Three firms can control pollution with the following marginal costs of pollution reduction:

MC1 = e1,MC2 = 3e2,MC3 = 6e3

where e1,e2, and e3 are the amount of pollution reduced by the first, second, and third firms respectively.

Assume that with no control at all, each firm would be emitting 1000 units of pollution, or a total of 3000 units for all firms. Suppose that the government sets a pollution goal of 1800 units of total pollution.

a. Compute the level of emission reduction per firm that is cost effective for society. Show your working. (4 marks)

b. What emissions fee (tax) should the government impose to achieve the cost effective solution you computed in part a.? Show your working. (2 marks)

c. Suppose the government imposes the emissions fee (tax) you found in part b. Compute the following:

i Firm 2's total tax bill. (2 marks)

ii. Firm 2's total abatement costs. (2 marks)