Question

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 #1

**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**

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