Firms A and D each produce 200 units of pollution. The federal government wants

Question

Firms A and D each produce 200 units of pollution. The federal government wants to reduce pollution levels. The marginal costs associated with pollution reduction are MCa = 240 + 4Qa and MCB = 60 + 2QB? for firms A and B, respectively, where Q A and Q B denote the amount of reduction. Society's marginal benefit of reduction is M B = 600-2/3 Qt where Qt is the total level of pollution reduction (QA +Qn = QT)- Answer the following: What is the socially optimal level of each firm's production? How much total pollution is there in the social optimum? Explain why it is inefficient to give each firm an equal number of pollution permits. Can the social optimum be achieved using a tax on pollution?

Explanation / Answer

Solution :

MCA = MCB = MB

240 + 4QA = 60+2QB

240 + 4QA - 60 = 2QB

180 + 4QA = 2QB

QB = 90 +2QA

MCB = M B

60 + 2QB = 600 - 2/3 QT

60 + 2( 90 + 2QA ) = 600 - 2/3 ( QA + 90 + 2QA )

60 + 180 + 4QA = 600 - 2/3QA   - 60 - 4/3 Q A

240 + 4QA = 600 - 60 - 2QA

6QA = 600 - 60 - 240

6QA = 300

QA   = 50 units

240 + 4QA = 60+2QB

240 + 4 X 50 = 60 + 2QB

440 = 60 + 2QB

QB = 190

b) QT = QA + QB

QT = 190 + 50

QT = 240

c) It is inefficient to give equal number of pollution permits because firm A is better at pollution reduction , it makes sense from society's point of view to concentrate pollution reduction at firm A , thereby there will be an overall reduction in pollution . If equal number of permits is granted then greater pollution is caused .

d) The social optimum can be acheived using a tax on pollution because the tax has the effect of increasing the price and thus firms will reduce the output and this will lower the pollution level .

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