A large firm that is a price leader in an industry characterized also by many small competing firms estimates that the market demand for its product to be as follows: Q_m = 20,700 - 75P, where Q_m is units per month.
It expects small firms in the industry to supply output according to the following function: Q_s = 700 + 25P. If the large firm's marginal cost is constant at $52, what quantity will it sell?

Question

Quizplus · Accepted Answer

To determine the quantity that the large firm will sell, we need to find the point at which its marginal cost equals its marginal revenue. The large firm's marginal revenue can be found by taking the derivative of the market demand function with respect to quantity: MR = d(Q_m)/dQ = 20,700/75 - (75P)/75 MR = 276 - P Setting MR equal to MC: 276 - P = 52 Solving for P: P = 224 Substituting this value for P into the market demand function, we can find the corresponding quantity: Q_m = (20,700 - 75P)/1 Q_m = (20,700 - 75(224))/1 Q_m = 7,400 Therefore, the large firm will sell 7,400 units when its marginal cost is constant at $52. The correct answer is D) 7,400.

A Large Firm That Is a Price Leader in an Industry