3. Consider the 2-firm Hotelling linear model, with quadratic transportation costs. As- sume 2 firms are in the market, producing at constant marginal cost=0. Consumers incur transportation costs which are quadratic in the distance travelled; specifically, a consumer located at position x incurs transportation costs of 2(a x)? in travel- ling 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 a two-stage game: they choose locations (4, b) in the first stage, and prices p1, p2 in the second stage. (a) Given locations a and b, derive each firm's best-response pricing functions. Given these, derive each firm's price function, as a function of the locations a and b. (b) Assume consumers derive not 5, but 10 units of utility from buying one unit of the product. Repeat part (a). (c) Assume symmetry, so that a = 1 b. What is the equilibrium location choice for each firm? (d) Solve for the symmetric location scheme which would minimize aggregate transportation costs in this economy. (e) (Stackelberg extension) Imagine that firm 1 can locate before firm 2. Where would firm 2 locate, given firm 1's choice of 4? (f) Given this, where would firm 1 choose to locate, if it could move before firm 2? Is there a first-mover advantage in this case