Two firms, A and B, sell the same good X in a market with total demand Q = 100 - P. The two firms compete on quantities and decides how much to produce simultaneously. Firm A cost function is C(qA) = 40qA. Firm B cost function is C(qB) = 60qB. 1. Find the best reply functions of both firms and represent them in a graph. 2. Find the quantity produced by each firm in a Nash equilibrium. 3. Find the firms and consumers surplus.
Two firms, A and B, sell the same good X in a market with total demand Q = 100 - P. The two firms compete on quantities and decides how much to produce simultaneously. Firm A cost function is C(qA) = 40qA. Firm B cost function is C(qB) = 60qB. 1. Find the best reply functions of both firms and represent them in a graph. 2. Find the quantity produced by each firm in a Nash equilibrium. 3. Find the firms and consumers surplus.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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
Transcribed Image Text:Two firms, A and B, sell the same good X in a
market with total demand Q = 100 – P. The
two firms compete on quantities and decides
how much to produce simultaneously. Firm A
cost function is C(qA) = 40qA. Firm B cost
function is C(qB) = 60qB.
1. Find the best reply functions of both firms
and represent them in a graph.
2. Find the quantity produced by each firm in
a Nash equilibrium.
3. Find the firms and consumers surplus.
4. Compare the surplus of firms found above
with the surplus arising when both firm
cooperate to sustain a monopoly outcome.
5. Assume now that A and B compete as in a
Stackelberg model. A chooses first and B
chooses after observing the choice of A. Find
equilibrium quantities produced by each firm
and the market equilibrium price.
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