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Two firms compete in prices along a linear city (as always, of distance one). One firm...

Two firms compete in prices along a linear city (as always, of distance one). One firm is located at the west end at point 0, the other is located in the center at point ½. Each firm has constant marginal cost equal to c. Each consumer i has unit demand and receives utility of uij = v - pj - tzij if she buys from firm j located a distance of zij away at price pj. She receives utility equal to zero if she does not buy. Assume that v is large enough that all consumers buy in equilibrium. Find the equilibrium price and profits for each firm.

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