Two firms are engaged in Bertrand competition. Both firms have a stable marginal cost of €7. Presently, every firm is allocated half the market. There are 10,000 people in the population and every of them are willing to pay at most €12 for one unit of the good. Further, consumers can Only purchase one unit of the good and it costs every of them ? to switch from one firm to another. Suppose that there is perfect information in this market, which means that customers know what prices are being charged. Law or custom restricts the firms to charging whole amounts (e.g., they can charge €8, but not €8.50).
a) Suppose that switching costs are zero. What are the Nash equilibria of this model? Why does discrete pricing result in more equilibria than continuous pricing?