The total cost function of a monopoly firm is: TC= 40 + 96Q - 2Q^2, where TC is
ID: 1096580 • Letter: T
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.