Question

Consider the Hotelling model of the competition between two firms discussed in class. Select all that apply a. If both firms are localized in position 1/2G.e., center of the line), neither firm has incentives to deviate and move to a different position D. In the Nash Equilibrium in pure strategies firms will localize together anywhere along the line. C. lf Firm 1 is located at position 1/2 (i.e., center of the line) and firm 2 is located somewhere else, then both firms have incentives to deviate and change their position along the line. d. If Firm 1 and Firm 2 localize at the same point along the line, they will each sell to 50% of the consumers.

Answer 1

As per the Hotelling model of competition between two firms, we assume that consumers are indifferent, and firms want to differentiate as much as possible. Consumers are uniformly distributed and go to the closest firm, as a rule.

a. Now, if both firms are located in postion 1/2, that is, the center of the line, neither has incentive to deviate and move to a different position. Both want to locate where the demand is. And in case of no price competition (that is, prices are regulated), both will want to stay near consumers and split the market. This statement is therefore, true.

b. In the Nash equilibrium in pure strategies, firms will localize together anywhere along the line. The Nash equilibrium is for both firms to select the median location, that is midway. Doing so guarantees the firm half the business. Deviating to any other location generates less business. Thus, firms cannot be located anywhere together for Nash equilibrium. This statement is false.

c. If Firm 1 is located at position 1/2 (i.e., center of the line) and firm 2 is located somewhere else, then both firms have incentives to deviate and change their position along the line. If this happens, let us assume the placement of firms to be as shown:

---------------------------------Firm1----------------Firm2-------
We can see that all customers from the left half, and some part of the right half will go to Firm 1. Firm 1 can shift its location closer to Firm2, slowly, drawing in even more customers. Firm 2, on the other hand, will want to move closer to the center, because it has less than optimum customers. Both firms want to deviate and change their position. This statement is true.

d. If Firm1 and Firm2 localise at the same point along the line, they will each sell to 50% of the consumers. This is true, considering no product differentiation and equal pricing, both will split the market 50-50. This statement is true.

Hope this helped!