Consider a model in which two rival firms set quantities for sale. Both firms have a constant marginal cost of $10 per unit (and no capacity constraints). The market demand curve is P = 40 - q1 - q2, where q1 is the quantity firm 1 produces and q2 firm 2's quantity.

(a) Assume both firms set their quantities for sale simultaneously. Derive the best response functions for both firms and illustrate them on a diagram. Explain your working. Determine the equilibrium quantities, price and profits in the market. Explain your answer, using your diagram to aid you. (5 marks)

(b) Now assume that firm 1 set its quantity first. This choice is irreversible and observed by firm 2, who them chooses its quantity for sale. Both firms then sell their quantities on the market, price is determined and the market clears. Determine the quantity sold by each firm, market price and their profits. Using a diagram, explain your answer. Given firm 1 moves first, why does it not make it unprofitable for firm 2 to produce anything at all in equilibrium? Use a diagram to help explain your intuition.