The demand function for private airplanes is Q = 300 2p. The marginal cost of firms is MCF = 30 + Q. There is a negative externality when consumers use their airplanes, resulting in a marginal cost of pollution of MCP = Q/2. a) What is the socially optimal quantity that should be produced? b) What is the dead-weight loss in competitive markets? c) What is the marginal cost and benefit of reducing pollution at the competitive quantity? What is it at the socially optimal quantity? d) The government considers imposing a linear tax r on private airplanes. What should the level of the tax be in order to implement the socially optimal quantity?