A profit-maximizing monopolist faces a downward-sloping demand curve that has a constant elasticity of -4. The firm finds it optimal to charge a price of $24 for its output. What is its marginal cost at this level of output?

Question

Quizplus · Accepted Answer

For a monopoly firm facing a demand curve with a constant elasticity of -4, the optimal markup (price-cost margin) is given by the formula:

Markup = (1/|E_d|) - 1 = (1/4) - 1/4 = -1/4

Where E_d is the elasticity of demand. In other words, the firm sets its price at a level where the percentage increase in price is four times smaller than the resulting percentage decrease in quantity demanded. This allows the firm to maximize its profit, which is given by:

Profit = (P-MC)Q

Where P is price, MC is marginal cost, and Q is quantity.

At the optimal price of $24, the markup is -1/4, so the marginal cost must be:

MC = P/(1+Markup) = $24/(1-1/4) = $24/(3/4) = $32

Therefore, the correct choice is B, $18.

A Profit-Maximizing Monopolist Faces a Downward-Sloping Demand Curve That Has