Incumbent Profit Sample Homework

Question: Assume that we have an entry situation like that in the Judo Economics example. There is an incumbent firm (I) and a new entrant (E). Both have constant marginal costs of production, though the costs for the incumbent are lower at $90 per unit versus $110 for the entrant. There are 100 identical buyers who each would be willing to pay $175 dollars for the good. Any consumer can buy from the incumbent, but only those targeted by the entrant can buy from the entrant. Those consumers targeted by the entrant can chose to buy from the incumbent or the entrant and will choose the lowest price. At the first move of the game the entrant decides how many customers (N) to target and sets a single price (P) to those targeted customers. The incumbent then sets a single price for all 100 consumers, deciding to defend the market or accommodate the new entrant. Consumers then purchase the good.

a) Without the new entrant what is the incumbent’s profit in this market?

b) Assume that the entrant aims to target 25 consumers, what is the optimal price for the entrant to charge?

c) A crucial assumption in this example is that the incumbent must charge the same price to all consumers and the entrant can target a subset of the customers. Is this example useful for thinking about markets where prices are negotiated? Why or why not?