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. Two firms produce a homogeneous product, but firm 1 has lower marginal cost of production than firm 2. The demand for the product is given by p=18-q, where q is aggregate output. Firm 1 has constant marginal cost of $2. Firm 2 has a constant marginal cost of $4.

. Two firms produce a homogeneous product, but firm 1 has lower marginal cost of production than firm 2. The demand for the product is given by p=18-q, where q is aggregate output. Firm 1 has constant marginal cost of $2. Firm 2 has a constant marginal cost of $4.

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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1. Two firms produce a homogeneous product, but firm 1 has lower marginal cost of production than firm 2. The demand for the product is given by p= 18-q, where q is aggregate output. Firm 1 has constant marginal cost of $ 2. Firm 2 has a constant marginal cost of $4. a) Suppose first that each firm i = 1,2 chooses its output q, taking the output of the other firm as given [Cournot Competition). i) Determine the best-response functions q (92) and q2 (91). Note that since marginal cost are different, these functions will not be sym- metric. ii) Calculate the Nash equilibrium quantities and the market price. b) Now suppose firm i 1,2 chooses its price p,, taking the price of the other firm as given [Bertrand Competition. Assuming that prices are quoted in dollars and cents (the smallest unit of measurement is a cent), determine the Nash equilibrium/equilibria prices and quantities. c) Now suppose the two firms collude, i.c., they choose either qı and q (under Cournot competition) or p₁ and p, (under Bertrand competition) so as to maximize joint profit. Determine the new equilibrium price and quantities. (Note: you have to be very careful about how the cartel will allocate production across 'plants because marginal cost of production differ). Under which type of competition is the incentive "cheat" (to break the cartel agreement) highest?
Transcribed Image Text:1. Two firms produce a homogeneous product, but firm 1 has lower marginal cost of production than firm 2. The demand for the product is given by p= 18-q, where q is aggregate output. Firm 1 has constant marginal cost of $ 2. Firm 2 has a constant marginal cost of $4. a) Suppose first that each firm i = 1,2 chooses its output q, taking the output of the other firm as given [Cournot Competition). i) Determine the best-response functions q (92) and q2 (91). Note that since marginal cost are different, these functions will not be sym- metric. ii) Calculate the Nash equilibrium quantities and the market price. b) Now suppose firm i 1,2 chooses its price p,, taking the price of the other firm as given [Bertrand Competition. Assuming that prices are quoted in dollars and cents (the smallest unit of measurement is a cent), determine the Nash equilibrium/equilibria prices and quantities. c) Now suppose the two firms collude, i.c., they choose either qı and q (under Cournot competition) or p₁ and p, (under Bertrand competition) so as to maximize joint profit. Determine the new equilibrium price and quantities. (Note: you have to be very careful about how the cartel will allocate production across 'plants because marginal cost of production differ). Under which type of competition is the incentive "cheat" (to break the cartel agreement) highest?
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