Let the inverse demand curve be p(q) = a − bq. Suppose there are two firms, with constant marginal cost equal to C.
Let the two firms be located at 0 and 1 on the unit interval. There are n consumers located uniformly along the interval, each with a reservation value of V . They incur transportation costs of t per unit of distance traveled from their location to the a store.
1) If the firms are both located at 1/2, what are their equilibrium strategies and what is the equilibrium outcome?