Question

Which of these two policies maximizes social welfare:
(a) Policy 1. Spend $1,000 per capita on regulation such that average cancer risk is 1 in 1 million from lifetime exposure to air pollution and 1 in 1 million for lifetime exposure to water pollution.

(b) Policy 2. Spend $1,000 per capita on regulation such that average cancer risk is 1.2 in 1 million from lifetime exposure to air pollution and 0.7 in 1 million for lifetime exposure to water pollution.

Answer 1

The policy that maximizes total social welfare is the policy 1. Let's why it is true, we need to maximize total social welfare. So this purpose we need to see which policy measure is better for society as a whole by doing cost benefit analysis. As you can see the cost for both the policy measures is same that spends $1,000 per capita. But in policy 1 the average cancer risk is 1 in million from lifetime exposure to air pollution and 1 in million from lifetime exposure to water pollution. Whereas in policy 2, the average cancer risk is 1.2 in million from lifetime exposure to air pollution and 0.7 in million from lifetime exposure to water pollution.

Policy 1 reduces the probability of cancer for kind pollution exposure while policy 2 increase the chance of cancer from 1 pollution and decreases the chance of cancer from another pollution. The problem with second policy is that it reduces the probability of cancer from water pollution in trade of increase in the probability of cancer from air pollution which not desirable for society as whole. Because we know that there is no trade off between these two sources of cancer. Since getting cancer from either source is equally likely so we must minimize the probabilities across all sources and reducing overall chance of getting cancer. Because one can get cancer from air pollution as well as water pollution, if at all we must minimize the probability of getting cancer from air pollution because we face air pollution more than water pollution.

So it is never socially optimal to decrease the probability of damage from one source by increasing the probability of damage from another source. Because damage can occur from either source. When the probability of damage from either source is equal then we say it's at optimal level. That's why policy 1 will maximize the social welfare.