Understanding Markets in Equillibrium

8/9/2019 Understanding Markets in Equillibrium

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Understanding MarketsUnderstanding Markets

ininEquillibriumEquillibrium

V.I.G.MenonV.I.G.Menon

Prerequisite: Elements Of LinearPrerequisite: Elements Of Linear

EquationsEquations


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Derivation ofDerivation of Phase RulePhase Rule ForFor

MarketsMarkets

The term Phase Rule is in Chemistry whereThe term Phase Rule is in Chemistry where

many individual chemicals react to formmany individual chemicals react to form

different Chemical Entities Calleddifferent Chemical Entities Called PhasesPhases

Similarly Our Purpose is to investigate theSimilarly Our Purpose is to investigate the

number ofnumber of Communities That can co existCommunities That can co exist

under certain Conditions Ofunder certain Conditions OfSupply/Demand and Price/IncomeSupply/Demand and Price/Income..


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Derivation ofDerivation ofPhase RulePhase Rule

We will do an exercise toWe will do an exercise to

evaluate the number of Markets thatevaluate the number of Markets thatCan Coexist in a Given priceCan Coexist in a Given price--demanddemand

conditions.conditions.


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Derivation of Degrees OfDerivation of Degrees Of

FreedomFreedom

a balancing ofa balancing of

FIXED PARAMETERSFIXED PARAMETERS

andandSYSTEM VARIABLESSYSTEM VARIABLES


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Definition Of Degrees OfDefinition Of Degrees Of

FreedomFreedom Degrees Of Freedom = number ofDegrees Of Freedom = number of

variablesvariables number of equations (number of equations ( 0).0).


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Fundamental AssumptionFundamental Assumption Let us Assume that any product comes inLet us Assume that any product comes in

atleastatleast threethreevarietiesvarieties.. For ExampleFor Examplericericeis available at a priceis available at a price

affordable by the Low Incomeaffordable by the Low Income Group,thenGroup,then

the middle class and then the variety forthe middle class and then the variety forthetheEliteElite

Similarly,MobileSimilarly,Mobile Phones,CarsPhones,Cars and otherand other

products tooproducts too


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Market EvolutionMarket Evolution

For Understanding this ,let us trace theFor Understanding this ,let us trace the

arrival of Mobile Phones into Societyarrival of Mobile Phones into Society

First it was a high priced featurelessFirst it was a high priced featureless

Then it was medium priced with moreThen it was medium priced with morefeaturesfeatures

Latest is optimal features but lowest priceLatest is optimal features but lowest price


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Market EvolutionMarket Evolution

Then there are product that (Then there are product that (re)evolvere)evolve

from Mass Consumption to High Valuefrom Mass Consumption to High Valuetypes.types.

Thus we have water available for aThus we have water available for anominal price from the municipalnominal price from the municipal

supplies,nowsupplies,now arriving in fancy and exoticarriving in fancy and exotic

packages.packages.


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Market TypesMarket Types

Low PriceLow PriceLow Volume (Nobody Bothers)Low Volume (Nobody Bothers)

Low PriceLow Price--High VolumesHigh Volumes (any Mobile)(any Mobile)

High PriceHigh Price--Low Volumes (Low Volumes (VirtuVirtu Mobile)Mobile)

Medium PriceMedium Price--High Volumes (Blackberry)High Volumes (Blackberry)


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QUESTION:HOW MANYQUESTION:HOW MANYVARIABLES ARE THERE IN AVARIABLES ARE THERE IN A

MARKET SYSTEM UNDERMARKET SYSTEM UNDEREQUILLIBRIUM?EQUILLIBRIUM?

Simplistically,Simplistically, 33,,

((Mean)DemandMean)Demand T, (Mean )Price P, MarketT, (Mean )Price P, Market--

Composition,Composition,

BUT, for more than one Communities andBUT, for more than one Communities andProducts what is the TOTAL number ofProducts what is the TOTAL number of

variables?variables?


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Excuse MeExcuse Me--What is a Community ?What is a Community ?

A community is a group of people withA community is a group of people withsimilar consumptionsimilar consumption profile.Seeprofile.See thethe

following profile of three imaginaryfollowing profile of three imaginary

groups all living in the same tradegroups all living in the same tradeenvironments.environments.


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38401552Community3

1520401015Community2

515253025Community1

LuxuriesTravel

Consumer

DurablesHousingFood

% Of Income Spent


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Community (Community (Consumption)ProfilesConsumption)Profiles

0

5

10

15

20

25

30

35

40

45

Community1 Community2 Community3

% Of Income Spent

Food

% Of Income Spent

Housing

% Of Income SpentConsumer Durables

% Of Income Spent

Travel

% Of Income Spent

Luxuries


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Market TransitionMarket Transition

We define Market Transition as a processWe define Market Transition as a process

whereby the equilibrium profiles ofwhereby the equilibrium profiles ofcoexisting communities change .coexisting communities change .


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Consumption ProfilesConsumption Profiles

So consumption Profiles indicate how theSo consumption Profiles indicate how the

income percentages are distributed withinincome percentages are distributed withina group (of similar income profiles)a group (of similar income profiles)

Let us moveLet us move

ahead!ahead!


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Allocate P Products betweenAllocate P Products between

C CommunitiesC Communities

For each Community ,MarketFor each Community ,Market -- Composition isComposition is

defined bydefined by (P(P--1)1) CompositionComposition terms,seeterms,see next slidenext slide

For ALL Communities in the system, CFor ALL Communities in the system, C(P(P--1)1) = the= the

number of composition terms.number of composition terms.

Can also vary Demand (by adjusting the supply) &Can also vary Demand (by adjusting the supply) &

Price , orPrice , or T(transactionsT(transactions) +) + P(PriceP(Price), which means), which means

22 more variablesmore variables

(P & T).(P & T).


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1) Product Fractions/Market Share % in Each Community Should sumto Unity (which is the total Market) ie.((X11+X12+X13+

=(X1i=1 to n) C(=m) equations with p-1 possibilities .The pth

possibility can be found from the equation ,hence p-1

Condition 1Condition 1


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Condition 2Condition 2

2)Transaction Potential T For Each Product in Each

Community must be Same -otherwise no equillibrium

(T11=T21=T31=Tm1,T12=.=Tm2) P(C-1) Equations


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Since the system is inSince the system is in

equilibrium,equilibrium, BY DEFINITIONBY DEFINITION, we, wehave already implicitly definedhave already implicitly defined

some of the variables.some of the variables.

TT = Transaction potential or flux= Transaction potential or flux

of Products between twoof Products between two

Communities with respect to aCommunities with respect to a

Transaction.Transaction.


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FromFrom Condition2Condition2 ,,we have forwe have foreach Product, there are:each Product, there are:

(C(C--1)1) independent equationsindependent equationsrelating the Trade potential,relating the Trade potential,

TT, of that component in, of that component in ALLALL

of the Communities.of the Communities.


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Now, the number ofNow, the number of

independent variables orindependent variables orthe total number ofthe total number of

variations which can bevariations which can be

made independently =made independently =

the total number ofthe total number of

variables, less those thatvariables, less those thatare automatically fixed.are automatically fixed.


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F= number ofF= number of FreedomFreedom factorsfactors

F = [C(PF = [C(P--1) +2]1) +2] [P(C[P(C--1)]1)]


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The variance of a system or theThe variance of a system or the

Degrees of Freedom =Degrees of Freedom =

F= PF= P--C +2C +2

Which we call theWhich we call the phase Rulephase Rulesimilar to the Gibbsimilar to the Gibbs Phases Phase

Rule in Chemistry.Rule in Chemistry.


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Previous Slide showsPrevious Slide shows a hypothetical phasediagram of a community showing the

markets in potential coexistence.At low levels of

Average Income ,inside the green zone, there are two

degrees of freedom(as with red and blue zones), and

so the basic versions exist in equilibrium with the

intermeidiate ranges.

.As average income level increases Basic (red)versions are in equilibrium with the intermediate

(green) and the Elite versions (Blue) ..At the the

junction all the three markets coexist Degree ofFredom is zero here.,wheras , along the Blue,Green,

or Blue Red,or Red-Green boundaries the degree of

freedom is one

Understanding Markets in Equillibrium

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