Question

This problem set reviews the basic analytics of cost-effective pollution control. Two

firms can reduce emissions of a pollutant at the following marginal costs:

MC1 = $12·q1;

MC2 = $4·q2,

where q1 and q2 are, respectively, the amount of emissions

reduced

by the first and

second firms. Assume that with no control at all, each firm would be emitting 40 units of

emissions (for aggregate emissions of 80 tons), and assume that there are no significant

transaction costs.

1) Compute the

cost-effective

allocation of control responsibility if a total reduction of 20

units of emissions is desired, i.e. how many units of emissions will each firm

reduce

under a cost-effective allocation? (10 points)

2) If the authority chose to reach its objective of 20 tons of aggregate reduction with an

emission charge, what per-unit charge should be imposed? How much government

revenue will the tax system generate, if the tax is levied on all units of emission? (10

points)

3) Let the marginal benefit function (same as marginal control cost) for pollution control be:

MB = 35 - 0.5·Q

What is the efficient level of pollution control (call it Q*)? Is the cost-effective tax you

calculated in question 2, above, just right, too low, or too high to achieve the efficient

level of control? What emission tax would achieve the efficient level of control? (10

points)

Answer 1

1) Computing the cost effective allocation of control resposibility when a total reduction of 20 units of emissions is desired

MC1 = MC2, q1 + q2 = 20

12q1 - 4(20-q1) = 0

16q1 - 80 = 0

q1 = 5 tons, q2 = 20 - q1 = 15 tons.

2) If the authority chose to reach its objective of 20 tons of aggregate reduction with an emission charge,then the per unit charge and government revenue generated from tax revenue

Tax = MC1 = MC2 = 12(5) = 60 or 4(15) = $60 per ton

Revenue = tax * (tons of pollution emitted)

Revenue = 60(40-5) + 60(40-15) = 2100 + 1500 = $3600