Question

Consider a “location” model of product differentiation. Suppose each firm chooses taste parameter θ to correspond to its “position” on the unit interval. Ex. The highest level of the taste parameter is θ = 1 and the lowest level is θ = 0. The center of the spectrum of course is θ = 0.5. Suppose there are two firms in the market. Assuming there is fierce price competition, where should they optimally locate?

Answer 1

Solution:

The firms will be located at the middle location where =0.5. This is because if the firms are located at the extremes then a firm can gain more consumer by shifting towards the center. For example, if firm 1 located at =0.2 and firm 2 located at =0.7, then firm 1 cover market from =0 to 0.45 ((0.2+0.7)/2) while firm 2 cover market from =0.45 to 1. Therefore, firm 2 would cover more market then firm 1. Hence, firm 1 will shift towards center more than firm 2. By continuing this process, both firms would be located at the centrer where they share equal market and cannot increase there share more after. Therefore optimally they should be located in the center.