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: $2.3 million

Firm 2's profits: $4 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: $7.3 million

Firm 2's profits: $____ million

*** I need help determining the profits for Firm 2***

The answer is not 0.35 mill, 0.7 mill, 0.1 mill, 0, or 0.9 million for firm 2's profits

Answer 1

1) At the current price of $8, firm earns a gross profit of (P - MC)*Q where when price is 8, quantity is

8 = 10 - 2Q

2Q = 2

Q* = 1 million so each firm sells 0.5 million units.

Gross profit for firm 1 = (8 - 2)*0.5 = $3 million. When the rent is paid, the net profit becomes 3 - 0.7 = $2.3 million

Similarly for firm 2, it is (8 - 6)*0.5 - 0.7 = $0.3 million

2) Now the price charged by firm 1 is lower than what firm 2 charges. So firm 2 will not sell anything. But it pays the rent

Quantity sold in the market at P = 6, is 2Q = 10 - 6 or Q = 2 million. Hence profits for firm 1 is (6 - 2)*2 = 8 million. Net profit after paying rent is 8 - 0.7 = 7.3 million

Net profit for firm 2 is 0 - 0.7 = -0.7 million.