Two firms X and Y, each produce 400 units of pollution. The government wants to reduce the total pollution levels. The marginal cost of pollution reduction for each of the firms is as follows:

MCx = 250 + 15QX

MCy = 100 + 30QY

QX = pollution reduction by firm X, QY = pollution reduction by firm Y

The social marginal benefit of pollution reduction is given by MB = 3100 – 15QT.

QT = total pollution reduction.

(i) What is the socially optimal level of each firm’s pollution reduction?

(ii) What is the socially optimal level of total pollution?

(iii) The government can achieve an efficient outcome by mandating that each of the firms reduce their pollution by equal amounts i.e. by an amount equal to half of the socially optimal level of total pollution reduction. True or false? Explain your answer.

(iv) A system of tradable permits where each firm receives an initial allocation of 200 permits can achieve the social optimum. True or False? Explain your answer. Assume that each permit allows the firm to emit one unit of pollution.