Oligopolistic models are based on behavioral assumptions. One behavioral assumption associated with differentiated product markets is that price increases will not be matched. This rather pessimistic view of pricing leads to the kinked demand curve. To examine why, consider the following simple model. Market inverse demand is given by
P(Q) = 10-Q.

a. Suppose firm A controls 50% of the market. What is the demand curve faced by this firm? White inverse demand in slope-intercept form.

Suppose the current price of the product is $6
b. What is the demand faced by firm A given P=$6? Call this quantity Qb
c. Suppose that if firm A increases its 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 above P=$6 and the segment below P =$6. What should happen to market shares for prices above $6? What happens to market share 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 $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. (Hint: the equation for the inverse demand curve must be done in two parts.)