Carcinogenic chemical with a linear dose-response relationship

Suppose that clinical studies on a particular chemical indicate that in high doses it increases the risk of breast cancer by 1 in 1,000. That is, if 1,000 people were exposed to the high dose we would expect about 1 extra case of cancer. Furthermore, suppose that the clinical dose is about 100 times larger than the dose people actually receive in the environment, and toxicologists believe the dose-response relationship is linear. Finally, suppose that a study has been done of people’s willingness to pay for reducing a similar risk and it was found to be $2 million per life saved.

1. Suppose that one million people are currently exposed to the chemical. Calculate the benefit of a policy that would cut the dose they receive in half. Would this policy be worth doing if it cost $8 million? Explain why or why not.
   
2. Some of the steps in doing the calculation in part (a) are subject to a great deal of uncertainty. Which ones and why? Given this uncertainty, if you had to choose between two equally expensive policies, one which cut the dose in half and one which reduced the exposed population by 50%, which one would you choose? Explain why.