Assume 2 firms are in the market, producing at constant marginal cost=0. Consumers incur transportation costs which are quadratic in the distance traveled; specifically, a consumer located at position x incurs transportation costs of 2(a-x)^2 in travelling to firm 1. A consumer buys only one unit of the product, and derives 5 units of utility from consuming it. The firms engage in two-stage game: they choose locations (a, 1-b) in the first stage, and prices p1, p2 in the second stage.
Given locations a and 1-b, derive each firm's best-response pricing functions. Given these, derive each firm's price functions, as a function of the locations a and b.