Consider a monopoly with inverse demand function p = 20

Question

Consider a monopoly with inverse demand function p = 20 - y and cost function c(y)= 4 + y². The profit maximizing output is: A)5. B)2. C)10. D)4.

Quizplus · Accepted Answer

The profit-maximizing output is found by setting marginal revenue equal to marginal cost. Marginal revenue is the derivative of total revenue with respect to output, and marginal cost is the derivative of total cost with respect to output. In this case, total revenue is given by TR = p * y = (20 - y) * y = 20y - y^2, and total cost is given by TC = 4 + y^2. Therefore, marginal revenue is MR = d(TR)/dy = 20 - 2y, and marginal cost is MC = d(TC)/dy = 2y. Setting MR = MC, we get 20 - 2y = 2y, which implies y = 5.