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?