Question

# An oligopoly firm faces a kinked demand curve. One segment is given by the equation P...

An oligopoly firm faces a kinked demand curve. One segment is given by the equation P = 100 – Q, and the other segment is given by P = 120 – 2Q. The firm has a constant marginal cost of \$45.

a) What is the firm’s profit-maximizing level of output and price?

b) What are the upper and lower limits which marginal cost may vary without affecting either the profit-maximizing output or price?

A]

The two demand segment faced by the firm is given as :

P = 100 – Q

P = 120 – 2Q

Now

100 – Q = 120 – 2Q

Q = 20

P = 100 – Q = 100 – 20 = 80

The firm’s profit-maximizing level of output is 20 and price is 80

B]

For upper limit substitute Q = 20 in MR1

TR1 = (100-Q)*Q = 100Q – Q^2

MR1 = 100 – 2Q(diff wrt Q)

TR2 = (120 – 2Q) * Q = 120Q – 2Q^2

MR2 = 120 – 4Q(diff wrt Q)

MR1 = 100 – 2Q = 100 – 2 * 20 = 60

For lower limit MR2 = 120 – 4Q = 120 – 4(20) = 120 – 80 = 40

The upper and lower limits which marginal cost may vary without affecting either the profit-maximizing output or price are 40 < MC < 60

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