Consider the setup of the standard vertical differentiation model. Suppose that consumers have types distributed with unit density on [2, 3] and that a consumer of type gets utility ui = si pi. when he pays a price pi and consumes a good of quality si. Suppose that firm 1 can produces a good of quality 2 at marginal cost of 0.

Suppose firm 2 is a potential entrant. If firm 2 pays a fixed cost of K it will be able to produce a good of quality 1 at marginal cost 0 and the firms will then play a simultaneous move pricing game. What is firm 1's profit as a function of K?