Consider two nightclubs in Pawnee". called the Snakehole Lounge and the Bulge. They both have the same constant {private}I marginal cost of production :3. The market demand for nightlife in Pawnee is D (p) , where p is the price of entry and demand is decreasing in p. The firms engage in price competition: The demand for the Snakehole Lounge is '0 F's 3" Fe De (Pepe) = in {re} P3 = Fe . D [Psi Ps *1 FE where :13 is the entry price set by the Snakehole Lounge and pH is the price set by the Bulge. The demand for the Bulge is defined analogously. In essence. the club with the lowest price captures the whole market and they both share the market equally if the}r set the same price. a. Argue mat the equilibrium price is 11; = pa = c. Hint: Consider what happens in the following alternative situations: (in fig s: c or pH if. c, and (ii) 113 2 p5 :1 c or Fe 2 Ps 3* E; [3 Pimsl Unforhmatelg both clubs cause noise pollutiona negative production externality that they do not internalize. Fortunately, there is a tecl'molog},r 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 cast or reducing 2 units of noise pollution is o: c e = zz. s K 1 2 0n the other hand, the cost for the Bulge is :3 (e) 2 $22. It is harder for the Snakehole Lounge to adopt the technology.r so a: .1:- ,3. b. Argue why none of the rms 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 banst sfnsise reduction is H [25 +33) = 25 +23, where as and 23 are the total reduction of the Snakehole Lounge and the Bulge respec- titrely. c. 1ir'ii'hat is the socially optimal amount of reduction? Underline your answer. Hint: The social benet of reduction is 23 +23 and the social cost of reduction is c3 [23) + C3 (23} . {it Pitl 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, (1'5, 1'3) , would be Pigoutrian subsidy on the marginal unit of noise reduction that each club emits. The quantity restriction, {55,53} , would be a tower based on the amount of noise reduction for each club. For example, the Snakehole Lounge must reduce noise pollution by at least 55. d. 1it"ti'hat is the optimal Pigouvian subside on the Snakehole Lounge, T5, and the Bulge, 1'3, to achieve the social optimum? Underline your answer. Hint: With subsidy; the Snakehole Lounge solves maximizes T533 c, [is] . [4 points] e. 1it"ti'l'iat is the optimal quantity restriction on the Snakehole Lounge, 55, and the Bulge, E3, to achieve the social optimum? Underline your answer. {It points} 1'. Do optimal Pigouvian tax policies achieve the same noise reduction as the optimal quantity restrictions in this setting? Please explain why in one sentence. [E- points} Suppose Leslie Knope knows that one of the clubs has cost E22 and the other has 13-22, but she does not lcnow which club has the high cost and which one has the low cost. Hence, she can only impose the same Pigouyian tax, r3 = TE, and quantity restriction, s=s=se+s- g. Are Pigouyian taxes equivalent to quantity restrictions in this case? Which policy is preferred? Please show your work. {ti points]I 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 :53 5- 51(3 + -) , but allows them to trade .5 theirlreductions at a price it as long as total reductions is larger than a limit: 25 + :3 33 - + __ I t3 h. Show that the marlcet equilibrium price is q = 1. Hint: The marlcet for permits has to cleartotal demand for permits 2 total supply of permits [which is 3-! + ,i'si' (5 points} i. Show that the trading of permits implements the social optimum. {5 points]I
