Assume there are two firms labelled 1 and 2 producing differentiated goods who compete by setting quantities. The inverse demand functions of firm 1 and firm 2, respectively, are given by: 1 291. Each firm produces at constant marginal cost c = 1. There are no fixed costs. (a) How much does each firm produce in Nash equilibrium and how much profit will each firm make? (3 marks) P = 2 - 91 1 292 P2=2-92 (b) How much would the firms produce if they were able to form a cartel that maximises joint profit, and what would be each firm's profit if they split it evenly? (3 marks)