A monopoly market is characterized by the inverse demand curve P = 1,200 - 40Q and a constant marginal cost of $200. If the marginal cost of production rises to $400, the profit-maximizing output level _____ units and the price rises by _____.

Question

Quizplus · Accepted Answer

To find the profit-maximizing output level, we first determine the marginal revenue (MR) from the given inverse demand curve, P = 1,200 - 40Q. The marginal revenue curve has the same intercept but twice the slope of the demand curve, so MR = 1,200 - 80Q. Initially, with a marginal cost (MC) of $200, setting MR = MC gives 1,200 - 80Q = 200, which simplifies to 1,000 = 80Q, or Q = 12.5 units. When the MC rises to $400, we set the new MC equal to the MR: 1,200 - 80Q = 400, simplifying to 800 = 80Q, or Q = 10 units. The output level decreases by 2.5 units (from 12.5 to 10). To find the price increase, we substitute the initial and new quantities into the demand equation. Initially, P = 1,200 - 40(12.5) = $700. After the cost increase, P = 1,200 - 40(10) = $800. The price rises by $100.

A Monopoly Market Is Characterized by the Inverse Demand Curve