Suppose that there are 60 consumers whose preferences for queen size mattresses are uniformly distributed over a unit interval characterizing the softness of the mattress. The leftmost end of the interval can be called Sinkingly Soft (very soft) while the rightmost end can be called Rest on a Rock (very hard). Currently, there are two mattress producers in the market; Firm A is located at the leftmost endpoint, while Firm B is located at the rightmost endpoint. The marginal and average costs to the firms are constant and equal to $90. Consumers face a transportation cost of $30γ, where γ represents the distance between their most preferred mattress type and the type they actually purchase.
1a. Suppose Firm A charges $100 for a mattress and Firm B charges $110 for a mattress. How many mattresses will Firm A sell? Firm B? Compute each firm's respective profits.
1b. Carefully graph the situation in part a; that is, graph the spatial market, the firms' locations, the delivered pricing schedules and indicate: i) the location of the marginal consumer, and ii) the market share for Firm A and the market share for Firm B.
