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 $0.5 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.

a. Based on the information above, what is the likely reason that Firm 1’s marginal cost is lower than Firm 2’s marginal cost? Limit pricing Second-mover advantage Learning curve effects Direct network externality

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

d. Suppose that, by cutting its price to $6, Firm 1 is able to drive Firm 2 completely out of the market. After Firm 2 exits the market, does Firm 1 have an incentive to raise its price? No Yes

e. Is Firm 1 engaging in predatory pricing when it cuts its price from $8 to $6? Yes No

Answer 1

P =10-2Q

Firm 1's MC= $2 and firm 2's MC= $6.

Market price, P= $8

(a) Firm 1's MC is lower than firm 2's MC because of learning curve effects. Because as P=10-2Q =$ 8

then, Q= 1 million. Hence, it implies that firm 1 produced 1 million units last year because last year market price was $8.

Now, for profit maximising price, MR=MC . Firstly calculate TR= 10Q-2Q² , therefore, MR= 10-4Q. So, MR=MC =10-4Q . Put Q=1 million in this . We get MR = MC= $6, this is the firm 1's last year MC which is the same as firm 2's current MC.

Hence, it means that firm 1's MC has fall due to learning curve effects.

(b) At the current market price = $8 implies Q =1 million. It means that each firm sells 0.5 million units because each firm has 50% share of the market as given in the question.The fixed costs of each firm are $0.5 million.

Firm 1's profits = $(P-MC)(Q1) - Fixed cost =

= $(8 - 2)(0.5) - $0.5

= $ 2.5 million.

Firm 2's profit = $(P - MC)(Q2) - FC

= $(8- 6)(0.5) - $(0.5)

= $ 0.5 million.

(c) If firm 1 reduced its price to $6 while firm 2 continued to charge $8 then ,

When Price = $6 then P=10-2Q =$6

Q = 2 million.

Therefore, quantity sell by firm 1 = 2 million. And firm 2 will not be able to sell any quantity at $8 price.

Therefore, firm 1's profits = $(6 -2)(2) - $0.5

= $ 7.5 million.

Firm 2's profits = (minus of fixed cost ) = - 0.5 million.

(d) Suppose that by cutting its price to $6 , firm 1 is able to drive firm 2 completely out of the market . After firm 2 exits the market, the firm 1 doesn't has an incentive to raise its price because if firm1 raise its price then firm 2 will again enter the market.

(e) Yes firm 1 is engaging in predatory price when it cuts its price from $8 to $6. Because predatry pricing implies that the pricing of good at such a low level that other firms cannot compete and are forced to leave / exit the market.