Problem 2: Negotiating over a Negative Externality. An electricity company's pro- duction process heats a small nearby lake. As the temperature of the lake increases, the water grows moldy in the summer. This negatively affects local residents. Every unit of electricity produced creates a marginal damage of M D = 4, 000. The private benefit of electricity use is P M B = 20, 000 500Q and the private cost of producing electricity is P M C = 1, 500Q. 1. Assume first that the two parties cannot negotiate. a) Find the competitive (private) quantity. b) Find the socially optimal quantity. c) Calculate deadweight loss associated with the competitive quantity in part a). 2. Now assume that the assumptions of the Coase theorem are satisfied. In other words, bargaining is costless and property rights are well-defined. a) If the riparian rights specify that the electricity company has the right to heat up the lake, describe what will happen. (Who pays? How much is paid in total? How many units are produced?) b) If the rights specify that the local residents can restrict heating, what will happen? (Who pays? How much is paid in total? How many units are produced?) 3. Finally assume the electricity company has the rights, but the company and the local residents have to pay a lawyer $2, 500 if they want to negotiate a contract. Will they hire the lawyer? Who (if anyone) ultimately pays the lawyer?