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Firms 1 and 2 produce horizontally differentiated products. The demand for firm 1’s product is given by the equation, Q1 = 100 − P1 + P2/ 2 The demand for firm 2’s product is given by the equation, Q2 = 200 − 4P2 + 2P1. Firm 1’s marginal cost is MC1 = $10, while firm 2’s marginal cost is MC2 = $20. The two firms compete in Bertrand competition, by simultaneously selecting prices.

Question 1: Is firm 2’s product a substitute or a compliment for firm 1’s product? Briefly explain. Your answer must reference firm 1’s demand function. (2 Marks)

Question 2: Does the demand for firm 2’s product satisfy the law of demand? Briefly explain. Your answer must reference firm 2’s demand function. (2 Marks)

Question 3: What is the equation of firm 1’s best-response function? (4 Marks)

Question 4: What is the equation of firm 2’s best-response function? (4 Marks)

Question 5: Find the equilibrium prices. (2 Marks)

Question 6: Find the equilibrium profits. (3 Marks)

Question 7: Which firm enjoys the greater market power? (3 Marks)

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7 Nov 2018
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Related questions

Firms 1 and 2 produce horizontally differentiated products. The demand for firm 1's product is given by the equation,

Q1 = 100 - P1 +P2/2

The demand for rm 2's product is given by the equation,

Q2 = 200 - 4P2 + 2P1.

Firm 1's marginal cost is MC1 = $10, while firm 2's marginal cost is MC2 = $20. The two Firms compete in Bertrand competition, by simultaneously selecting prices.

Question 1: Is Firm 2's product a substitute or a compliment for Firm 1's product? Briefly explain. Your answer must reference firm 1's demand function. (2 Marks)

Question 2: Does the demand for firm 2's product satisfy the law of demand? Brieflyexplain. Your answer must reference firm 2's demand function. (2 Marks)

Question 3: What is the equation of firm 1's best-response function? (4 Marks)

Question 4: What is the equation of Firm 2's best-response function? (4 Marks)

Question 5: Find the equilibrium prices. (2 Marks)

Question 6: Find the equilibrium profits. (3 Marks)

Question 7: Which firm enjoys the greater market power? (3 Marks)

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.

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

Direct network externality

Second-mover advantage

Learning curve effects

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?

Yes

No

e. Is Firm 1 engaging in predatory pricing when it cuts its price from $8 to $6

Yes

No

I just need part 3 for this problem!! Thank you!!

 

Part 1 Suppose the inverse market demand function for a two-firm Cournot model is given by P=49-Q where Q=q_1+q_2 is the total output produced in the market, P is the market price, q_1 is the quantity of output produced by firm 1, q_2 is the quantity of output produced by firm 2. The marginal costs of the two firms are MC1=2 and MC2=3. For a linear inverse demand function P=a+bq, the marginal revenue is given by MR=a+2bq.

1. Find the marginal revenue MR1 of firm 1 as a function of q_1 and q_2.

2. Setting MR1=MC1, determine the reaction function of firm 1.

3. Find the marginal revenue MR2 of firm 2 as a function of q_1 and q_2.

4. Setting MR2=MC2, determine the reaction function of firm 2.

5. What quantity of output will each firm produce? That is, use the two reactions functions to find q_1 and q_2.

6. What is the market price P.

7. Determine the profits of each firm assuming there are no fixed costs.

 

Part 2  Now, suppose the inverse market demand function for a two-firm Stackelberg model is given by P=49-Q where Q=q_1+q_2 is the total output produced in the market, P is the market price, q_1 is the quantity of output produced by firm 1, q_2 is the quantity of output produced by firm 2. Firm is leader and firm 2 is follower. The marginal costs of the two firms are MC1=2 and MC2=3.

1. What is the follower’s reaction function?

2. Determine the equilibrium output level for both the leader and the follower.

3. Determine the equilibrium market price.

4. Determine the profits of the leader and the follower assuming there are no fixed costs.

 

Part 3 Use information from parts 1 & 2 to compare the output levels and profits in settings characterized by Cournot and Stackelberg.

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