Use a model with horisontal productdifferentiation. Suppose that two firms compete. They are situated at opposite sides on a linje with length 1. Firm 1 in point 0, and firm 2 in point 1. The konsumers transport costs are linear in the distence to the firms localisation (denoted d1 and d2), and the consumers are uniformly distributed on the interval (0,1) where x in (0,1) denotes the consumers preferences (localisation).

The consumer buys maximum one unit of the good, either from firm 1 or firm 2. The utility of consumer x by buying from firm i is given by

\(u = s-p_{i}-t|x-d_{i}|\)

where s is the maximum willingness to pay and t is transport costs for each "distance-unit" between the consumer and the firm's localisation.

The firm's have constant marginalcosts denoted c1 and c2.

a) Find the two firms reactionfunctions,

\(p_{i}=R_{i}(p_{j})\)

b) Find the two firm's Nash-equilibrium prices (as a function of the two marginal costs c1 and c2) and the firms profit.