Consider a linear city of length 1 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 will buy one unit of the product, that transportation cost are quadratic (td^2, where d is distance), and that marginal production costs are zero.
-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.