Oligopolistic models are based on behavioral assumptions. One behavioral assumption associated with differentiated product markets is that price increases will not be matched, but price decreases will be matched. This rather pessimistic view of pricing leads to the kinked demand curve discussed in Figure 9.3. To examine why, consider the following simple model: Market inverse demand is given by
P(Q) = 10 - Q.
a. Suppose firm A controls 50 percent of the market. What is the demand curve faced by this firm? Write inverse demand in slope-intercept form.
Suppose the current price of the product is $6.
b. What is demand faced by firm A given P = $6? Call this quantity Qb.
c. Suppose that, if firm A increases price from this point, other firms do not match the price increase. But if A decreases price, other firms decrease price to maintain their market share. The demand in this instance has two segments: the segment above P = $6 and the segment below P - $6. What should happen to market share for prices above $6? What happens to market share for prices below $6?
The final question that must be answered is how quickly does market share decline as price increases. Suppose A's demand is linear above P = $6 and A is unable to sell any output above P = $8.
d. Describe algebraically the inverse demand curve faced by the firm in this instance. Provide a graph that is consistent with your answer. Based on this graph, explain why this is called the kinked demand model.