Suppose a large firm is the price leader in an industry that is comprised of itself and a few other smaller firms. The large firm estimates the market demand for the industry’s (homogeneous) product to be QM = 81,000 – 200P, and it expects the smaller firms to supply output according to the following function:
QS = 1,000 + 50P.
The large firm’s marginal revenue function is MR = 320 – 0.008QL and its marginal cost function is MCL = 100 + 0.014QL.
What price should the large firm set for the industry?
How much will the large firm sell at this price?
How much will the smaller firms (collectively) sell?