2. Indifference Curve, economics, budget line

Indifference Curve

1. The Ordinal Approach to Utility Analysis:
Indifference Curve Approach
1. Limitations of Cardinal Approach to Utility Analysis
Ordinal Approach :
2. Assumptions of Ordinal utility analysis
3. Concept of Indifference Curve and its graphical presentation:
4. Definition and Properties of an Indifference curve:
5. The Budget Constraint or Budget Line or Price Line:
6. Equilibrium of the Consumer/Optimal Consumption
The Ordinal Approach to Utility Analysis:
Indifference Curve Approach
1. Limitations of Cardinal Approach to Utility Analysisand Overcoming by
2. Assumptions of Ordinal utility analysis
3. Concept of Indifference Curve and its graphical presentation:
4. Definition and Properties of an Indifference curve:
5. The Budget Constraint or Budget Line or Price Line:
6. Equilibrium of the Consumer/Optimal Consumption Point

2. Thelimitationsofthecardinalapproachto
1.Subjective units for the measurement of utility does not provide any satisfactory
solution
2.The assumption of Constant utility of money is also unrealistic
Utilitycannotbemeasuredinanyabsolute
muchthemarginalutilityofonegoodexceeds
indifferenceanalysis.Thisdoesnotinvolvemeasuring
butmerelyrankingvariouscombinationsof
assumesthatconsumerscandecidewhetherassumesthatconsumerscandecidewhether
another.
Theaimofindifferenceanalysis,then,istoanalyse
rationalconsumerchoosesbetweentwogoods
indifferencecurvesandbudgetlines.
toutilityanalysis
units for the measurement of utility does not provide any satisfactory
The assumption of Constant utility of money is also unrealistic
sense.Wecannotreallysay,therefore,byhow
exceedsanother.Analternativeapproachistouse
measuringtheamountofutilityapersongains,
ofgoodsinorderofpreference.Inotherwords,it
whethertheypreferonecombinationofgoodstowhethertheypreferonecombinationofgoodsto
analyse,withouthavingtomeasureutility,howa
goods.Indifferenceanalysisinvolvestheuseof

3. Assumptions of Ordinal Approach
i)Rationality:Consumersaresaneandwant
andpricesofthecommodities.
ii)UtilityisOrdinal:
iii)ConsistencyandTransitivity:
iv)Diminishingmarginalrateofsubstitution
v)Totalutilityisafunctionofcommodities:
Assumptions of Ordinal Approach
wanttomaximizetotalutilitygivenmoneyincome
substitution:

4. AA
ii) Utility is Ordinal :
Ranking: A
B
Or C
A > B > C
B C
Cardinal Utility:
A = 2500 util; B = 1500 utiland
C =700

5. Indifferencecurves
Anindifferencecurveshowsallthe
thatgiveanequalamountofsatisfaction
words,Indifferencecurverepresents
combinationsoftwogoodsbetween
thosecombinationsthatgivethesame
tableshowingthesameinformationtableshowingthesameinformation
thevariouscombinationsoftwogoods
satisfactionorutilitytoaconsumer.Inother
representsalineshowingallthose
betweenwhichaconsumerisindifferent:i.e.
samelevelofutility.IndifferencesetA
informationasanindifferencecurve.informationasanindifferencecurve.

6. Thistableisknownasanindifference
oftwogoodsthatyieldthesamelevel
anindifferencecurve.
MRS
--
6:1
4:1
3:13:1
1.3:1
1:1
.4:1
indifferenceset.Itshowsalternativecombinations
levelofsatisfaction.Fromthiswecanplot
An Indifference
curve
MRS=Slope of IC=
MUx/MUyMUx/MUy

7. iv)MarginalRateofSubstitution(MRS)
iii)Thereisconsistency;thatis,ifthe
basketB,thenthisconsumerwillnever
Thereistransitivity;thatis,ifAispreferred
C.
DefiningMRS:Themarginalrateofsubstitution
ofYthataconsumeriswillingtogiveupin
remainonthesameindifferencecurve).As
curve,theMRSxydiminishes.
isDiminishing
theconsumerisobservedtopreferbasketAto
neverpreferBtoA.
preferredtoBandBtoC,thenAispreferredto
substitutionofXforY(MRSxy)referstotheamount
inordertogainoneadditionalunitofX(andstill
Astheindividualmovesdownanindifference

8. Marginalrateofsubstitution
consumption):
Theamountofonegood(Y)(pear)that
ordertoobtainoneextraunitofanother
Diminishingmarginalrateofsubstitution
consumesofgoodXandthelessofgood
personbepreparedtogiveupinorderpersonbepreparedtogiveupinorder
ΔY/ΔXdiminishes.
The reason for a diminishing marginal rate of substitution
principle of diminishing marginal utility
(MRS)(betweentwogoodsin
thataconsumerispreparedtogiveupin
anothergood(X)(orange):i.e.ΔY/ΔX.
substitution(MRS):Themoreaperson
goodY,thelessadditionalYwillthat
ordertoobtainanextraunitofX:i.e.ordertoobtainanextraunitofX:i.e.
diminishing marginal rate of substitution is related to the
principle of diminishing marginal utility

9. The relationship between the marginal rate of substitution and marginal
utility:
IntheaboveFigure,consumptionat
consumptionatpointb.Thustheutility
beequaltotheutilitygainedbyconsuming
themarginalutilityofanorangemust
Therefore,MUoforanges/MUofpears
marginalrateofsubstitution.WithXmeasured
ontheverticalaxis,then:
MRS=(MU
X/MU
Y)=theslopeof
sign)
The relationship between the marginal rate of substitution and marginal
utility:
pointayieldsequalsatisfactionwith
utilitysacrificedbygivingup6pearsmust
consumingonemoreorange.Inotherwords,
besixtimesasgreatasthatofapear.
pears=6.Butthisisthesameasthe
measuredonthehorizontalaxisandY
ofindifferencecurve(ignoringnegative

10. Properties of an Indifference curve
1.Downwardslopingtotheright
2.Ahigherindifferencecurve(IC)shows
lesssatisfaction.Thus,indifferencecurves
ofutility.
3.Indifferencecurvesdonotintersecteach
4.Indifferencecurvesareconvextotheorigin
Properties of an Indifference curve
showsagreateramountofsatisfactionandalowerone,
curvesshowanordinalratherthanacardinalmeasure
eachother
origin
Property 1 & 2
IC3
IC1
IC2

11. .A.
B
C
IC-1
IC-2
Property 3
ΔX
Pear
Y
IC-2
At IC-1: B = C and at IC-2 : A = C
i.e., A = B; But according to property 2, A is on a higher
position , so A > B. Therefore, its an ABSURD that two
ICs intersect each other.
ΔX
Orange X O
ΔX
ΔX
ΔY1
ΔX
ΔY3
ΔY2
Property 4
(if it is Concave)
Pear
Y
i.e., A = B; But according to property 2, A is on a higher
position , so A > B. Therefore, its an ABSURD that two
ΔX
What happens if IC is not convex.
Hence ΔY1<ΔY2<ΔY3, which does
not conform with the MRS principle
Orange X Orange X O

12. ThefollowingTablegivespointsonfour
(a)SketchindifferencecurvesI,II,III,
indifferencecurvesshow?
fourdifferentindifferencecurvesforaconsumer.
III,andIVonthesamesetofaxes.(b)Whatdo

13. b)Indifferencecurvesareagraphic
preferences(inutilityanalysis,theconsumer’s
thetastesoftheconsumer).Theconsumer
differentcombinationsofXandYonthe
pointsonahigherindifferencecurveto
wehavechosentorepresentaconsumer’s
indifferencecurveshere,thefieldofindifference
areaninfinitenumberofthem).Alltheareaninfinitenumberofthem).Allthe
giveustheconsumer’sindifferencemap
indifferencemaps.Whenthetastesof
indifferencemapchanges.
graphicpictureofaconsumer’stastesand
consumer’stotalutilitycurveintroduced
consumerisindifferentamongallthe
thesameindifferencecurvebutprefers
topointsonalowerone.Eventhough
consumer’stastesbysketchingonly3or4
indifferencecurvesisdense(i.e.,there
theindifferencecurvesofaconsumertheindifferencecurvesofaconsumer
map.Differentconsumershavedifferent
ofaconsumerchange,thatperson’s

14. INDIFFERENCE MAP
Morethanoneindifferencecurvecan
successiveindifferencecurveshowsa
goodsalongIC-2inthefiguregivea
alongIC-1.ThosealongIC-3giveahigher
soon.
INDIFFERENCE MAP
canbedrawnonagraphwhereeach
ahigherlevelofutility.Combinationsof
higherutilitytotheconsumerthanthose
higherutilitythanthosealongIC-2,and
Indifferencemap:Agraphshowinga
wholesetofindifferencecurves.Thefurther
awayaparticularcurveisfromtheorigin,
thehigherthelevelofsatisfactionit
represents.

15. BUDGET LINE
Whereasindifferencemapsillustratepeople’s
dependontheirincomes.Thebudgetlineshows
isabletobuy,given(a)his/herincomeavailable
Budget line A graph showing all the possible combinations of two goods that can
be purchased at given prices and for a given budget.
BUDGET LINE
people’spreferences,theactualchoicestheymake
showswhatcombinationsoftwogoodsaconsumer
availabletospendonthemand(b)theirprices.
A graph showing all the possible combinations of two goods that can
be purchased at given prices and for a given budget.

16. Consumption Possibilities for Budget $30 and $40
Achangeinincome:
Iftheconsumer’sincome(andhencebudget)increases,
theoldone.
Achangeinprice:
Therelativepricesofthetwogoodsaregivenbythe
budgetlineequalsP
X/P
Y.Ifthepriceofeithergoodchanges,
Consumption Possibilities for Budget $30 and $40
increases,thebudgetlinewillshiftoutwards,parallelto
theslopeofthebudgetline.Thustheslopeofthe
changes,theslopeofthebudgetlinewillchange.

17. Budget Line Showing Income change (left) and price change (right)Budget Line Showing Income change (left) and price change (right)

18. Theoptimumconsumptionpoint
Wearenowinapositiontoputthetwoelementsof
andabudgetline.Thiswillenableustoshowhow
consumerwillbuyfromagivenbudget.Theconsumer
highestpossibleindifferencecurve.Thisiscurve
suchasIC-4andIC-5,althoughrepresentinghigher
region:theyrepresentcombinationsofXandYthat
TheconsumercouldconsumealongcurvesIC-1and
respectively,buttheygivealowerlevelofutilitythan
oftheanalysistogether:theindifferencemap
howmuchofeachofthetwogoodsthe‘rational’
consumerwouldliketoconsumealongthe
curveIC-3atpointt.Higherindifferencecurves,
higherutilitythancurveIC-3,areintheinfeasible
thatcannotbeaffordedwiththecurrentbudget.
andIC-2,betweenpointsrandv,andsandu
thanconsumingatpointt.

19. Theoptimumconsumptionpointfortheconsumer,
‘tangentialto’)thehighestpossibleindifference
theconsumerwouldgetalowerlevelofutility
curve,theywillhavethesameslope.(Theslope
pointinquestion.)Butaswehaveseen:
Theslopeofthebudgetline=Px/Pyandand
MUx/MUy.Therefore,attheoptimumconsumption
Px/Py=MUx/MUy.
Butthisistheequi-marginalprinciplethatwe
thistime,usingtheindifferencecurveapproach,
wehaveneededtodoistoobserve,foranytwo
preferredonetotheotherorwasindifferentbetween
consumer,then,iswherethebudgetlinetouches(is
indifferencecurve.Atanyotherpointalongthebudgetline,
utility.Ifthebudgetlineistangentialtoanindifference
slopeofacurveistheslopeofthetangenttoitatthe
andtheslopeoftheindifferencecurve=MRS=
consumptionpoint:
weestablishedinthefirstpartofthischapter:only
approach,therehasbeennoneedtomeasureutility.All
twocombinationsofgoods,whethertheconsumer
betweenthem.

20. CONSUMER EQUILIBRIUM
Whatconstraintsorlimitationsdoestheconsumer
utilityfrompersonalexpenditures?(b)
consumerequilibrium.(c)Explainthemeaning
(a)Inseekingtomaximizethetotalutilityfrom
incomeandpriceconstraintorlimitation.That
overaspecificperiodoftimeandfacesgiven
seekstopurchase(i.e.,theindividualconsumer
givenindividualincomeandpriceconstraints,givenindividualincomeandpriceconstraints,
totalutilityfromexpenditures.
(b)Theconditionforconsumerequilibriumcan
MUx/Px=MUy/Py=....
subjecttotheconstraintthat
PxQx+PyQy+....=M(theindividual’smoney
consumerfaceinseekingtomaximizethetotal
Expressmathematicallytheconditionfor
meaningofyouranswerstopart(b).
frompersonalexpenditures,theconsumerfacesan
Thatis,theconsumerhasagivenandlimitedincome
givenandfixedpricesofthecommoditiesheorshe
consumeristoosmalltoaffectmarketprices).Thus,
constraints,therationalconsumerseekstomaximizetheconstraints,therationalconsumerseekstomaximizethe
beexpressedmathematically,asfollows
moneyincome)

21. (c)Theabovetwoexpressionsmeanthatthe
mustbeequaltothemarginalutilityof
commoditiespurchased,subjecttotheconstraint
(PxQx)plustheamountofmoneyspenton
othercommoditiespurchasedbythisindividual
income(ifweassumethatthetotalincome
saved).
themarginalutilityofthelastdollarspentonX
thelastdollarspentonYandsoonforall
constraintthattheamountofmoneyspentonX
Y(PyQy)plustheamountofmoneyspentonall
individualexactlyequalstheindividual’smoney
incomeisspent;i.e.,ifweassumethatnothingis

22. Whatistherelationshipbetweenthecardinal
approachtoconsumerdemandtheory?(b)
twoapproaches?
a)Theindifferencecurveapproachtothestudy
alternativetotheolderutilityapproachforthe
asequilibriumandexchange)andderivingaconsumer
(b)Thebasicdifferencebetweentheutilityapproach
thattheutilityapproachrestsonthestronger
ismeasurableinacardinalsense,whilethe
ordinalmeasureofutilityorsatisfaction.That
thattheconsumerbeabletodecidewhether
satisfactionthanotherbasketsofgoods,without
utilitytoeachbasket.
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cardinalutilityapproachandtheindifferencecurve
(b)Whatisthebasicdifferencebetweenthese
studyofconsumerdemandtheorycanbeusedasan
thepurposeofanalyzingconsumerbehavior(such
consumerdemandcurveforacommodity.
approachandtheindifferencecurveapproachis
andsomewhatunrealisticassumptionthatutility
theindifferencecurveapproachrequiresonlyan
Thatis,theindifferencecurveapproachrequiresonly
onebasketofgoodsyieldsmore,equal,orless
withouttheneedtoattachaspecificnumberofutilsof
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