Question

Consider two firms that sell differentiated products and compete by choosing prices. Their demand functions are Q1 = 72 – 3P1 + 2P2 and Q2 = 72 – 3P2 + 2P1 where P1 and P2 are the prices charged by firm 1 and 2, respectively, and Q1 and Q2 are the corresponding demands. All production costs are assumed to be zero.

(a) Suppose the two firms set their prices simultaneously and non-cooperatively. Find the resulting Bertrand-Nash equilibrium. What price does each firm charge, how much does it sell, and what profit does it make? [6%]

(b) Suppose now that the two firms collude and maximise joint profits. What will be the prices, quantities and profits for each firm in this case? Can the collusive prices be supported in a static one-shot game (i.e. if the firms only act once)? Explain. [7%]

(c) Suppose Firm 1 sets its price first and then Firm 2 sets its price after observing Firm 1’s choice. What price does each firm charge, how much does it sell, and what profit does it make. [6%]

(d) If Firm 1 could choose, would it prefer (a) to set its price first; (b) to set its price second; or (c) that they set prices simultaneously? [6%]

Answer 1