4. Consider two firms i = 1, 2 in a certain industry. They want to maximize their profit, they have no marginal cost of producing goods. Consumers are uniformly distributed along the interval x [0, 1] t = 1, two firms choose location a, b simultaneously, with restriction a [0, 1/2], b [1/2 , 1].

t = 2, two firms choose their price p1, p2 simultaneously, pi > 0. Consumer has quadratic transportation cost m2 for traveling distance m. Each consumer will buy one product no matter how much it cost, and he will buy from the firm with cheaper cost.

a. Find demand q1, q2 as functions of choice variables p1, p2, a, b.

b. Taking a, b as given, find the optimal pricing scheme (best responses functions) for each firm and t = 2 Nash Equilibrium. Are prices strategic complement or substitute?

c. Solve for t = 1 Nash equilibrium of location choice. Find the outcome of the entire game.

d. Consider a new game: firm 1 is leader and can commit on his location a first. Firm 2 is follower, it observes a and choose b. Then both firms choose their prices simultaneously. What's the outcome of location choice of firm 1 and 2?