Question

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?

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

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

Answer #1

a) The monopolist will choose p=MR (or derive from first order condition of profit function).

So, a-2bq = c

Solving for q

Q = (a-c)/2b

The price follows from plugging the optimal output into the demand

P=a-b(a-c)/2b = a-(a-c)/2 = (a+c)/2

b) The profit comes from plugging the price and quantity into the profit equation:

Pi=[(a+c)/2-c](a-c)/2b-F

= (a-c)^{2} /4b-F

c) Find F such that Pi = 0:

F* = (a-c)^{2}/4b

For F>F*, profits will be negative.

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