14. Cournot Oligopoly Problem 2 - heterogeneous costs duopoly Suppose the following: • Inverse demand is given by P = 24-4Q 2 • 2 firms compete in the market. • Firm 1 has constant marginal cost of c₁ and fixed costs of F₁. • Firm 2 has constant marginal cost c₂ and fixed cost F2. (a) Solve for equilibrium quantities, prices, and firm profits, assuming that both firms will find it pr table to ce. (b) How, if at all, does firm 1's profit vary with c₂? (c) Why? (d) Now suppose c₁ = 4 and c₂ = 2. i. Compute the generalized Lerner Index for each firm in equilibrium. ii. Which firm has the higher markup? iii. Why? iv. What does that mean? (e) Now suppose that both firms are potential entrants into a new market that is currently not served by anyone. The equilibrium values you have computed represent the outcome should both firms choose to enter the market. Continue to assume that = 4 and C₂ = 2. Suppose that fixed costs are the only costs of entry into the market. i. For what values of F₁ will firm 1 choose NOT to enter? ii. For what values of F₂ will firm 2 choose NOT to enter? iii. What would each firm's profit be if it were the only (monopoly) supplier to the market? = iv. Finally, suppose F₁ F₂ = 0, but imagine that we allow firms to pay money to "construct" entry barriers for their opponents. For example, firm 1 could pay 1 to add 1 to F₂ and vice versa. In this imaginary world, which firm(s) would be willing to pay enough to keep the other from entering?
14. Cournot Oligopoly Problem 2 - heterogeneous costs duopoly Suppose the following: • Inverse demand is given by P = 24-4Q 2 • 2 firms compete in the market. • Firm 1 has constant marginal cost of c₁ and fixed costs of F₁. • Firm 2 has constant marginal cost c₂ and fixed cost F2. (a) Solve for equilibrium quantities, prices, and firm profits, assuming that both firms will find it pr table to ce. (b) How, if at all, does firm 1's profit vary with c₂? (c) Why? (d) Now suppose c₁ = 4 and c₂ = 2. i. Compute the generalized Lerner Index for each firm in equilibrium. ii. Which firm has the higher markup? iii. Why? iv. What does that mean? (e) Now suppose that both firms are potential entrants into a new market that is currently not served by anyone. The equilibrium values you have computed represent the outcome should both firms choose to enter the market. Continue to assume that = 4 and C₂ = 2. Suppose that fixed costs are the only costs of entry into the market. i. For what values of F₁ will firm 1 choose NOT to enter? ii. For what values of F₂ will firm 2 choose NOT to enter? iii. What would each firm's profit be if it were the only (monopoly) supplier to the market? = iv. Finally, suppose F₁ F₂ = 0, but imagine that we allow firms to pay money to "construct" entry barriers for their opponents. For example, firm 1 could pay 1 to add 1 to F₂ and vice versa. In this imaginary world, which firm(s) would be willing to pay enough to keep the other from entering?
Chapter1: Making Economics Decisions
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Transcribed Image Text:14. Cournot Oligopoly Problem 2 - heterogeneous costs duopoly
Suppose the following:
• Inverse demand is given by
2 firms compete in the market.
• Firm 1 has constant marginal cost of c₁ and fixed costs of F₁.
• Firm 2 has constant marginal cost c₂ and fixed cost F₂.
-
(a) Solve for equilibrium quantities, prices, and firm profits, assuming that both firms will
find it profitable to produce.
(b) How, if at all, does firm 1's profit vary with c₂?
(c) Why?
(d) Now suppose C1
4 and C₂
=
P = 24 - 4Q
2.
2
i. Compute the generalized Lerner Index for each firm in equilibrium.
ii. Which firm has the higher markup?
iii. Why?
iv. What does that mean?
(e) Now suppose that both firms are potential entrants into a new market that is currently
not served by anyone. The equilibrium values you have computed represent the outcome
should both firms choose to enter the market. Continue to assume that c₁ = 4 and
C2 =
= 2. Suppose that fixed costs are the only costs of entry into the market.
i. For what values of F₁ will firm 1 choose NOT to enter?
ii. For what values of F2 will firm 2 choose NOT to enter?
iii. What would each firm's profit be if it were the only (monopoly) supplier to the
market?
F2
=
=
iv. Finally, suppose F₁
0, but imagine that we allow firms to pay money to
"construct" entry barriers for their opponents. For example, firm 1 could pay 1 to
add 1 to F2 and vice versa. In this imaginary world, which firm(s) would be willing
to pay enough to keep the other from entering?
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