The inverse demand for a drug that treats melanoma (a skin cancer) 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 find the profit-maximizing price, first determine the marginal revenue (MR) by differentiating the total revenue (TR = P*Q = (3000 - 10Q)Q) with respect to Q, which gives MR = 3000 - 20Q. Set MR equal to the marginal cost (MC = $10) to find Q: 3000 - 20Q = 10, solving gives Q = 149.5. Substitute Q back into the demand equation to find P: P = 3000 - 10(149.5) = $1,505.

The Inverse Demand for a Drug That Treats Melanoma (A