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?