Download Lecture 31: Duopoly

Microeconomics
Course E
John Hey
Welcome!
• Professoressa Maria Covadonga de la
Iglesia Villasol,
• Departamento de Fundamentos del
Análisis Económico I,
• Universidad Complutense de Madrid.
• Is here through Erasmus to share ideas on
teaching.
This week
• The final week of the course.
• Today, Tuesday: Duopoly.
• Tomorrow, Wednesday: Example 1 of the
exams.
• Thursday: Example 2 of the exams.
• Before tomorrow, try Example 1 and before
Thursday, try Example 2.
• It is a waste of your time coming to the
lectures if you have not done so.
Game Theory
• In Chapter 29 we talked about games, in
which two players have to choose
simultaneously the value of some decision
variables, the values of which affect both
players.
• We introduced the idea of a Nash
Equilibrium in which each is optimising
given the decision of the other.
• Today we will apply that in Duopoly.
Chapter 31
• Duopoly
• A market in which there are two
sellers – two firms – Firm 1 and
Firm 2, selling an identical good.
• The demand curve in the market
is given by:
• p = a – b(q1 + q2)
The Cournot Model
• Each firm chooses independently
its output.
• The price is determined by the
demand curve.
• What outputs do the firms
choose?
Profits
• Let us denote the profit of firm 1
by π1.
• Suppose that the total cost
function is given by: C(q1) = cq1.
• Hence profits are given by:
• π1.= pq1 - cq1
= [a – b(q1 + q2)]q1 - cq1
Isoprofit Curves
• For firm 1 an isoprofit curve is
given by:
• π1.= constant
• Hence
• [a – b(q1 + q2)]q1 - cq1 = constant
Reaction Curves
• If Firm 1 chooses its output to
maximise its profits given a level
of output of Firm 2, we get:
• q1 = (a-c-bq2 )/2b
• …the reaction curve of Firm 1.
The Nash Equilibrium
• … is given by the intersection of the
two reaction curves…
• Total output = 2(a-c)/3b
• With monopoly = (a-c)/2b
• With perfect competition = (a-c)/b
• The output with a duopoly is between
the monopoly output and the
competitive output.
• Let’s go to Maple...
The Bertrand Model
• Each firm independently chooses
its price.
• The demand all goes to the firm
with the lowest price.
• What prices will the firms choose?
What happens with a duopoly
• Is very sensitive to the rules of the
game…
Summary
• With quantity-setting rules in the Nash
Equilibrium the total output with a duopoly is
between the monopoly output and the
competitive output.
• A collusive outcome is better for both firms – but
is unstable.
• For a firm it is better to be the leader.
• With price-setting the Nash Equilibrium has price
equal to marginal cost (and therefore like
competition).
Chapter 31
• Goodbye!