Problem 3: Regulating an Externality. An energy company's production process spits toxins into the air. At high enough concentrations, these toxins can increase the incidence of cancer for those living in the area. The true marginal cost of pollution reduction (R) is M C = 2R. The government thinks the marginal cost of reduction is M Cg = 3R. The marginal damage curve is given by M D = 120 3R. a) What is the socially optimal level of pollution reduction? Label this R?. b) What does the government think is the socially optimal level of pollution reduction? Label this Rg. c) The government, confident that the marginal cost is M Cg, decides to use a Pigouvian tax to achieve the level of reduction Rg. What tax per unit of pollution will the government choose? Label this tax tg. d) What tax per unit of pollution achieves the true socially optimal level of reduction, R?? Label this new tax t?. Is the tax tg from part c) too high or too low? e) Calculate the deadweight loss associated with the tax tg from part c).