Suppose that there are 1000 agents with a positive willingness to pay for a good (say, cars). The agents are heterogenous in their willingness to pay. These willingness to pays are uniformly distributed between 1 and 1000. Hence, someone has willingness to pay 1000, someone has willingness to pay 999, someone has willingness to pay 998,..., someone has willingness to pay 2, and someone has willingness to pay 1. The consumption of this good has a negative externality on others. The total size of this externality is e(q) = 1000 4q for all q > 0 and e(q) = 0 for q = 0; where q is the number of agents consuming the good. The good is produced by a competitive industry. The total cost of producing the good is T(qi) = 300qi for all firms in the industry, where qi is the quantity produced by the firm. a) Draw the market demand curve. b) Draw the industry supply curve (in the absence of any taxes). c) Solve for the competitive equilibrium allocation and price (in the absence of any taxes and other government interventions). d) Solve for the efficient allocation. e) (challenging) Solve for the optimal tax policy. f) (challenging) Calculate total surplus under three scenarios: (1) when there is no government intervention, (2) when government imposes the optimal tax, and (3) when government bans the production of cars. g) (challenging) Calculate the deadweight loss associated with the competitive equilibrium in the absence of any government intervention.