Consider the horizontal quality model on the unit interval from 0 to 1. There ar
ID: 1206158 • Letter: C
Question
Consider the horizontal quality model on the unit interval from 0 to 1. There are Nconsumers located uniformly along the interval. There are two firms, with zero marginal costs, initially located at 0 to 1. Consumers will buy one unit of the good from the lowest cost retailer as long as the effective price is below V. They have transportation costs of t getting from their location to the store and back.
1. If both firms locate together at the middle, what is the equilibrium price?
2. Show that firm 1 has a profitable deviation from locating at the middle with the other firm.
3. Show that if firm 1 moves away from firm 2, firm 2 will want to deviate as well.
4. Explain why there is no pure strategy Nash equilibrium in this game.
5. In principle, what objects must on solve for to find the mixed strategy equilibrium?
Explanation / Answer
This question related to Hotelling's Law of location. The answers are as follows:
1. If both firm locate together at the middle - the equillibrium price charged by each seller will be the same, since there cannot be any price differentiation when the two sellers are so close to each other.
2. Firm 1 will find it profitable to relocate from the middle and step over to Firm 2 area in the hope that he can get firm 2's customers. This is assuming that the added revenue for him will be more than the cost of relocation
3. If firm 1 moves away, firm 2 will want to deviate and move closer to initial point in order to minimise the distances for his customers (who are going to come largely from the other end of the interval)
4. There is no pure nash eqm since this is sequential game - in which 1 firms action is dependent on the other firms action