Quantity regulations versus Pigouvian taxes Consider

Two firms that operate in a perfectly competitive market. While producing their products, these firms generate pollution. Assume that it is possible to reduce pollution by adopting an expensive technology. The marginal cost of pollution reduction is MC_A= 6x_A for firm A and MC_B= 4x_B for firm B (where x is the number of abated pollution units).

a) Suppose that the government introduces a quantity regulation and mandates each firm to reduce pollution by 20 units. In other words, x_A=x_B= 20. What is the total cost of pollution abatement in this case?

b) Now consider an alternative regulation: a Pigouvian tax on pollution. Following the notes from class, solve for and when the government introduces a tax on pollution of $96 per unit of pollution. Note that, if your solution is correct, x_A + x_B should be equal to 40. What is the total cost of pollution abatement in this case?

c) Which type of regulation is more efficient and why? Would your answer to this question change if the marginal cost was the same for both firms? Explain why.

d) Now assume that the marginal cost of pollution abatement for firm A increases to MC_A= 12x_A, While the marginal cost for firm B remains at MC_B= 4x_B. Compute the Pigouvian tax that would achieve x_A + x_B = 40.