An unregulated electric company is a monopolist and faces demand of Q = 50 - 10P. If the company has zero marginal costs,its profit-maximizing price is

Question

Quizplus · Accepted Answer

To find the profit-maximizing price, we first need to express the demand equation in terms of P. The given demand equation is Q = 50 - 10P. Rearranging for P gives P = 5 - 0.1Q. Since the company has zero marginal costs, its profit is maximized where revenue is maximized. Revenue (R) is P*Q, which from the demand equation is (5 - 0.1Q)Q. To find the maximum revenue, we would typically differentiate this with respect to Q and set it to zero. However, since we are asked for the price, we can observe that the initial rearrangement to solve for P shows that as Q decreases, P increases. The midpoint of the linear demand curve (where elasticity is -1) maximizes revenue. Setting Q = 25 (half of 50) in the demand equation gives P = 5 - 0.1(25) = 2.5, which is the profit-maximizing price.

An Unregulated Electric Company Is a Monopolist and Faces Demand