Question

2. Suppose two firms are competing in prices (Bertrand) in an industry where demand is P-200-8Q. Assume neither firm faces any fixed costs. (a) If both firms have MC-120, what is the equilibrium price and profits for each firm? (b) Suppose one firm has MC-150 and one has MC-0. How much profit does each firm make? (c) Suppose one firm has MC-120 and one has MC-100. Approximately how much profit does each firm make?

Answer 1

A) For identical products, the undercutting of prices will reduce price level down to MC. Hence price level is same and is equal to MC = 120. Quantity is 120 = 200 - 8*Q or Q = 10 units in total and 5 units each bt the two firms. Profits are zero since P = MC and there is no fixed cost

B) Firm with MC = 0 will set a price slightly lower than the MC of the rival, which is therefore less than 150. It will capture the entire market. This firm will produce 150 = 200 - 8Q or 6.25 units and earn a profit of $937. The other firm will not produce any thing

C) Again, Firm with MC = 100 will set a price slightly lower than the MC of the rival, which is therefore less than 120. It will capture the entire market. This firm will produce 120 = 200 - 8Q or 10 units and earn a profit of $1200 approx. The other firm will not produce any thing