Bertrand with differentiated products. Suppose two firms compete by choosing prices and their demand curves are given by the function qi = 12 2pi + pj where i, j = 1, 2 with i 6= j. Neither firm has any marginal cost of production (i.e. perhaps they are software producers). Suppose the firms compete with each other every day so that the price game of question 5 is an infinitely repeated game. The firms discount profits at a rate of 0 < < 1.

(a) Assuming cooperation, what prices will they set?

(b) If one firm were to deviate from the agreement, what price would it set?

(c) What is the minimum can be to sustain cooperation?