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Consider the following variant of Hotelling's product differentiation model. Suppose that the consumers are uniformly distributed on a circle with...

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consider a following variant of hotelling's product differentiating model

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2. Consider the following variant of Hotelling’s product differentiation model. Suppose
that the consumers are uniformly distributed on a circle with perimeter d = 1. Firms are also located on the circle, each selling a homogenous product. Each firm has
marginal cost 0 > 0 and also faces a fixed entry cost f. Firm i’s profit is: 7,, _{ (Pa: —C)y¢ — f if it enters 0 otherwise ’ where y,— is the demand it faces. Consumers want to buy one unit of the good and have
a unit transport cost of t. There are two stages: in the first, all firms simultaneously
choose whether or not to enter. Let n denote the number of entrants. The firms do
not choose the location on the circle, but are automatically located equidistant from
each other. In the second stage, the n entrants compete in prices. (a) What is the (pure) strategy set for each potential entrant i? What is the equilib-
rium concept in this game? (b) Find the best-reply function for firm i and use it to find the equilibrium prices in
the market. (c) How many firms in,“ will there be in the market in equilibrium?

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