Question

An oligopoly firm faces a kinked demand curve with the two segments given by: P = 230 – 0.5Q and    P = 280 – 1.5Q. The firm currently has a constant marginal cost, MC of $150.

1. State the assumptions of the kinked demand model in terms of price-matching and elasticity.

2. Determine the quantity and price at the kink.

3. Calculate how much higher the marginal cost must be before the firms would change the profit-maximizing output and therefore the price.

Answer 1

a)

The Assumption of the kinked demand curve model is that the competitor of the oligopoly firm matches its rival prices in case of a price cut, thus the portion of the demand curve is relatively inelastic to the right of a kink. On the other hand, the rivals do not follow a price increase and thus the demand curve is relatively elastic to the left of the kink.

b)

At the kink both portions of the demand curve intersect. Therefore at the kink

c)

The firm has a discontinuous MR curve at Q=50. The MR segment for both the curve is

At Q=50,

As long as MC lies between these two MR, or 180<MC<130, the firm will produce at the kink. To change the price and quantity the MC must rise above $180 or fall below $130.

The MC must rise above $180 to change the price and quantity.