Multiple Source Pollution Control

Water pollution from two sources

Suppose you've been put in charge of cleaning up water pollution in a river. The marginal benefit of cleaning up the pollutant is given by MB=500-Q, where Q is the total quantity of abatement, measured in tons. Pollution is currently uncontrolled and totals 1000 tons. It comes from two sources, each of which is now emitting 500 tons. For source 1, the marginal cost of abatement is given by MC1=Q1 (where MC1 and Q1 are the marginal cost and quantity of abatement for source 1) while for source 2 the marginal cost is constant: MC2=100.

  1. Show that the efficient total amount of pollution is 600 tons. Calculate the amount of abatement that should be done by each firm. Show your work and explain what you're doing! Since the answer is given, points will only be awarded for deriving the answer correctly.
  2. Suppose that the legislature becomes concerned about this problem and passes a law requiring each source to reduce emissions by 40%. Would this be efficient? If so, explain why. If not, explain as specifically and non-technically as you can why it is not and calculate the deadweight loss of the policy.
  3. What emissions tax policy would achieve efficiency? Calculate how much such a policy would cost each firm including both abatement costs and taxes. Would the firms prefer this policy or the one from part (2)? Explain why and be specific.
  4. Now suppose the legislature is a bit more enlightened and passes a law requiring emissions to be reduced to 600 tons in such a way that the firms share the burden equally. (That is, their total costs must be equal -- they do not necessarily need to reduce emissions by the same amounts.) Design a tradable permit policy that would accomplish this. How many permits would you give to each source? Why?
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Peter J Wilcoxen, The Maxwell School, Syracuse University
Revised 04/07/2006