Consider two firms that provide a differentiated product, which they produce at the same constant marginal cost, MC = 3 (no fixed cost). The demand function for Firm 1 is q1 = 10 - p1 + 0.5p2 and for Firm 2 is q2 = 20 - p2 + 0.5p1, where p1 is Firm 1's price and p2 is Firm 2's price.

a) Write the profit functions for these firms. (2 marks)

b) What are the equilibrium prices and quantities? (10 marks)

c) Assume now Firm 1 has the advantage to set its price first followed by Firm 2, after Firm 2 observed the price set by Firm 1. What is the equilibrium price for each firm? (6 marks)