Question

Two firms compete in a homogeneous product market where the inverse demand function is P = 10 -2Q (quantity is measured in millions). Firm 1 has been in business for one year, while Firm 2 just recently entered the market. Each firm has a legal obligation to pay one year’s rent of $0.7 million regardless of its production decision. Firm 1’s marginal cost is $2, and Firm 2’s marginal cost is $6. The current market price is $8 and was set optimally last year when Firm 1 was the only firm in the market. At present, each firm has a 50 percent share of the market.

b. Determine the current profits of the two firms.

Instruction: Enter all responses rounded to two decimal places.

Firm 1's profits: $____ million

Firm 2's profits: $____ million


c. What would each firm’s current profits be if Firm 1 reduced its price to $6 while Firm 2 continued to charge $8?

Instruction: Enter all responses to two decimal places.

Firm 1's profits: $____ million

Firm 2's profits: $____ million

Answer 1

b) Current price is $8 and so market quantity is (10 – 8)/2 = 1 million. Each firm has 50% market share so each of them will produce 0.5 million units. Profit will be revenue – cost.

Profit for firm 1 = 0.5 million x 8 - 0.5 million x 2 – $0.7 million = $2.3 million

Profit for firm 2 = 0.5 million x 8 - 0.5 million x 6 – $0.7 million = $0.3 million

c) Products are identical so when Firm 1 reduced its price to $6 while Firm 2 continued to charge $8, firm 1 will be able to sweep the market. It would sell (10 - 6)/2 = 2 million units.

Profit for firm 1 = 2 million x 6 - 2 million x 2 – $0.7 million = $7.3 million

Profit for firm 2 = 0 million x 8 – $0.7 million = - $0.7 million