cournot model

COURNOT MODEL FOR DUOPOLY MARKET

Presented by,Yagnesh Sondarva04-2664-2015MSc. Agri.ExtensionBACA, Anand

Market Structure

1) Number of firms in market2) Product Differentiation

Markets are often described by the degree of concentration

Monopoly is one extreme with the highest concentration - one seller

Perfect competition is the other extreme with innumerable sellers

Oligopoly involves few sellers engaging in strategic competition

Number of SellersDegree of Product Differentiation

Many Few One Dominant

One

Firms produce identical products

Perfect Competition

Oligopoly with homogeneous products

Dominant firm

Monopoly

Firms produce differentiated products

Monopolistic Competition

Oligopoly with differentiated products

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PERFECT

Perfect Competition

1) Many Firms2) Homogeneous Productsexamples: farm commodities like wheat, Pulses

Monopolistic Competition

1) Many Firms2) Differentiated ProductsExamples: retail trade

Monopoly 1) One Firm2) One ProductExample : railway , post , electricity, Insurance

(government monopoly)

Oligopoly

A) Homogeneous Products Oligopoly

1) Few Firms2) Homogeneous ProductsExamples: steel ,chemical.

B) Differentiated Products Oligopoly

3) Few Firms4) Differentiated ProductsExamples: automobile , computer

Oligopoly

Market has a small number of sellers Pricing and output decisions by each firm

affects the price and output in the industry Oligopoly models (Cournot, Bertrand) focus on

how firms react to each other’s moves

Oligopoly – Characteristics

Product differentiation may or may not exist Barriers to entry Small number of firms

Scale economies Patents Technology Name recognition Strategic action

Oligopoly

Examples Automobiles Steel Aluminum Petrochemicals Electrical equipment

Management Challenges

Strategic actions to deter entry Threaten to decrease price against new competitors

by keeping excess capacity

Rival behavior Because only a few firms, each must consider how

its actions will affect its rivals and in turn how their rivals will react

Interdependence

Your actions affect the profits of your rivals.

Your rivals’ actions affect your profits

An ExampleYou and another firm sell

differentiated products such as cars.

How does the quantity demanded for your cars change when you change your price?

Oligopoly – Equilibrium

If one firm decides to cut their price, they must consider what the other firms in the industry will do

Could cut price some, the same amount, or more than firm

Could lead to price war and drastic fall in profits for all

Actions and reactions are dynamic, evolving over time

Oligopoly – Equilibrium

Defining Equilibrium Firms are doing the best they can and have

no incentive to change their output or price All firms assume competitors are taking

rival decisions into account Nash Equilibrium

Each firm is doing the best it can given what its competitors are doing

We will focus on duopoly Markets in which two firms compete

Duopoly models

Cournot model Edgeworth model Chamberlin model Price leadership model Bertrand model Kinked demand curve Centralized cartel model Market sharing cartel model

Cournot model

Developed by French economist

Augustin cournot in 1838.

Cournot model

Oligopoly model in which firms produce a homogeneous good, each firm treats the output of its competitors as fixed, and all firms decide simultaneously how much to produce

Assumptions of Cournot ModelFour assumptions:

1. there are two firms and no other firms can enter in the market,

2. the firms have identical costs,

3. they sell identical products

4. the firms set their quantities simultaneously.

O A B

DDB = demand curve Suppose OA=AB max daily output of each producer

Total output=OA+AB=OB

D

K

O A B

P

DB= demand curve OA=daily max output OA= max profitMa x revenue =OAPK

Profit of AAs profit

A producer

P

Q

D

O A H B

B producer B assume A will produce ½ of OB=OA PB = demand curve for himB produce AH=1/2 AB

Total output OA+AH=OH Price fall =HQ

Total profit=OHQFIs less than OAPK of 1st condition

As profit = OAGFBs profit =AHQGProfit of A reduced due to AH produced by B

Bs profit

G

K

FAs profit As profit

P

Q

D

O A H B

G

K

FAs profit As profit

A PRODUCER A will consider & assume B will continue produce AHSo A produce 1/2(OB-OH)=OTReduce OA to OT A produce= OT B produce=AH

Total output=OT+AH=ONPrice =NR

Total profit=ONRSAs profit =OTLSMore than OAGF Bs profit=TNRLMore than AHQF

T

R

N

S L

As profit Bs profit

G

B surprised by reduction of output to OT by A and Also find his share of total profit is less than A So B assume A will continue produce OT And B find his maximum profit by producing output=1/2(OB-O T)=1/2 TBB increase output to ½ TB

Producer A consider and find that he can maximize his profit by producing output=1/2 OB-output of B

This process of adjustment and readjustment by each producer will continue ,A being forced gradually to reduce his output B being able to increase his output gradually until total output OM is produced OM=2/3 OF OBAnd each producing same amount of outputA= OCB=CMOC=CM

P

Q

D

O A H B

G

K

FAs p

T

R

N

S L

A will consider & assume B will continue produce AHSo A produce 1/2(OB-OH)=OTReduce his production

A produce= OC B produce=CM

Total output=OC+CM=OMPrice =MJ

Total profit=OMJEAs profit =OCWEBs profit=CMJW

As profit

E J

C

W

Bs profit

M

Throughout the process of adjustment & readjustment each producer assume that the

Other will keep his output constant at the present level

& then always find his maximum profit by producing output½(OB-present output of other )

P

Q

D

O A H B

G

K

FAs p

T

R

N

S L

As profit

E J

C

W

Bs profit

M

A producer start by producing OA=(1/2OB)And continue reduce until OCFinal output OC of A =OB(1-1/2-1/39…….)=1/3 OB =1/2 OM

B producer start by producing AH=1/4 of OBAnd continue increase until CMFinal output CM of B=OB(1/4+1/16+1/64…..)=1/3 OB=1/2 OM

TOTAL OUTPUT =0B(1-1/2+1/4-1/8+1/16-1/39+1/64……)=2/3 OB=OM

A = 1/3 OB = OCB = 1/3OB= CM

½ (OB-1/3 OB) which is equal to 1/3 OB=OC=CMWhen each producing 1/3 OB so that total output of both are 2/3 OB no one is able to increase profit by further adjustment in output

EQUILIBRIUMTotal output is 2/3 of OB Each one producing 1/3 of OB

Criticism Behavioural pattern of firm is naive . Means firm

not know from past miscalculation of competitors reaction.

Quantity produced by competitor is as assumed constant at a each stage

Model can be extended to many number of firms however it is a closed model in that entry is not allowed number of firms remain same through out adjustment process.

It doesn’t say how long adjustment period will be.

Thank you