1. Consider testing of chemicals for potential carcinogens. To properly test each chemical costs $10 million. If Q chemicals are tested a typical household places value $(1 - 0.01×Q) on each chemical tested. There are 100 million households in the U.S.

Question

1. Consider testing of chemicals for potential carcinogens. To properly test each chemical costs $10 million. If Q chemicals are tested a typical household places value $(1 - 0.01×Q) on each chemical tested. There are 100 million households in the U.S.
(a) Calculate the social marginal benefit schedule.
(b) Hence give the optimum number of chemical tests that should be sponsored by the national Institutes for Health.

economyst · Answer

As I see it, the total benefit per person function is (1-.01Q)*Q = Q-.01Q^2. So, the national total benefit function TB is 100Q-Q^2.

The marginal benefit schedule is the first derivative of the TB function. So, MB=100-2Q

MC of a test is given as 10. Set MC=MB and solve for Q. That is 10=100-2Q