(1) Two firms produce goods that are imperfect substitutes. If firm 1 charges price p₁ and firm 2 charges price p2, then their respective demands are 91 = 12 - 2p1 + P2 and 92 = 12 + p₁ - 2p2. So this is like Bertrand competition, except that when p₁ > p2, firm 1 still gets a positive demand for its product. Regulation does not allow either firm to charge a price higher than 20. Both firms have a constant marginal cost c = 4. (a) Construct the best reply function p (p2) for firm 1. That is, p₁ = p (p2) is the optimal
(1) Two firms produce goods that are imperfect substitutes. If firm 1 charges price p₁ and firm 2 charges price p2, then their respective demands are 91 = 12 - 2p1 + P2 and 92 = 12 + p₁ - 2p2. So this is like Bertrand competition, except that when p₁ > p2, firm 1 still gets a positive demand for its product. Regulation does not allow either firm to charge a price higher than 20. Both firms have a constant marginal cost c = 4. (a) Construct the best reply function p (p2) for firm 1. That is, p₁ = p (p2) is the optimal
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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I only need the answer for part C. Thank you!
Transcribed Image Text:(1) Two firms produce goods that are imperfect substitutes. If firm 1 charges price p₁ and
firm 2 charges price p2, then their respective demands are
91 = 12 - 2p1 + P2 and 92 = 12 + p₁ - 2p2.
So this is like Bertrand competition, except that when p₁ > p2, firm 1 still gets a positive
demand for its product. Regulation does not allow either firm to charge a price higher
than 20. Both firms have a constant marginal cost c = 4.
(a) Construct the best reply function pi (p2) for firm 1. That is, p₁ = = pi (p2) is the optimal
price for firm 1 if it is known that firm 2 charges a price p2. Construct a Nash equilibrium
in pure strategies for this game. Are there any Nash equilibria in mixed strategies? If yes,
construct one; if no provide a justification.
(b) Notice that for any given price p₁, firm 1's demand increases with p2, so firm 1 is better
off when firm 2 charges a high price p2. What is the best reply to p2 = 20? What is the
best reply to p2 = 0?
(c) What prices for firm 1 are not strictly dominated? What prices would survive two
rounds of strict dominance? Provide a reason for each strategy that you eliminate.
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