Measuring Environmental Benefits

Nonlinear dose-response relationship

Imagine that the government is considering what, if anything, should be done about a carcinogenic air pollutant in a city of 1 million people. No epidemiological studies of the substance are available. There has been a single clinical study in which a dose of 100 units of the chemical were shown to cause 10 fatal cases of cancer in a population of 1000 rats. However, the usual dose that people are exposed to in the environment is 1 unit.

  1. Suppose that a pollution abatement policy is available that would reduce the average dose to 0.5 units at a total cost of $15 million. Under the usual assumptions used in risk analysis, how high would the population’s willingness to pay per life saved have to be to justify this policy? How does this value compare to real world estimates of the willingness to pay to save a life? Is this likely to be a good policy? Why or why not?
  2. Now suppose that a second clinical study is conducted, but at a higher dose. This time, 150 units of the chemical produce 20 fatal cases of cancer per 1000 rats. The new study leads toxicologists to revise their opinion about the dose-response function. One group believes that the function has the form: R=A+B*D, where D is the dose, A and B are unknown constants, and R is the number of cases of cancer per 1000 animals. The other group believes the function is quadratic: R=E*D + F*D^2, where E and F are constants. If the first group is right, would you want to adopt the abatement policy? Explain why or why not and calculate any numbers that are important for your argument. What would you want to do if the second group is right? Why? Again, calculate any important numbers and justify your answer.
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Peter J Wilcoxen, The Maxwell School, Syracuse University
Revised 04/07/2006