Use clearly labelled diagrams to illustrate your answers in parts (a)-(e).

The market demand for pork is given byPd= 120 - Q, whereQis the quantity demanded by consumers when the price the consumers have to pay isPd. Pork is competitively supplied by large number of small farms according to the inverse supply curve (and marginal private cost)MPC= 2Q, whereQ is the amount farmers will produce when they receive a price equal toMPC. The production of pork releases a toxic effluent into the water supply, creating a marginal external cost ofMEC=Q.

(a)What is the free-market equilibrium price of pork? How much pork is bought and sold in the market? [2 points]

(b)Calculate the consumer surplus and the producer surplus associated with pork production and consumption in the free-market equilibrium. What is the social cost of the negative externality? [5 points]

(c)Suppose, the government wants to eliminate the social cost of externality by restricting the quantity of pork production. What size of quota would lead to a socially optimal outcome? What are the consumer surplus and the producer surplus under this policy? [8 points]

(d)Now suppose that the government, instead of quota, introduces an effluent fee payable by farmers. What is the fee rate per unit output that will lead to a socially optimal outcome? What are the government revenues, the consumer surplus and the producer surplus under this policy? [8 points]

(e)As an alternative, to correct for the externality the government is considering a sales tax payable by consumers. That is, when producers receive a price equal toMPC, the price consumers have to pay is(1+t)MPC, wheretis the sales tax rate. What is the sales tax rate that will lead to a socially optimal outcome? What are the government revenue, the consumer surplus, and the producer surplus under this policy? [8 points]

(f)Briefly compare and contrast these three policy instruments (quota, effluent fee, and sales tax). Comment on their relative advantages and disadvantages. [4 points]