Consider a Cournot oligopoly with n = 2 firms. Firm 1 cost function is TC₁ (9₁) = 20 + 12q₁ + q², while firm 2 cost function is TC₂ (9₂) = 50 +8q2 + q² . The total market demand is P(Q) = 50 – 2Q, where Q is the total quantity produced by all (active) firms in the industry. a- Compute the Cournot equilibrium total quantity, price, quantity for each firm, and profit for each firm. Which firm is making higher profits? b- Consider the situation in which a third firm (firm 3) enters the market. What is the total equilibrium quantity, price, quantity and profit for each firm if TC3 = TC₁? [hint: q₁ and 93 will be the same, since 1 and 3 are identical] c- How would your answer at point b change if instead TC3 = TC₂? Would consumers prefer firm
Consider a Cournot oligopoly with n = 2 firms. Firm 1 cost function is TC₁ (9₁) = 20 + 12q₁ + q², while firm 2 cost function is TC₂ (9₂) = 50 +8q2 + q² . The total market demand is P(Q) = 50 – 2Q, where Q is the total quantity produced by all (active) firms in the industry. a- Compute the Cournot equilibrium total quantity, price, quantity for each firm, and profit for each firm. Which firm is making higher profits? b- Consider the situation in which a third firm (firm 3) enters the market. What is the total equilibrium quantity, price, quantity and profit for each firm if TC3 = TC₁? [hint: q₁ and 93 will be the same, since 1 and 3 are identical] c- How would your answer at point b change if instead TC3 = TC₂? Would consumers prefer firm
Chapter15: Imperfect Competition
Section: Chapter Questions
Problem 15.3P
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![Consider a Cournot oligopoly with n = 2 firms. Firm 1 cost function is TC₁ (9₁) = 20 + 12q₁ + q²,
while firm 2 cost function is TC₂ (9₂) = 50 +8q2 + q2 . The total market demand is P(Q) = 50 — 2Q,
where Q is the total quantity produced by all (active) firms in the industry.
a- Compute the Cournot equilibrium total quantity, price, quantity for each firm, and profit for
each firm. Which firm is making higher profits?
b- Consider the situation in which a third firm (firm 3) enters the market. What is the total
equilibrium quantity, price, quantity and profit for each firm if TC3 = TC₁? [hint: q₁ and q3 will
be the same, since 1 and 3 are identical]
c- How would your answer at point b change if instead TC3 = TC₂? Would consumers prefer firm
3 to enter with the total cost of firm 1 or firm 2?
d- What would be the highest one-time cost that firm 3 would be willing to pay to enter the
market and then compete in a Cournot game with total cost equal to firm 1?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7ab08e71-823b-4ac2-9b77-e229e5037797%2F574af140-ab94-4af4-9598-4cf96323f556%2Fcm4l0v5_processed.png&w=3840&q=75)
Transcribed Image Text:Consider a Cournot oligopoly with n = 2 firms. Firm 1 cost function is TC₁ (9₁) = 20 + 12q₁ + q²,
while firm 2 cost function is TC₂ (9₂) = 50 +8q2 + q2 . The total market demand is P(Q) = 50 — 2Q,
where Q is the total quantity produced by all (active) firms in the industry.
a- Compute the Cournot equilibrium total quantity, price, quantity for each firm, and profit for
each firm. Which firm is making higher profits?
b- Consider the situation in which a third firm (firm 3) enters the market. What is the total
equilibrium quantity, price, quantity and profit for each firm if TC3 = TC₁? [hint: q₁ and q3 will
be the same, since 1 and 3 are identical]
c- How would your answer at point b change if instead TC3 = TC₂? Would consumers prefer firm
3 to enter with the total cost of firm 1 or firm 2?
d- What would be the highest one-time cost that firm 3 would be willing to pay to enter the
market and then compete in a Cournot game with total cost equal to firm 1?
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