The inverse demand curve for a monopolist changes from P = 100 - 2Q to P = 120 - 2Q, while the marginal cost of production remains unchanged at a constant $20. After the change in the demand curve, the profit-maximizing price rises from _____, and the profit-maximizing output rises from _____.

Question

Quizplus · Accepted Answer

Before the change, the inverse demand curve is P = 100 - 2Q. The marginal cost (MC) is constant at $20. To find the profit-maximizing quantity (Q), set MC equal to marginal revenue (MR). MR is derived from the demand curve, which has the same intercept but twice the slope, so MR = 100 - 4Q. Setting MR = MC gives 100 - 4Q = 20, solving for Q gives 20 units. Substituting Q back into the demand curve gives the price: P = 100 - 2(20) = $60.After the change, the inverse demand curve is P = 120 - 2Q. Following the same process, MR = 120 - 4Q. Setting MR = MC gives 120 - 4Q = 20, solving for Q gives 25 units. Substituting Q back into the demand curve gives the price: P = 120 - 2(25) = $70.Thus, the profit-maximizing price rises from $60 to $70, and the profit-maximizing output rises from 20 units to 25 units.

The Inverse Demand Curve for a Monopolist Changes from P