The total cost function of a monopoly firm is: TC= 40 + 96Q - 2Q^2, where TC is

Question

The total cost function of a monopoly firm is: TC= 40 + 96Q - 2Q^2, where TC is the total cost and Q is the output. The demand function is: P = 120 - 3Q (P being the price and Q is the quantity). a. Find out the optimal output and the price. Explain. b. Suppose now that the demand function changes to: P = 80 -1.5Q. Find out the optimal output and the price. Explain. c. It is impossible for a monopoly to produce where average cost is decreasing. Do you agree or disagree with this statement? Explain. d. Why will a monopolist's profit maximizing rate of output be in the region of elastic demand? Explain.

Explanation / Answer

1.

TC=40+96Q-2Q^2

MC = 96-4Q

MR =P=120-3Q

For profit maximization MR=MC

96-4Q = 120-3Q

Q=0 firm will not produce in the market.

2.

MR=MC

96-4Q=80-1.5Q

2.5Q = 16

Q = 6.4, P =70.4

3.

No for this cost function average cost function is always decreasing and firm is producing at Q=6.4 units.

4.

A profit maximizing monopoly will always set price on the elastic part of the demand curve, as marginal revenue is positive in this region which is equal to marginal cost.

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