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?
Answer:
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
Get Answers For Free
Most questions answered within 1 hours.