Question

Question 2 (7 marks)

A monopolist faces the demand for its product: p = a - bQ. The monopolist has a marginal cost given by c and a fixed cost given by F. Answer the following questions, while showing all of your derivation steps. Just providing final answer does not warrant any mark.

2-a) Assume that F is sufficiently small such that the monopolist produces a strictly positive level of output. What are the profit-maximizing price and quantity? (3 marks)

2-b) Compute the maximum profit for the monopolist. (2 marks)

2-c) For what values of F will the monopolist earn negative profit? (2 marks)

Answer 1

Given pa ba Here Monopolist clume p-MR Destue: The first order conditional profit functim Then a-e6q = 0 taking The q to solve Q = (a-c)/26 The price follows from plugging The optimal output into the demand. pza-b (0-0)/2b I pe a=(a-C)/2 =) p = (a+C)/2 Nere profit comes from plugging the price & quality into 6 profit qualion pi-[cate)/2-C] (a-C)/26-F Il Ri= (a-c)² ub-F

finding F Pico Here F* = (a-c/ub for at Then profits will be negative.