Two firms compete by choosing price. Their demand functions are Q1 = 20 - P1 + 0.4P2 and Q2 = 20 + 0.4P1 - P2. Marginal costs are 3.
a. Suppose the two firms set their prices simultaneously. Find the resulting Nash Equilibrium prices. How much will each firm sell? What will each firm's profits be?
b. Suppose Firm 1 sets its price first and then Firm 2 sets its price. What will the SGPE prices be? How much will each firm sell? What will each firm's profits be?
c. Suppose you are one of these firms, and there are three ways you could play the game: (i) both firms set prices simultaneously; (ii) you set price first; (iii) your competitor sets price first.
If you could choose among these options, which would you prefer and why?