Please no written by hand and no emage 1. Two firms produce a homogeneous product, but firm 1 has lower marginal costof 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. Firm2 has a constant marginal cost of $4.a) Suppose first that each firm i = 1,2 chooses its output q, taking theoutput of the other firm as given [Cournot Competition).i) Determine the best-response functions q (92) and q2 (91). Note thatsince 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 theother firm as given [Bertrand Competition. Assuming that prices arequoted 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 andquantities. (Note: you have to be very careful about how the cartel willallocate production across 'plants because marginal cost of productiondiffer). Under which type of competition is the incentive "cheat" (tobreak the cartel agreement) highest?

There are two firms : 1 & 2 Demand function : p = 18- q MC 1= 2 MC2 = 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.

. 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

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Please no written by hand and no emage

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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