preference

ChapterThree

Preferences

消费者偏好

WhereAreWeintheCour?

Wearestudyingthe1stofthethreeblocksof

microeconomics:Consumerbehavior,production

theory,andmarketequilibrium

Withinthe1stblock,weareworkingonthe2nd

ofthethreecomponents:choicet,

preference,andconsumerdemand

WhatDoWeMeanby

Preference?（偏好）

Itreferstotheorderedrelationshipamong

alternativechoicesgivenbyaneconomicagent.

Inmosteconomicliterature,consumer

preferenceistreatedastheultimateexogenous

element.

PreferenceRelations

Comparingtwodifferentconsumptionbundles,

xandy:

-strictpreference:xismorepreferredthan

isy.

-weakpreference:xisasatleastas

preferredasisy.

-Indifference:xixactlyaspreferredas

isy-

Notations

Adenotesstrictpreference;

-denotesindifference;

切denotesweakpreference;

PreferenceRelations

x；yandy；ximplyx~y.

x>yand(noty>x)implyx卜y.

AssumptionsaboutPreference

Relations

Completeness:Foranytwobundlesxandyit

isalwayspossibletomakethestatementthat

either

x；y

or

y；x.

AssumptionsaboutPreference

Relations

Reflexivity:Anybundlexisalwaysat

leastaspreferredasitlf;i.e.

x；x.

AssumptionsaboutPreference

Relations

Transitivity:If

xisatleastaspreferredasy,andyis

atleastaspreferredasz,then

xisatleastaspreferredasz;ie

X切yandy；z—x；z.

IndifferenceCurves

无差异曲线（或无差异篥

Takeareferencebundlex'.Thetofall

bundlequallypreferredtox'isthe

indifferencecurvecontainingx';thetof

allbundlesy~x'.

Sinceanindifference“curve”isnot

alwaysacurveabetternamemightbean

indifference"t”.

IndifferenceCurves

IndifferenceCurves

IndifferenceCurves

Allbundlesinare

strictlypreferredto

allinl2-

Allbundlesinl2

arestrictlypreferred

to*allinl3.

x

3

IndifferenceCurves

JWP(x),thetof

x

I(x

IndifferenceCurves

bundlesweakly

preferredtox.

WP(x)

includes

l(x).

IndifferenceCurves

ISP(x),thetofXI

bundlesstrictly

preferredtox,、

IndifferenceCurves

doesnot、

include

l(x)、、l«.

IndifferenceCurvesCannot

Interct!（不相交!）

|2FromI,x~2,x~z.

Thereforey-z.

IndifferenceCurvesCannot

Interct

SlopesofIndifferenceCurves

Whenmoreofacommodityisalways

preferred,thecommodityisagood.

Ifeverycommodityisagoodthen

indifferencecurvesarenegativelysloped.

SlopesofIndifferenceCurves

Twogoods♦a

negativelyslopedindifference

curve.

>Good1Iflessofa

commodityisalways

Good2

0

SlopesofIndifferenceCurves

preferredthenthecommodityisa

bad.

SlopesofIndifferenceCurves

Oneandone

bada

positively

slopedindifference

curve.

Ifaconsumeralways

regardsunitsof

Good2

ExtremeCasofIndifference

Curves;PerfectSubstitutes

commodities1and2aquivalent,thenthe

commoditiesareperfectsubstitutesand

onlythesumofthetwocommoditiesin

bundlesdeterminestheirpreferencerank-

order.

ExtremeCasofIndifference

Curves;PerfectSubstitutes

Slopesareconstantat-1.

Bundlesinl2allhaveatotal

of15unitsandarestrictly

preferredtoallbundlesin

hichhaveatotalofly

8unitsinthem.

Ifaconsumeralways

consumescommodities1

2

815

ExtremeCasofIndifference

Curves;PerfectComplements

and2infixedproportion(-to-one),

thenthecommoditiesareperfect

complementsandonlythenumberofpairsof

unitsofthetwocommoditiesdeterminesthe

preferencerank-orderofbundles.

ExtremeCasofIndifference

Curves;PerfectComplements

ExtremeCasofIndifference

Curves;PerfectComplements

Sinceeachof(5,5),

(5,9)and(9,5)contains

5pairs,eachisless板preferred

thanthe

bundle(9,9)which

contains9pairs.

PreferencesExhibitingSatiation

Abundlestrictlypreferredtoanyotheris

asatiationpointorablisspoint.

Whatdoindifferencecurveslooklikefor

preferencexhibitingsatiation?

IndifferenceCurvesExhibiting

Satiation

Satiation(bliss)point

IndifferenceCurvesforDiscrete

Commodities

Acommodityisinfinitelydivisibleifit

canbeacquiredinanyquantity;e.g.

waterorchee.

Acommodityisdiscreteifitcomesin

unitlumpsof1,2,3,…andsoon;e.g.

aircraft,shipsandrefrigerators.

IndifferenceCurvesforDiscrete

Commodities

(studythisyourlf)

Suppocommodity2isaninfinitely

divisiblegood(gasoline)whilecommodity

1isadiscretegood(aircraft).Whatdo

indifference“curves”looklike?

IndiiierenceCurvesWitha

DiscreteGood

(studythisyourlf)

Indifference“curves”

arecollectionsof

discretepoints.

01234Aircraft

Gas-

oline

Well-BehavedPreferences

Apreferencerelationis"well・behaved”

ifitis

-monotonicandconvex.

Monotonicity:Moreofanycommodityis

alwayspreferred(/.ationand

everycommodityisagood).

Well-BehavedPreferences

Convexity(凸性)：Mixturesofbundlesare

(atleastweakly)preferredtothebundles

,the50-50mixtureofthe

bundlesxandyisz=(0.5)x+(0.5)y.

zisatleastaspreferredasxory.

Well-BehavedPreferences・・

Yi

Convexity.

W=(txi+(1・t)y”tx2+(1-t)y2)is

preferredtoxandy、、for

all0

y2

x

Well-BehavedPreferences・・

Yi

Convexity.

Preferencesarestrictlyconvex

whenallmixtureszare

strictlypreferredto

theircomponentbundles

xandy.

Well-BehavedPreferences・・

WeakConvexity.

Preferencesareweakly

convexifatleastone

mixtureziqually

preferredtoacomponent

bundle.

Yi

Non-ConvexPreferences

Themixturezisless

preferredthanxory.

y2

Yi

MoreNon-ConvexPreferences

Themixturezisless

preferredthanxory.

y2

MarginalRate-of^Substitution

（边际替代率）

Theslopeofanindifferencecurveisits

marginalrate-of-substitution（MRS）（边

际替代率）

HowcanaMRSbecalculated?

MarginalRateofSubstitution

MRSatx'istheslopeofthe

indifferencecurveatx'

MarginalRateofSubstitution

MRSatx'islim仏

X2/AXJ皿―0=dxg/dx-!

atx'

△

x

AX2

I

MRS&roperties

MarginalRateofSubstitution

dx2=MRS'dx1so,atMRSis

therateatwhich

Itheconsumerisonlyjust

willingtoexchange

,commodity2forasmalldx上＜amount

ofcommodity1.

Twogoods■anegatively

slopedindifferencecurve

♦MRS<0.

Good2

>Good1

MRS&roperties

MRS&roperties

Good2

Onegoodandonebada

positivelysloped

indifferencecurve

■kMRS>0.

MRS&roperties

Good2

MRS=・5

MRSalwaysincreaswith(becomesless

negative)ifandonlyif

preferencesarestrictlyconvex.

MRS=.°・1

MRS&roperties

X2

MRS=■

0.5

MRSdecreas

(becomesmorenegative)as

increasnonconvex

preferences

MRS=■5

MRS&roperties

increasingas

nonconvex

preferences-

X2

MRS=-1

MRS=■

2

MRSisnotal

increas

Summary:

TheKeyConceptofthisChapter

Itistheindifferencecurve(IC)!

Itconsistsofalltheconsumptionbundlesthatare

indifferenttotheconsumer;

TheshapeofanICtellsalotabouttheconsumer's

preference:

■“Itsslopeiscalledthemarginalrate-of-substitution;

■•-Wecandefineconvexityofapreferencewhich

correspondstotheshapeoftheIC.