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A course on Industrial Organization

Xavier Martinez-Giralt

Universitat Aut`onoma de Barcelona

xavier.martinez.giralt@uab.es

Fall 2009-2010 - p.1/133

Static Oligopoly Pricing - Homogeneous Product

Quantity competition

Price competition

Price-Quantity competition

Fall 2009-2010 - p.2/133

Homogeneous ProductDefinition

Two products are homogeneous if at the eyes of the consumer they provide exactly the same service.

Illustration

Assume consumers' preferences are rough enough so that all chairs are perceived exactly alike regardless of whether they have arms, wheels, made of wood, metal, etc. In such a case, consumers will simply demand chairs. Thus, there can only bea single demand function for chairs.

Examples

Difficult. Sulphuric acid, electricity

Fall 2009-2010 - p.3/133

OligopolyDefinition

An industry is said to be oligopolistic whenever the decision of one firm affects and is affected by the decisions of the other firms in the industry .[STRATEGIC INTERACTION]

Features

Typically, such situation is associated with a

limited number of firms in the industry Decision variables: prices or quantities; entry; R&D, ...

Decision "timing"

across firms : simultaneous, sequential (commitment)

Decision "timing"

across decisions : simultaneous, sequential

Equilibrium concept

: Nash (and some variations) Starting point: Cournot oligopoly model (modern version); (Original 1838)

Fall 2009-2010 - p.4/133

Cournot model - AssumptionsStructural

Static model

Technology: cost functionCi(qi)

Aggregate demand functionQ=F(p)

Homogeneous product market

Large number of consumers

There arenfirms in the industry,i= 1,2,...,n

No entry, no exit of firms in the market

Strategic variable of the firms: production levelsqi

Fall 2009-2010 - p.5/133

Cournot model - Assumptions (2)Behavioral

Firms choose production levels to maximize profits Each firm knows that its production decision depends on its expectation over the rivals' decisions. Also, every rival's decision depend of what each of them expects all the other competitors will decide.

All firms take

simultaneously their respective production decisions.

Consumers

choose a consumption bundle to maximize utility

Fall 2009-2010 - p.6/133

Cournot model - Assumptions (3)On demandQ=F(p)

(A1)

1.f:R+→R+

2.?

Qs.t.f(Q)?

>0ifQ < Q, = 0ifQ≥Q 3.? p <∞s.t.f(0) = p

4.f(Q)is continuous andC2in[0,

Q]

5.f?(Q)<0forQ?(0,

Q)

Implication

:qi?[0, Q]?i

Fall 2009-2010 - p.7/133

Cournot model - Assumptions (4)On technologyCi(qi) (A2)

For alli,

1.Ci:R+→R+

2.Ciis continuous and continously differentiable?qi>0

3.Ci(qi)>0?qi>0

4.Ci(0)≥0

5.C? i(qi)>0?qi≥0 Note

Symmetry

across firms meansCi(·) =Cj(·),?i,j, i?=j

Fall 2009-2010 - p.8/133

Cournot model - ProfitsDefinitions

q= (q1,q2,q3,...,qn)is a production plan. Πi(q) =qif(Q)-Ci(qi)is firmi's profit function. Π(q) = (Π1(q),Π2(q),Π3(q),...,Πn(q))is a distribution of profits in the industry.

Assumptions

(A3)

1.Πi:R+→R+

2.Πiis continuous andC2?qi>0

3.Πi(q)is strictly concave inqi,?qs.t.qi>0,Q <

Q.

Fall 2009-2010 - p.9/133

Cournot model - More definitionsFeasibility

qiis a feasible output for firmiifqi?[0, Q].

The setF ?Rndefined asFdef= [0,

Q]×n times...×[0,

Q], is the

set of all feasible production plans in the industry.

Fis a compact set.

Space of outcomes

The space of outcomes is the set of all possible distributionof profits in the industry:{Π(q)|q? F}def= Π(F).

Π(F)is also a compact set.

Pareto optimal outcomes

PO={Π(q)|q? Fs.t.?q?? F,Π(q)>Π(q?)}, whereΠ(q)>Π(q?) meansΠi(q)≥Πi(q?)?i, and?j s.t.Πj(q)>Πj(q?).

Fall 2009-2010 - p.10/133

Cournot model - EquilibriumDefinitions: Cournot-Nash equilibrium A production planqcis a C-N equilibrium if no firm canunilaterally improve upon its profit level by modifying its production decision. A production planqcis a C-N equilibrium if no firm has any profitable unilateral deviation. Letqc-idef= (qc1,qc2,...,qci-1,qci+1,...,qcn).We say that a production planqcis a C-N equilibrium if i(qc) = maxqiΠi(qi,qc-i)?i.

A production planqcis a C-N equilibrium if

A production planqcis a C-N equilibrium if

q ci=argmaxqiΠi(qi,qc-i)?i.

Fall 2009-2010 - p.11/133

Cournot equilibrium - IllustrationDuopoly: Firms 1 and 2 p Q f(Q) q2 qc1( q2) 0 f(Q)- q2

Firm 1's residual demand

Firm 1's marginal revenue

Firm 1's expectation on Firm 2

C?1

Fall 2009-2010 - p.12/133

Cournot model - Game theoryThe Cournot model is a one-shot, simultaneous move,non-cooperative game [in pure strategies].Extensive form

F1q1 0 Q F2 Q q2 0 Q q2 0

Π1(

Q,0)...Π1(

Q, Q) 2(

Q,0)...Π2(

Q, Q)

Π1(

Q,0)...Π1(

Q, Q) 2(

Q,0)...Π2(

Q, Q)

Fall 2009-2010 - p.13/133

Cournot model - Game theory (2)Normal form

:(N,F,Π)

N= 1,2,...,n(set of firms)

F def= [0,

Q]×n times...×[0,

Q](strategy space)

Π(q) = (Π1(q),...,Πn(q))(payoff vector)

Payoff matrix (duopoly).

2/1 0 ...q1... Q 0

Π1(0,0),Π2(0,0)

Π1(q1,0),Π2(q1,0)

Π1(

Q,0),Π2(

Q,0) q2

Π1(0,q2),Π2(0,q2)

Π1(q1,q2),Π2(q1,q2)

Π1(

Q,q2),Π2(

Q,q2) Q

Π1(0,

Q),Π2(0,

Q)

Π1(q1,

Q),Π2(q2,

Q)

Π1(

Q,

Q),Π2(

Q,

Q)Fall 2009-2010 - p.14/133

Cournot equilibrium and Pareto optimalityProposition 1.Letqc?0be a Cournot equilibrium production plan.

ThenΠ(qc)is not Pareto optimum.

Proof.

ShowQcdef=?

iqci< Q.

Asqc?0it satisfies FOCs. Also,∂Πi

∂qj=qif?(Q)<0?i,j i?=j. Hence a simultaneous reduction of the output levels of any two firms,qiandqjwould improve their profits. Thus,?qsuch that i(q)>Πi(qc)?i. Althoughqi< qci,?ihas a negative impact on firmi's profits, it is second order effect and offset by previous (first order) effect.

Fall 2009-2010 - p.15/133

Cournot equilibrium and Pareto optimality (2)IntuitionFirmiwhen decidingqiconsiders adverse effect of price on its

output but ignores the effect on aggregate production.

Impact of variation ofqion pricef(Q)is given by

∂f ∂qi=df dQ∂Q ∂qi+? j?=idf dQ∂Q ∂qi∂q jquotesdbs_dbs16.pdfusesText_22