Reference no: EM132396920

This quantitative problem reviews the basic analytics of cost-effective pollution control. Two firms can reduce emissions of a pollutant at the following marginal costs: MC1 = $6·q1 MC2 = $3·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 20 units of emissions (for aggregate emissions of 40 tons), and assume that there are no significant transaction costs.

a) Compute the cost-effective allocation of control responsibility if a total reduction of 10 units of emissions is desired, i.e. how many units of emissions will each firm reduce under a costeffective allocation?

b) If the authority chose to reach its objective of 10 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?

c) The aggregate marginal cost function for the two-firm industry is: MC = 2·Q where MC and Q represent marginal control costs and aggregate control levels, respectively. Explain how to derive this function graphically, or provide the algebraic derivation.

d) Let the marginal benefit function for pollution control be: MB = 40 - 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?