To firms compete, and they are placed in each end of a line with length 1. Firm 1 at point 0 and firm 2 at point 1. The consumers transportation cost are linear in the distance to the firms localisation (d1 and d2) and the consumers are uniformly distributed on the intervall (0,1) where x E (0,1) denotes the consumers preferences. The consumer buys maximum one unit of the good, either from firm 1 or from firm 2. The utility of consumer x from the good from firm i is: \(u = s-p_{i}-t|x-d_{i}|\)
where s is the maximum willingness to pay and t transportation cost per distance unit between the consumer and the firm's localisation.
The firms have constant marginal costs given by c1 and c2.
a) FInd the two firm's reactionfunctions pi = Ri(pj) and give a graphical illustration
b) Find the two Nash-equilibrium prices as a function of the marginal costs c1 and c2, and the firm's profit.