The inverse demand for a drug that treats melanoma is given by P = 3,000 - 10Q, where Q measures the number of drug treatments and P is the price per treatment. Suppose that the marginal cost per drug treatment is constant at $10. What is the profit-maximizing price per drug treatment?

Question

Quizplus · Accepted Answer

To maximize profit, we need to set marginal revenue equal to marginal cost. Marginal revenue can be found by taking the derivative of the inverse demand function, which is: MR = 3000 - 20Q. Setting this equal to the constant marginal cost of $10, we have:

3000 - 20Q = 10
2990 = 20Q
Q = 149.5

Now we can find the price that will maximize profit by plugging this quantity back into the demand function:

P = 3000 - 10(149.5)
P = $1,505

Therefore, the profit-maximizing price per drug treatment is $1,505, which is choice (B).

The Inverse Demand for a Drug That Treats Melanoma Is