Differentiated Bertrand. Consider a Differentiated Bertrand model in which demand is given by q1 = 100 – p1 + p2 and q2 = 100 – p2 + p1 for firm 1 and firm 2 respectively and where both firms faced zero fixed costs and constant marginal cost = c.
a) Suppose that firms choose prices simultaneously. Solve for the Nash equilibrium (i) price (ii) output and (iii) profits of each firm as functions of c.
b) Now suppose that firm 1 chooses price first and then firm 2 chooses price taking firm 1’s price as given. Solve for the Sub-game Perfect Nash equilibrium (i) price (ii) output and (iii) profits of each firm as functions of c.
c) Use reaction functions to explain why making firm 1 a first mover results in both firm 1 and firm 2 raising price.