Two firms compete in a homogeneous product market where the inverse demand funct

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

Explanation / Answer

(a) Learning Curve effects

(b)

When P = $8,

8 = 10 - 2Q

2Q = 2

Q = 1

Each firm's share (q) = 1/2 = 0.5 (million)

Profit = q x (P - MC) - Fixed cost

Profit, Firm 1 ($) = 0.5 x (8 - 2) - 0.7 = 0.5 x 6 - 0.7 = 3 - 0.7 = 2.30

Profit, Firm 2 ($) = 0.5 x (8 - 6) - 0.7 = 0.5 x 2 0.7 = 1 - 0.7 = 0.30

(c)

For Firm 1, When P = $6:

6 = 10 - 2Q

2Q = 4

Q = 2

Firm 1 new profit $) = 2 x (6 - 2) - 0.7 = 2 x 4 - 0.7 = 8 - 0.7 = 7.30

Firm 2 profit remains the same at 0.30.

(d) No

P = 10 - 2Q

2Q = 10 - P

Q = 5 - 0.5P

When P = $6 and Q = 2,

Elasticity of demand = (dQ/dP) x (P/Q) = - 0.5 x (6/2) = - 3

Since absolute value of elasticity is higher than 1, demand is elastic. With elastic demand, an increase in price reduces total revenue.

(e) Yes

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