Consider a market with network effects (i.e., a consumer’s utility

Consider a market with network effects (i.e., a consumer’s utility depends on the number of users of a product) in which each consumer has a willingness to pay equal to xi where xi is the number of consumers buying product i = 1, 2. The products are functionally identical and thus consumers are indifferent between any products in the market, given equal numbers of units sold. Suppose that the incumbent firm has served mass 2/3 of consumers in the previous period. These old consumers already have experienced product 1 and are not willing to consider product 2. There is mass 1/3 of new consumers, who have not previously experienced product 1. All costs are assumed to be equal to zero. In (1) to (3) firms first set prices and after observing prices, consumers make their purchasing decisions.

1. Suppose that the incumbent firm cannot distinguish between new and old consumers and that firm 2 sets its price before firm 1. What is a subgame- perfect Nash equilibrium that gives the highest profit for the incumbent firm among all equilibria? Characterize this equilibrium.

2. Under the same circumstances as in (1), what is a subgame-perfect Nash equilibrium that gives the highest profit for the entrant firm among all equilibria? Characterize this equilibrium.

3. Suppose now that the incumbent firm can distinguish between new and old consumers and that firm 2 sets its price before firm 1. What are the highest profits that the entrant can make in any subgame-perfect Nash equilibrium? Provide a formal justification of your answer.

4. Discuss the economics behind your results in (1) to (3).

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