A monopolist with marginal cost equal to zero has two stores, one located at the westernmost point and one located at the easternmost point of a circular city. Assume a consumer gets utility u=v-p-tz if she purchases one unit from a firm a distance of z away and zero otherwise. Let v be sufficiently large that all consumers are served in equilibrium. Finally, assume the monopolist has no fixed costs and cannot relocate her stores.

a. Find her equilibrium prices and profits in equilibrium.

b. An entrant considers entering by building a store on the southernmost point on the circle, and competes with the incumbent in prices (chosen simultaneously.) Find the profits of each firm. If the entrant faces a start-up fee of F, for what values of F is entry blockaded?

c. The entrant instead decides to build the store at the easternmost point of the city, in the same location (or infinitely close to) the monopolist. What are the equilibrium prices and profits of each firm? Assume the entrant is able to (somehow) commit to its choice.

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