limits each club to reduce emissions by at least 25 = 23 = % (i + %) , but allows them to trade their reductions at a price if as long as total reductions is larger than a limit: 25 + 23 2 ,1; + %. Assume that both clubs have deep pockets so their budget constraints are non- binding. h. Show that the market equilibrium price is L} = 1. Hint: The market for permits has to cleartotal demand for permits = total supply of permits (which is i + %). (5 points) i. Show that the trading of permits implements the social optimum. (5 points)