Question

Consider a linear city of length L in which the consumers are uniformly distributed. There are two firms located at the extremes of the linear city: firm 1 is located at the left-hand extreme, and firm 2 is located at the right-hand extreme. Assume that every consumer buys one unit of the product, that transportation cost are linear (td, where d is distance), and that marginal production costs are zero. Given their location, the firms engage in price competition: they set prices simultaneously as in the Bertrand Model.

-Derive the demands faced by every firm.

-Find the equation of the best response function of every firm

-Find the Bertrand-Nash equilibrium set of prices.