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.

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

To calculate the social marginal benefit schedule, we need to determine the value that each household places on testing each additional chemical. The value placed on each chemical tested is given by $(1 - 0.01×Q), where Q represents the number of chemicals tested.

(a) To calculate the social marginal benefit for each chemical, we multiply the value placed by each household by the number of households. Since there are 100 million households in the U.S., the social marginal benefit for each chemical tested can be calculated as follows:

Social Marginal Benefit = $(1 - 0.01×Q) × Number of Households
= (1 - 0.01×Q) × 100 million
= 100 million - 1 million×Q

Therefore, the social marginal benefit schedule is given by the equation: Social Marginal Benefit = 100 million - 1 million×Q.

(b) To determine the optimum number of chemical tests that should be sponsored by the National Institutes for Health (NIH), we need to consider the social marginal cost as well.

The cost of testing each chemical is $10 million, so the social marginal cost for each chemical tested is constant at $10 million.

To find the optimum number of chemical tests, we need to equate the social marginal benefit and the social marginal cost. So, we set:

Social Marginal Benefit = Social Marginal Cost

100 million - 1 million×Q = $10 million

Rearranging the equation, we get:

1 million×Q = 100 million - $10 million
= 90 million

Dividing both sides by 1 million, we find:

Q = 90

Therefore, the optimum number of chemical tests that should be sponsored by the NIH is 90.