micro consumption

8/3/2019 Micro Consumption

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Contentsofthelecture

neoclassicalmicroeconomictheoryofconsump2on


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Neoclassicaleconomy

Founda2ons:perfectra;onality:peoplemaketheirchoicessoastomaximizetheiru2lityunderabudgetconstraint

perfectinforma;on:alltheinforma2ontheyneedinordertotaketheirdecisionisavailablewithoutcosts

u2lityismeasurablethankstoascoringsystemormonetaryunits-problem:theu2lityofoneunitofmoneyisnotabsolutebutdependsontheconsumerswealth

independenceofUifromqj:U=U1(q1)+U(q)++Un(qn)marginalu2lityposi2veanddecreasing:

)q(UU iii =

0q

U

,0q

U2i

i

2

i

i


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Cardinalu;lity

iq

iU

0

iq

i

i

q

U

00

iq 'qi0

iq 'qi

tg

tg

0q

U,0

q

U2

i

i

2

i

i

eachaddi2onalunitconsumedincreasesthe

levelofsa2sfac2on,butatdecreasingratesasthesatura2onlevelisreached


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Axioma;ctheoryofpreferences

2q

1q

0

1q

2q

two-goodsbasket:q=(q 1>0,q>0)

subsistencebasket

collec2onXofall

availablebaskets

undertheperfectra2onalityand

perfectinforma2onassump2ons,a

ra2onalsubjectisabletoexpresshis

preferences.Forexample,hecouldsay:

aq

bq

cq

ab qq cb qq


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Axiomsfororderingpreferences:

1.

reflexivity:. completeness:foreachcoupleofbaskets,weeitherhave

3. transi2vity:

4. nonsatura2on:themoreofagood,thebeRer:

5. strictconvexity

:Xq,q,q,q cba

qq

caqq

~

ba qq

~

cb qq

~

ab qq ~

ba qq ~

or

if and then

( ) ( ) b2a2b1a1b2b1ba2a1a qqorqqifq,qqq,qq >>==

babacba qq,10forqqqq)1(q +


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ThesetXcollec2ngallbaskets(eachbasketbeingassociatedtoapreferencelevel)is:

1. closed:itincludesitsboundary. convex:

3. strictlyconvex10withXb)1(a +

10withIntXb)1(a +

A B

NONCONVEX

A

B

CONVEX

A

B

STICTLYCONVEX

Thereexixtsatleastonepairof

thesetwhoselinearcombina2onmayfalloutsidetheset

Anylinearcombina2onofanytwo

elementsofthesetfallseitherinsideorontheboundaryoftheset

Anylinearcombina2onofany

twoelementsofthesetfallsstrictlyinsidetheset

C

D


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Indifferencecurve

Indifferencecurve:curveconnec2ngallindifferentbaskets

Features:

1. decreasing(fromnonsatura2onaxiom). atdecreasingrates(fromstrictconvexityaxiom)3. notintersec2ngcartesianaxis(qi>0)4. nonintersec2ngotherindifferencecurves(transi2vityaxiom):ifthey

intersected,theintersec2onbasketwouldbeassociatedtotwodifferentlevelsofu2lity

2q

1q

0

1q

2q

2q

1q

0

1qq

'q

cq

aq

bq

qcannotbeonthesameindifferencecurveofqa,qborqc,becauseqa,qb

andqchavemoreofbothgoods,soforthenonsatura2onaxiomtheymust

bepreferred.Forabundletobeonthesameindifferencecurveofq,itmusthavelessofonegoodbutmoreoftheother,soastocompensate;qcould

meetthisre uirement.Thus indifferencecurvearedecreasin .

1. .

q

'q

cq

aq

bq

2q

theincrementalquan2tyneededtotradeanabundant

goodhastobehigherthantheincrementalquan2ty

neededtotradeascarcegood:togiveuponeunitofascarcegoodIwantalargequan2tyoftheothergood.

This ivestheindifferencecurveastrictl convexsha e


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Mapofindifferencecurves

2q0

2q

1q

1q

q

aq

cq

bq

bc qq ac

qq ab qq

qqa

qqqq acb

thehigheristheindifference

curve,thehigheristheu2lityprovided:theu2lityprovidedby

basketqb(orequivalentlybyqc)is

higherthantheu2lityprovidedby

qa,whichinturnispreferredtoq


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Marginalrateofsubs;tu;on

MRS:themarginalrateofsubs2tu2onisthefirstderiva2veoftheindifferencecurve.

Characteris2csofMS:

1. nega2ve(goodsaresubs2tutes:thedisposalofoneunitofonegoodrequirestoaddupsomeunitsoftheothergoodsinordertoleavethelevelof

u2lityunchanged). increasing(ordecreasinginabsolutevalue):goodsareimperfect

subs2tutes

2q

1q

0

.aq

bq

2q

1q

0

1.aq

bq

0tgqU

qU

dq

dqMRS

1

2

2

1


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Ordinalu;lity

thecardinaltheoryhasoneimportantflaw:itassumesitispossibletoquan2fytheu2lityassociatedtoonebasketinabsoluteterms,butthisisnotrealis2candmoreovertheu2lityof

oneunitofmoneyisnotabsolutebutdependsontheconsumerswealth.So,wehavetogive

uptheideaofassocia2ngeachbasketacardinalamountofu2lity,andresignourselvestojust

putallthebasketsinaordinalranking.Thatstheideaoftheordinalu2litytheory.

u2lityisnotmeasurableinabsolutetermsdependenceofUfromqj:U=U(q1,q,qn):u2litybecomesaconven2onallabelbuiltinsuchawaythatitreflectstheorderedpreferencesonthesetXofallbaskets.

)q,,q,q(UU n21 =

)q(U)q(Uqqif baba >

)q(U)q(Uqqif baba =

)q(U)q(Uqqif baba


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Isou;litycurves

2q0

2q

1q

1q

q

aq

bq

0dqq

Udq

q

UdU 2

2

1

1

=

+

=

thehigheristheindifference

curve,thehigheristheu2lityprovided:theu2lityprovidedby

basketqb(orequivalentlybyqa)is

higherthantheu2lityprovidedby

q

0U

0U'U >

Isou;litycurve:curveconnec2ngallthosebasketsprovidingthesamelevelofu2lity.

0qU

qU

dq

dqMRS

1

2

2

1firstordercondi2ons

ofthemaximiza2onproblemarenotverified

(theslopeofthebudgetlinewillneverbe

equaltotheslopeofisou2litycurves):notangentinternalsolu2on.

onecornersolu;on

2M21 pCq,0q ==

solu2on:

=>= tgpptgdqdqif 1221

ofcoursesolu2oncouldalsostandontheothercornerif

isou2litycurveswereflaRerthanthebudgetline


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Specialcases

3.NONCONVEXITYINONEINTERVAL

betweenqaandqbthereisadiscon2nuity;

firstordercondi2onsofthemaximiza2on

problemcannotbewriRen(theisou2lity

curvesarenotdifferen2able)

mul;plesolu;ons2q0

1q

1

M

p

C

2

M

p

C

aq

bq


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individualdemand

Eachconsumerhandlesthemaximiza2onproblemandgetsasolu2onwhichcons2tutesherindividualdemand.

Thesolu2onofthei thconsumercancons2tute:

ademandfunc;on(whengoodsareimperfectsubs2tutes,thatistheisou2litycurveisstrictlyconvex):givenCM,p1,p,oneandonlyonebundlecons2tutesthe

op2malsolu2on:

ademandcorrespondence(whengoodsareperfectsubs2tutes,thatistheisou2litycurveisconvexbutnotstrictly):giventheternCM,p1,pmorethanone

bundlecons2tutestheop2malsolu2on

adiscon;nuousdemand(whenisou2litycurveisnonconvex):inthiscaseanequilibriummayNOTexist!

rememberweareworkingwithinthe

neoclassicalseng,whichmeansthat

consumerisra2onalandperfectlyinformed

( ) 2,1iforp,p,Cqq 21Mid

i ==

Thedemandcurveishomogeneousofzerodegreeinpricesand

income:ifallpricesandtheincomechangeinthesamepropor2on,qddoesnotchange:absenceofmonetaryillusion


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Marshalliandemand

Inordertoretrievethemarshalliandemandweneedtoworkundertheassump2onofcardinalu2lity

( ) ( )2211M21 qpqpCq,qUZ +=

0pqUqZ 111 ==

0pqUqZ 222 ==

0qpqpCZ 2211M ==

firstorder

condi2on

M

M

2

2

1

1

C

U

UZ

CZ

p

qU

p

qU

=

==

=

( )iiii

i qppq

U1p =

=

lagrangian

0q

Ufor0

dq

dp2

i

2

i

i

ifCM

increases,thebudgetline

shisup.

Ifthegoodisnormal,increasing

theincomecausesanincreaseinits

consump2on.


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Incomeeffect

2q0

1q

2

M

p

C

'U

'q

U

q

2

M

p

'C

1M p'C

1M pC

INFERIORGOODS

0C

q

M

d

1subs2tu2oneffect

. thedecreaseinphasincreasedtheresourcesoftheconsumer,soshecanbuymoreofboth

goods->incomeeffect

U

Then,onepricechangesfromp top.Assumeforexample:

22 p'p


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Price-consump;oncurves

Thankstoesandec,wecanclassifygoodsin:

2q0

1q

inferior

good

normal

good

Giffen

good

0e,0e Cs

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