Firms A and B each produce 100 units of pollution. Firm A has a marginal cost of
ID: 1168690 • Letter: F
Question
Firms A and B each produce 100 units of pollution. Firm A has a marginal cost of pollution reduction of MCA= 10+2QA. Firm B has a marginal cost of pollution reduction of MCB=3QB. The marginal benefit of pollution reduction is $150 per unit.
a. What is the socially optimal level of pollution reduction for each firm?
b. How much total pollution is there in the social optimum?
c. Explain why it would be inefficient to divide this optimal level of pollution by two and give each firm an equal number of pollution permits if they are not allowed to trade them.
d. How can the social optimum be achieved if firms are given equal numbers of pollution permits but are allowed to trade them?
e. A social optimum can also be achieved using a tax on pollution. What level of tax should the government choose?
Explanation / Answer
a. The marginal costs of pollution abatement are MCA=10+2QA and marginal cost of MCB=3QB .The socially optimal level of pollution abatement for each firm is where the marginal cost is equal to the marginal benefit.Therefore for firm A 10+2QA=150, on solving further we get 2QA=140(150-10) i.e QA= 70(140/2) and for firm B 3QB=150 i.e QB =50(150/3).Firm A should reduce pollution by 70 units, and firm B should reduce pollution by 50 units.
b. The total pollution is of 120units (70+50) for social optimum.
c. For the market to be in equilibrium ,the marginal cost shall be equal across the firms .It would be inefficient to divide this optimal level of pollution by two because they are not allowed to trade them.
d. If the firms are given equal level of permits i.e 60 units each for firm A and firm B. Permits for firm A should be reduced by 10 units and permits for Firm b shall be increased by 10 units to achieve social optimum.
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