A farmer must decide how much of an area of land she should use for corn production. Market demand for corn can be written as Q = 450 - 2P. Quantity is measured as units, and price is measured as $/unit. The farmer's private marginal cost of corn production can be represented by the following function: MCP = Q. Note, any land brought into corn production accelerates its erosion and nutrient runoff into the local river. Therefore, there are additional costs of bringing land into production not captured by the farmer's private marginal cost function. The social marginal cost of corn production (i.e., the sum of the farmer's private marginal cost and the negative externality of erosion) can be represented by the following function: MCS = 2Q. a. (12 marks) Graph the demand function, the private and social marginal cost functions. b. (10 marks) What will be the market equilibrium price and quantity if external costs are not accounted for? c. (8 marks) What should be the market equilibrium price and quantity in an efficient allocation? d. (8 marks) What level of Pigouvian tax achieves efficient allocation. Show it on the graph in part a.