GaUs Reading

II

3

Efficiency

OVERVIEW

W e hLvc tlllLs ll txllsed OIl individual Lltionalitv wht is it to

Ill a ratiollal actor and how call we flJrlllally llodcl such 11l

Ictor This ehlptcr begills with that COllClTll but thcll turm to all

how rlliollal actors illterlct-~middotIhl subject of th( ITIIllindcr

of thl book Thl lliaill COIlClf1l of this chapter is to explore the relatioll betwce]] rational actio]] lIld the idea of ctrlcicllcy the

starts With eHlciellcy of the COIISUllIptioll dccisions of olle perSOIl and thell IlHlV~S to the idea of all dhjcnt cxchange all intlllctioll

llttwlcll two (collolllildly ratillnll Igtnts The illiporLllIt ide1gt of l)dYlto slIj1criorily llld Pareto optillalit) an introduced Thl secolld plrt

Df till chapter briefly skltches vlI-knllwll Elilurcs of vlriollS Ilotions of ctlTl1i1itics

31 RATIONALITY AND EFFICIENCY

Everyone knows that cconomics is about diicicllcy and most of us

have SOlllC pro Of COil lttitud about IbM SOIllC of 1I~ Ire all [(JI

while others i1lsist that dlicie1lt) i a cold eUJI1011lic value

that mllst lIot Ollle before tquit) COllcern (H the needy or prortc tiOll of tht envirolllllent Tim it is Iid wc Ileed to trade ott efEcicllCY against othtr ydues I But while most of us kllovv vlhether

we art fe) it or Jgill it we art oftcll Ilot surt what it is Just what

72

I EFFICIENCY

IS trtIC1lllCY I it simply Olll vahlt JIllung othcrs---ollt that tumoshyIllists but not the rest of LIS find vtry attralt(ive-or it is sOl1lehow a tl1ldalllenral idt1 that we callnot do without V hleh we tllllilt not to

sacrificc flJr othtr thillgs~

Efficiency and Rational Individual Choice

Let liS reflcct Oil wlllt wc know Ibout ollr ratiolul ecollolllic 111111

As a Lllionll hooser UOIIIO I(ollolllims lLIS a well-[(JrlllCd utility

fimctioll sltisfying the requirelllents oj urility 1 henr we calllillcd in SectioJli 22 alld 2t His nrdlTellccs 11 haraetlrind

dellland Cllr(S

sI11)titution of goods ill Section

J11110 1coIIlJlllioS Ius 1 prcrlrlllle ttll pin

How Illuch pilla is it rltiOlul fur -101110 hollOlllims to COllSllllll~

Suppose tint the cost oj pinl comtlllt It II() we Illmt rCIllclllhn

that cost wc 111111 the toLl I PIOlllllil) (lsi of C()JlUlllil1g

tl)]golle opportlillitil to satist~ othlr prctl-rcllces ) poillt )) It is 1I11porLmt to stress that cost does lot

Illclsslrilv mcall a mOlletary pIYllIellt or sOllllthing that VOli don I

ill 1 emt oftaklllg this ((Hirst IS that I have to take tct) III

the lCllI10111ists sellse the nl)t ofgttillg your rJ1t choice of1

is thll you hld to ()rgo your ccontl choice of 1 bo of hickell

whcl1 you h1Vl to choose hetweell good things the cost of your (kcision i tht thillg you didnt cIH)osl This cm be

in knns of 1101110 1(oll(lllli(JIs [llrgolll utility-middot-call this It i the utility you would hlve received tiOI11 vour scCtmd

elwin Nov consider Air decisloll to ((mSUllll the first slice of It satisfies hi prd(rllHc [llr pina his utility ftllctioll

We call represellt tim SOIlIC Lltilitv bClldit cdl it

(thH is if the utilitv bendits ar~ grlHer thall or thell it vill he ratiolld tll] hilll to purcha~ the slice of

pizza But hould ht hill oul Olll slice) Well we kllow that since the

cost of nizz is comLlIlt per LlIlit the COit of the second pilcc will he

But htCHISC of decreasing marginal utility the bcnefitlt of the

sltcoml piece will be Ic th111 twill 1(raquo c111 this I(il) + 11(1) III I IS 1 Illlillber less th]]1 11(1))) The cruei1i idcl

hert is that vhltevcr the lItilitv benefits or the tlN pien II(h) I the

of the second will be pOitivl

but slllalkr than thc utility orthc first picce (hence

is what IS melnt bv

73

is hertel vill be ulility

Total Costs

3[i(C)]

2[1 (c)]

Idc)

utility tmnefits

CHAPTER 3

Number 01

FIG U R E 3-1 Efficient Consumption where (b) m middotn

Total Benefits

I(b)

I I (b) + [I (b)

II(b)

It will be rational f()r Air to COllSUllle two slices if the utility benefits of two slices is greater thall or equal to the utility costs or two slices~

+ 111(1)-111 21f1(r)l Because the costs are constant benefits arc decreasillg at S011le point it will be the Glse that

or as ecollomists say Illarginal (utility) benefIts that frolll sOllle slice of pizza will be less thall the marginal (utility)

costs he had to iucur ill order to get thlt slice 111 that else it would be irrationll for Homo h((lllolllims to COIlSUIlIl that additional slice of

because the preferellces he then would be satisf)llng an ranked below the prdlrellces he is fillmiddotgoing Figure 3-1 is a graphic repre sentation of a specific example of this simple choice problelll 011 the

left vertiCll axis we measure HOlllo lrollollliwss total utility costs while Oil the right vertical axis we llIeaSLIre his total utility Figure 3-1 it is rational ftlr Olll (01101111015 to purchase three slices of pizza (but no

Homo Erollolllims will conslIme up to the point whtre 1I1Il~~illill bCll~its eqllal lIIil~~illll (os This is olle definitioll of efllciency 1101110

chooses in this way not because ht values more th1I1 a ratiollal actor seeks to IIIltlximize utility

this decisi()ll is simply required rationality To choose any other

74

r

+ [JI(b)-m]

but the

benefits In

EFFICIENCY

Chicken wings for All

4 I 10

Pi128 lor 2 Betty

o I)

Chicken wings for

FIG U R E 3-2 A Simple Edgeworth Box

would be to choose a lowermiddot of course is the essellce of

over 1

is sil1lply

Pizza for AI

There is thcll a clOSt rebtioll betweell etlicicllcy and ratiollal choice to be ntionll is just to choose ill a WJY tlllt hest satistlls 01lts

as sitllations in

Chapter 4 when rationality and dli(illlcy break Ipart III many of these cases we are 1IIKLTt1II1)lIst what i the truly rational to do

that II1cans that the lIIarlinal glillS lre at least

great as the

Efficiency and Rational Exchange

Let liS 1l10Ve to a two-person case Wl will rLprCSl1lt the ell oice problelll in terms of indiHlrence curves plot olles preferences over bundles ofgoods

rates ofsubstitution between thelll (Sectioll 13 poillt Alf has four slices of pizza ~Ild Betty has eight BulEtlo chicken wings And suppose that they have pretty Illllch the sallie preferences over

which it will be dClTelsing

alld chicken so that their indiftircIIlT curves are the sallle Figure 1-2 gives their indifference llIaps Bettys (solid)

indifference curves start in the lower left Alfs curves COllle down from the upper right SllppOSC that ill this worth Box 2 Alf lI1d Betty arc at Doint PI AII has Illlir slices of plzza

and 110 wings while Betty has

75

CHAPTER 3

1 t is to remelllber that Air is inditterent bctvveell all

combinations of pizza and chicken wings on tht indifflrence curve however he prefers 111 hundles on curve Alf to 111 bundles 011

The dotted arrow cOllling dovn frolll the top right comer shows that as All J1loves southwest he reccivcs incrc)singly prcshy

fiened combin1tions of pizza and chickcll wings If hc moves all the WIY to the southwest comer he receivcs all the pizza and all thc

chickcll wings The solid arrow represcnts the direction that Betty to 1110C startillg at the lowc1 lett corner he prcftrs c01llbishy

lations of chickell wings ald pizza that are to the l1orthclst So is indifltrCIlt lwtwcen all hundlcs of pizz1 and chicken wings on

the indiffercnce curve Betty I hut she prdirs 111 the bUlldk on lktty to any of the hundles Oil Betty I (AmI of course sht is indit1(rlllt

between the hundlls on Iktty2) Now any point III the f()]lllCd the Alfl-LkttYI indittershy

lnee curves improves thl utility of both AIr 1l1d Bettv over point PI allY pOInt ill the eye Illoves cach to a higher indiffercllce ClrVl

Pick allY point ill the cye you will sec that Betty and Alfhlve both

llloved liOI11 PI ill their preflrred dlr~dJollS What this show is that

both em he made better orf hI excilange CI1II t01I11r 11(1 IIddillOIl1i UIlC ICC ((((ed An exchange that moved both Alfand Betty to

poilll p on Figure -2 would Ilnke both of thcm better ofl both In

raised to a higher indifTlT~l1cl curve lote that jgt is Oil

Bcttygt We Clll say thcn that point raquo Oil 1~lguIT 1-2 is

to point Igt I at ]elst olle p~rson is better olLmd 110 Olll is worse olf 111 this case both pcople- arc better olr

But dthough the hlrglill at p is Pareto-superior to PI thcre arc still Pareto-superior bargaills that Alf and Betty can make stlrtJllg at 1gt2 The gains fiom trade have 110t becll exhamtld 0 long as Paretoshysuperior l110ves are 1V1ihhlc AILlIld Bettv can kccp (lll trading and at

least olle will bcnefit Whcn lrc the possihle gains ii-olll trade lxhaustecP We call easily scc tiOI11 Figurl 3-3 til]t when tlly reach 1 hlrgain at which their illdit1lrclKl curves Ire Llllgcnt Paretoshysu perior IlIOVlS arc ex hlllsttd

Consider Il)f exalllple point l At point 1 AII em only lllOVl

ineiitttgt[(IlCt curve if Betty 1l100lS to a lower indifltrcllcl

that would make her worse Jnd a 1110ve

IS on Iv igtlrtto-lll)fr]or if no one is made worst otr So too starting at

vIY th11 lkttv can rise to a highn inditlercllce curve is ifAlf moves to a lower Ollt -that is he IS worse off Point 1 is thus a P1YCfO-Olllilll1 hmlin any departure frol11 point P v would

76

4

Pizza for 2 Betty

deg

8

deg

EFFICI NCY

Chicken wings for

4

4

Chicken wings Betty

FIG U R E 3-3 A Contract Curve

o

P2middot P 1

1deg

Pizza for Alf

lJJ]kc either Alfor Lktty worSt otr Point I therdl)re is etlicient all the gaillS 110111 possible exdLJIlgl have 11lTIl Cxhllisted But

IS Ilot unique in this lcgml ally blrglin that occupics a which AU and Bctty illllitTercllcc curvcs are tl11gcnt i Jgtaretoshy

Thc line A-B (which is called the (Ollimet nrlc) represcnts

Ill slIch possihle etliciellt b]rg)il1S~(lIleS tiIat usc all thc possihle

110111 tLldl ()bviously st)fting tJOI11 point 11gt sOllle or the el11cient

contrlCts Llvor Betty while others llT better for AWl rates of

rationll people Notice two thin~s hlsl the

substitution is lTucid ill trade with c]ch other Because they eKh prellT varied to

hundles ltT(lods if AIr is ninl-rich he will

Betty

77

over

those last two slices 01 [(Hlr chichll wings)

CHAPTER 3 EFFICIENCY

slices of pizzJ Thus as I have depicted the problem it is irratiol1Jl for Alf Jnd Betty to refrain fi-om trading if they keep their bundles at PI they Jre satisfying lower- over higher-ranked preferences

We are now in a position to understand the concept of PJreto or allocative efliciency~ We can say that distribution )) is Parctoshy

slIperor to (more efficient than) I) I if and only if no person is on a lower indifllrence curve ill 1)2 than that person is in [) I and at least one person is on a higher indifference curve in I) than she is in ]) I If despite the possihility of a move to a pJreto-superior distribution we stay in ]) I therc is at least one person who could achieve J higher level of preference satisflction without lowcring anyone elses Thus in Figure 3-3 the distrihution identified by P is Pareto-superior to the distribution of P I As in all the cases we luve discussed thus tlr (but see Section -1-2) there is something irrational ahout maintaining Pareto-inferior distributions In addition to being Pareto-superior to hoth P I and P2 point P is also Pareto-optIIIII just becallse there is no alternative distribution which is Pareto-superior to it That is if Alf and Betty have arrived at P there is no way in which one of them can be raised to a higher indifltTcnce curve without the other l110ving to a lower curve

Is the Pareto Criterion a Moral Ideal

Paretian Welfaristn The Pareto criterion is often IInderstood not simply as J requirement of ratolltllit) qlla cftiCIency but as a standard by which wc cm judge the 101111 desirability of a distribution or in gencraL a social stateS To many it seellls c1car that distribution 1)2 is morally better than D I if (alld only it) somc persons wcltlre is highcr in D and 110 ones is lower than it was in I) I Especially in politics it is thought what is good fllr pcople-their weltlrcshymnst be thc (sole) critcrion ofa good policy This view has clear roots in utilitarian Illoral theory which identified promoting hUl11an hapshypiness as the sole goal of morality and politics Recall the rcmark quoted in Section 11 from Nassau Willial11 Scnior a leading political economist of the ninetcenth century economics he said could aSSUl11e that everyone seeks wealth because wealth and happiness are vcry scldol11 opposed The nltimate aim was clearly human happiness even if the proximate aim of econol11ics was the growth of wealth Now contemporary wclfare ((oIIOI1lrs typically understands a persons weltlre to bc mcasured bv her utilitv function If the utility of Betty is II in ditribution ))1 md 1+n in U 2 then it is aid

her welfare is higher in I) than in I) I and D2 is a better distribution than 1)1 Here however things get complicated The early utilitarshyians such as Jerel11Y Bentham and his followers believed that utility (pleasure) was a cardinal measure (it could be measured along a metric) and that when contcmplating a move from I) I to U we could scnsibly add the utility Alf received from the move fi-om I) I to ))2 to the utility Betty received and then subtract the loss of utility to Charlie (who let us say was better offin I) I) Having done our sums we could then decide whether ovcrall the move from )) I to 1)2

increases overall aggregate utility Bnt we have secn (Section 23) tlLlt there is no particularly good reason to add von Neumann-Morgenshystern cardinal utilities of different people unless there is a special else for some additive function it is simply arbitrJry to SUlll up cardinal ntilities The contcmporary welflrist seems to have a problem how to compare social states without ll1terpersonal complrisons of uti Ii ti es

The Pareto criterion sce11lS to onlr a way out of this problem if no one is worse off in ])2 than she was in ]) I and at least one person is better ofT in ]) than he was in ]) I then ]) is Plrcto-superior to I) I And since the welElre economist has identified a persons welLlre with her utility It looks as if we call say that ))2 does better tr011l the perspective of human welElre Now it is otten thought that this cannot be a very usefiil criterion of moral betterness it oilly yields a judgl11cnt that 1)1 is better than I) I if 10 (Jll is worse off in I )2 But how otten is it the casc tlLlt no one is ll1ade worse ofP On the Parcto test if in ])2 one l11illion people are made better otf thm they were in I) I but one person is worse off we canllot say thlt 1)2 is Paretoshysuperior to I) I Is there ever we might well wonder a Paretoshysuperior 1I10Ve to be made We Ire now in 1 position to see the econol11ists deep attractIOn to market transactions Under certain idealizing conditions (eg full information no third-party ef1ects) each market transaction moves us to a Pareto-superior distribution When people trade they prefer what the other persoll has to what they offer to give lip and so we move to a Pareto-superior lhstribushytion As long as we have not exhausted the possibilities fllr exchange-as long as there are trades that people Wll1t to makeshywe have not exhausted the possibilities ftlr Pareto-superior moves

Althongh market transactions are otten moves to Pareto-superior outco111es it is much harder to see how a collective public policy em meet the Pareto tcst It is hard to think of any uniform policy that does not disadvantage someone(gt To avoid thi~ conclusioll (ie that

78 79

CHAPTER 3

the Pareto critenol must he violated wclbre economist llld Parctiall adopttd what is known t the

llllit(JrllL sOllle

han

dislrilJIIlilll J) 110 OJ is (1ell 111111 SOIlC lose U) IIIOIllIgIOIiI lJ I 10

(IS IllllSC 11110 do lite IlIllle could laquo1111pCIISIle IiiI loSls - To grasp what it l1IellllS to say that a persoll wilid be

t()r a cOllsider AIf~ who wc m is the

sole persoll who has hetLL 11Lilde worse tht 11I0ve tlOI1l Dl to 1)2

make the casc SlllLp1lt asUlI]( that lverYOl1C else is hctter otr ill D21 To say that All ha bccll madc worse 011 llleIIlS that he is Oil a lowcr iLlditllTl1ce curve ill I) thaLl hl was ill I) I Nox iLlLagilll

after the move to I) the trallSterred ellough of their to Alf [() raise hill hlck to thl iLlditl(rcllce curve tint he

this would brillg Ilbout a Ilew distrihutioll 1 ) which is iLldced

to I) I because everyolle etelt All is It II higher indifflTlLlcl curve ill I) thl1l they were ill ))1 Illld Al(i LlOW back

OJl the lIlle inditllilLlCl cUne (as he vIlS ill l) 1 W l CllIl say

thlt 1)2 i Kaldor-Hicks Paretosllperior to 1)1 iftlllrc is a distribution I) that (I) could be L1roduced bv rldistribulilll the 1110Vlllg Iiom I) I to I) alld I) is the llorJlul larlloshy

) and (2) 1lS hcCII

has bl~n

to I) I Note the Kaldor-llicks test SllyS that to I) I (1(1

I )jstrihutioll I) is that ill which

lllade bllt Kaldor-Ilicks docs lIot say silllpl) thlt I) is Plrctoshy

to (more dllcicLltto 1)1 it says thlt I) is

I) 1 evell thollgh SOIllC pcopk the 1110VC llOlll 1)1 to 1)2 Belallsl Iraquo (ltlIld becausc I) 1I(1111d be Pareto -sllperior to I) I

Paleto-sllplTior to I) 1

To lIUllY tIllS S(lIllS

blSCd Oil the dClllld tht vcry odd

fill SOllle ClIIl

illcurrld losses give rise to I) alld I) is Kaldor-I-Jeks

which WlS

IS lOW elllployell to

DtlLers The lllove iolll I) that hellLtit SOllll at the expCIlSl of

to 1)1 lIukes Stlllll peop1lt worse ofl~ yet it IS Iusttlell as a

backdoor way of

alld gil ins within II Paretillll tiullcwork

Kaldor-Hicks looks like a

U)lllplmSlJllS of utilit loss

Even if we put aside the controvlTsilll Iltaldor-Ilicks interpnlltioll

or the Plrlto crittrioll llJOll rdlectioll thl Panto test is l10t as U11COI1middot

troversid as is ofkll thought Much othl lppllll of the Parltu criterion

lies ill the question Who could posltibly object to all improvell1ent that lllakes everYOlll better olP Figure ~f suggests IIll answer

80

r EFFICIENCY

--_93 Bettys

Dgt

o utility

FIG U R E 3-4 A Series of Paretian Moves

wc start at point O and lliake the Plnto-superlOr l1l0Ve to

A which is OIlL possible distributioll alollg l) I the Plrlto

Frolltier the set of possibk Plllto improvemLllts frolll O Ollct WL

are It A tht Pareto impwvcllltllts to I)gt Ilrl liLllitld to thosl lwtwttll

poillts W llld X other thllli ill l) I so are llot Pareto illlproVllllCllts Assume thcll tInt at soml

distributioll 1)2 becolllcs 1 poisibllity Alf llld Bctty makc the

Pareto move to poillt B 011 1)2 Suppose now that ill the ttlture 1)1

becolllcs possibk llO the possible PIlrLto improveLlllms are limited to

thOSl bllillg bctelll Y and Z We em sce that successive applicatiollS

of the Parcto critcrloll Illove distrihwiollS alollg a plth that is incHs

illglv [wlldieill to AlfaLld urless bCllefit to Bctty Ifwc Iud bcell abk to

JUIllP to I) all at Ollce cvcrythillgoll it would be1 Pareto over 0 hut ollce we have llladc the interlllediatc lllOVeS to A IlIld B

lllOSt of 1) is cduded by the Plfeto crlterio]l Perhaps

would havc good rcaSOll to objcct to the illitial Pareto LllOVC to The Pareto prillciple allows a wide rJllgc of movcs llld it Illay matter a

lot which of those is 1Cltllllly made alld ill whlt ordeL

Welfare and Preferences aside thest problems with the

Plrcto criterioll it also SlelllS doubttttl that we should accept the

idciltiticatiuLl of prelerlIlCe SJtlsLlctioll with welflre We llve

cell that prekrlllcls Illld lot be Jbnut olles own good or self

interest anytilllc OllC rallks all outcome above another Olle hilS 1

21) llClll our last-Llllmgo rdtslr frolll Sectioll

is llot to take the List LlllllgO though as Slll llotlS

she would like thJt lllJllgO and would WdCOlllC SOllleOlle thrustillg

81

CHAPTER 3

the mango on her III that case it seel11S doubtful that we should say that her welfare is enhanced by satistying her pnferellce not to take the last mango since her civility preference instructs her not to do what would be good filr her Those who identity wef1re with preference satisfaction often simply seem driven to stipulating that in this case ones wel6re IIIl1sf be advanced because one is what one prefers Here I think is a perfect example of the way that the ambiguity between the techniGlI and ordinary senses of

21) leads to serious confusions Preterellees regarding others also posc f(x Plretian

welfllmiddotis111 Suppose Alf is a prude who ~1 sOllwwhat racy book such as Lady I LeweY It seems tlut

to Paretian wcltJris11I book cannot he approved of by the Pareto vorsc ofT whell she felds the book we might normally think she has right to

illditrerel1ce curve The way in which the Pareto principle call COI1shy

flict with all individuals rights to decide what she is to do has been analyzed All1arty~l Sen) Sen conceives of a person having 1 right as having lllthority to dtcicle the sociJi preference over at le~lst one pair of alterIlJtivts (xy) such that if~l person chooses x gt- l th1t is the social preference us cl11 this social prdlHllce xP)) and if the person chooses ygt- x then yPx (ie the social prellrence is y over x) Sen shows that attributing sllch rights to two persons and asslll11ing all possible of social states are permissible the s(leiJI olltcOl11e selected by the rights can conl1iet with a version of the Pareto

accordillg to which if fOf evcryone xgt- y then xfly That is if everyone prefers x to y then the social preferellce nHlst he x ()vtr y Sen nicely un1111arizes his lrgUll1ent

There is a book (eg Lilly Chatterleys L(1(I) which may be

read hy Mr A (the prude) or Mr B (the bscivious) or neither Given other things thest three alternatives define

social stHes ltI Ii and ) respectively Consider now the following possibility The A most (1 (no one

then l (Ill take the hurt on and lastly ) that lasciviolls lapping it up) The Iasciviol1s

prefers 1110St tl Cit will that lilywhite baby a lllce stwek) then b (it will be fun) and last () (whJt 1 waste of a book) 011 grounds of individual freedom si nee B wan ts to read the book rather than 110 one reading it

82

T

EFFICIENCY

sil1le A does not wallt to read it (l is soudly better than lt But t1 is Plreto-superior to

If)ltl

So we get hfl (by Mr Bs right) oPa (by Mr As md (f Ph Pareto since in both Mr As and Mr Bs lt1gt- b) so wt

gct lJoJgtiI))-m illtDllsitivl result Sell saw this not as a case rights but as showing the unalceptlbility of the 1lIITto universal ruk 11 Sometimes it seems that a cOJ11mitment [0 Pareto

ClIl ICHlllS astrIY lt- )I1C WIY to respolld to this problem is to

exclude sOl11e sorts of prcflrCllClS tjOIll cOllsiderltion thus we restrict Ollr weltlle Paretianislll to ellces over diftlrcllt Stltcs of ones own litc) and so ignore that other people do rather thm not do ccrtlill things not read Llther thlIl rcad ccruin hooks) But this solve all the

over lllany expellSlve OllCS Given thesc structures Pl1Tlian wclt~ms11l approves ofdistriblltiolls tint

r1l~e liS both to hiuhcr indifilrlnCl curves-- livilH llll lxplnih Illd 12 you

Fair and Unfair Starting Points Perhaps the 1llOSt seriolls probkll Pllltil11 wlIElI-isl1l is thlt it is instllsitive to the distributions ti-oll

which we Suppose thlt 111 of Alfs 111d

over quantities ofpiZlt 1l](1 chickcll wings hut and 111 the chickcli wings ami Bltty has nOllto

Pmto principle this is all dlicient distributioll Since Bctty hIS notil ing to t]J(Je thne is no way to nuke her bettll off without lllaklllg AII worse ()f1~ so wc have achieved Pareto optimality 13m this hardly setlllS a moral reason to e111hr1Cc the distribution Thc hl~lrt of the Paretian project is to make pcople hetter ofT and WhCIl no 011( call he made hettcr off without lowering S()llleOIH elses utility the Pareto criterion Ius llothing lllort to say---we hlv( achieved optil1lalitv_ But liol11 the perspective of advmcing 11l1111m Welf~l1T it is hard to

conceive of situ at lOllS where Betty has IlothiIlg lS optind Plausihle versiollS of Parltilll welfllism thus seelll COllllllitted to S0111( idca of1 flir starting point mel flim can hold that Plflto-lpproVld moves l111lk from the illitil t1ir startim poillt arc mOLll

83

(xlcrlulilic All

this impact 1S

bellefit

prodllcns or C(lIlUlIlcrs cost

11IlPOSlS extcrtlliities

I ratiollli ccollomic Igcnt Air

CHAPTER 3

32 EFFICIENCY EXTERNALITIES

AND PUBLIC GOODS

Externalities and Property Rights

to the cHIcielltour f(1ClIS tI0111 tile eltlcicllt

that you ideJ 1IS

our allalysls of all et1iciellt COllSlllllptioll decision you up to tbe point where your marginal bendits

your 111lrglllal costs lfyoll stop producing pizza wilile yuur

your Illanrinal l()sts it looks

pizza how l1lucb beln

benetlts are still greater thall

illsoClr as production of1I1 extr1 t~lCtion th1Il it costs (rlllItmber our concern is opportunity costs) To produce pizza above md the pOlIlt where your

bcnetlts equal yOUI lllarglllal costs 111lIllS thlt your LIst pin cost

you Illore (ill tLTlIlS of prdtTtIHT sltis6ction) than you received ill which again looks to be all irratiol11 decisioll So I ration11

lIllXilllizer will produce up to the point where her lllargilLIl

benetts equal her lIlargi 1111 costs

The nwbklll is that this lIeed not be the dticiellt level of

ClIglgC ill it up to the point were iis Illarginal bCl1dits ll]lIal iis costs

Alf willllot uke accollnt of the (mts to Betty But if AIr lip to tilt Jloillt wltere his IIIlrgilla] cmts lIld 11lnetits are there Irl additiollal cot to Betty it looks IS if the tot11 ()cial costs

(thl cost to All ami of Alls last unit of productioll lxceednl

tlte entire social bcndits This would violate thl Plreto cnterion AI

has Illoved them both to a 11l distributioll (with thl extrl

lInit of pizzl) which bendits Alf at I cost to Betty A sillli1r l11alysis applies to external bCllefits if Illy production 111 bClIdits to you 1S wcll as to Ille then if- I SlOp production whcn lily muginal bCl1dlts

Illy margiml costs fWIlI a socia] Doint of view (which includes

the bcnetits and costs to everyone) the social mamillal bcnefits still excecd socid 111argin11 osts sincl lily

not taken into account the bellefits you receive

84

EFFICIENCY

Extnmlities 1re a chlt-f source of market f~lilure-the ililurc of the market to produce eHicicllt results Oilly if Bltty)iilly illftTIIIlIics all

the costs alld belldts ofber lctiity will slie stop at just the poillt wlllrt

social lIluginai bendils clt]uII social lllnginal costs So too III a trade

IiAII1nd lkttv ftdlv mternalizt the costs lIld [wndts oCtheir trade

Clll Wl SIY lhe trade lllcesltlrilv moves lI) to l Parlto-sllplTior state If

then l1T tlllrdpartv costs extcl1ldiIlCS) AII llId Betty

Iluke trades where the soci1i marginal costs exceed the social

belldits because they do lint take ICCollnt of the costs to Chlrlic if

the

-----------~--~-~

[xlIeiits exist All llId Belly Illay Ilot tLltlC CVCll thollgh the

bendts lXCCld tlte sociallliarglllal costs

market would SCelll~()(IIICC ctticicllt outshy~- ~-s~~-~l~opert l~lgTt~-IllI~hv ~

--j--~- _--_ --------- - _shytCOllOIlIIC Igcllt illcllltliics ((11- dlld Jmcirs r IllS tlllilil) he

obtlillS the full bClldits Illd PIVS the fidl cost of his llllvlty

Consider thl lII kllO1I os ufthe trlgcdy olthe COIIIIIIOIIS such IS tisheris 1 MI1lY lisheries Irolllld till ~orid liT overtished result

illg ill ] deplctioll oftocks No it would IlroJlblv be to the belletit

of fishlr1l1llI Alf to rnlucl his each llext year it If( lIld h1 (IIilIIl lt lt)hlllillillI 111 lite liilre IIIs r(dll(1d rield Ihis ltlir But hl call1lot if lktty lIId CiJlrlic lish IIIYWI

the stocks will still 1)( dlpktn AII will hwc plid I cost but wlil llot

g1111 lhl full bllIdts orbis rcstLlillt COllvl1sciy Betty Illd Charlie do

lIot pay the full costs of their overllshlllg sillce the costs of Ire trallsi(rnd to other tlshermcll slich ]S Alf Thlls the fisherics 11(

lIld the IIl1rgill1I socid costs lxcecd till lI]1rgill11 bell efi tgt

A schellll tklt illllrnliI7ld III costs lIld bendit -~-u-fJ~~-T the probklli Cltllme we hIVl this

IWClllSl p1llperty rights OHT iish in the onI11 Ire (lItticult to

probll1I1

tiollllizl (tlsh tllId to swilll IWlllld I

I-OVlVer thl ide11 of] SystlllI or property rights th]t illtlr1]lhzcs

benciit Ind cols is lIllre1Iizlblc II II less we restnct vhat Ullints IS 11

l~tlrtli1ity Think abollt SUIs case ofMr Prlldes alld Mr laclviouss

abollt rladillg Lad) L11lIIcrlC(S LtlllT If Mr LISliviom extrLilS 1m ngln l1ld rC1ds till hook thnl is all Mr Prude IS 11ll(k or on~ SIIKl Mr Prude prlill tllal 110 olle

rcads it to Mr Lasclviolls rcldillg it Mr LlscivlOliS It] lJlgltivdy

impactcd the utility fUllctiol1 of Mr Prude If people havc prCflrllHes over thell extlrI1alillcs will hl tVtlYhl~

-- - AlfprdlTs tlw people shop at farget tT WI-Mlrt if

so every tLlIlSlctlOI1 at Wal-Mart involves a Ilegtivl

85

EFFICIENCYCHAPTER 3

be said to illlpose recogniznl social costs 011 OtlHTS whcn certain interests which ought to be considered

One possible solution to this difficulty might be called the r(lllsshy

liascd 1011111011 to which Alfs actioll h~ls a negative external-Betty if and only if it violates a right of lkttys Rights we

i1llpinging Oil Ihose

individual The rightsshyconstitutes cost who was especially based solution to other ttlr every

to otherscost they Impose upon dont like Mill fiOI11 performing lctions that their

should~lrgued that slich costs should be ignored md set back

as rights 1(

Thus says

lIltliction OIl thC1ll or lilY loss tllsdlOOd or

unfJir or ungencrous usc of

over them even eHish abstincncc frolll dd(lldshy

injury---these arc lit of morallIlg them ill grave cases of ll10ral retribution andreprobatioll

1 17PUIlIS 1ll1ellt

The idea then is that we identity a crucial set of intellt~ (or sets of prefercnces over certain aspccts of ollr lite) and hold that if an action or transaction imposes costs 011 other parties ill tenm of tliese I)cirshyCII(CS the action or transaction has a sorill cost rights h]ve heel]

That the lCtiOl1 involves a s(lei11 cost doe not show that it

should be [)fohibited since the social bcnefits Illay still OlltWllgh tht

costs I K

This results in I 1l1Oralistic knuw which subscts of a persons prdcrcJlces are rights bd(lrc we elll know what constitutes all eHlUlnt level of lCtivity It IS Mill el1lphltiCllly lrgucd 110 one has l right that others dont read (rather thaIl reael) books onc tlnds offensive Mr Prude incur 110 cost when Mr Lasciviolls reads Lady CIIil I IcrC) s LOFershythere is no externality became IlO right was viobted There arc

real worries about this moralistic view For Olle it dots not make sense of a core argument of most liberal political econol1lists

viz that we should evaluate systellls of ri~hts ill terllls of their efficiency-promoting characteristics If we are to say that property rights promote eftlciellcy we must be able to first what an efficiellt level of production would be ami then show that

Jre apt to result ill this level But to solution we must know what our property and other we call identify externalities and so etTiciellt outshy

cOllles Say that Alf vallts to build a LlvenJ on his land and objects What is the eHlcient outcollle If Alf has the 011 his side thell the efficiellt outcome is that he builds it if Betty Ius the rights Oil her side she h1s J right not to have her property v~lllles

lowered by living Ilext to a tavern-then the et11cicllt outcome is that the tavern is Ilot built Ifboth have rihts then we must still sOInellOw

up the costs and benefits Ronald Coase proposes

view on Coases view lChievillg all etlitient outcome does not depend Oil thl way that the illiti~]l

Suppose that we live in a world flTe of trmsactioll and l)~lrgallllllg costs and in this world Alf has a flCtory that produces vhatchacallits tint generates smoke as a by-produlmiddott suppose that Betty has a lll1ndry llId

her costs Ire increased because of the Slllokl frolll Alfs tactory Alls products a ncg]tiw externality So if Alf produccs

whatchlcl11its up to the point whlTl hi lllarginal costs equal his nLlrshytoo many whatchacallit~ will bc produced Suppose that

per year Betty presently earns $24000 fIolH her but she would make $3 L()O() if Alfs sllloke didllt illne~N

her costs AlL theil Ill

against pollutioll we call still achieve Pareto ctllClcncy Iktty em pay Alf$()(JJ to stop producing whatchlcIllits he will be hetter otralld so will she so thc 11IOC is Pareto-superior

It is importallt that Coascs theorelll applies rlglrd1ess of how the property rights arc divided betwelll Alf and Betty 1 Pareto outCOllll Gill be reached whether All Ius a right to pollutl or Betty has 1 right that he llot pollute SUPPOSl that Alf is now lllaking $ ](IO()() proshy

whatchacallits while Bettvs llrotlts rCl1)l1l the SlIl1e f2t()()()

has

her $7( J() 1 to rdi-ain from According to theu ill tile IlhsCII(C cr trIISII(filll Inri

costs parlies to 1m WliFit) IPitil exmltllities 11111 (~lln 10 Sllll

alNdtloll lr resollrces I(I(JI(Icss of til( illilitll dislriiJlfliOIl or ropcrl) rllhs

Coases theorem calls into qUlstion olle of the traditional jllstificJtiolls for government regu1JtiolJ In the abselKe of a peJillt schellll of propshyerty rirrhts that internalizes both costs Illd 1)llletiti it has beell widely

8786

~


government is necessJry to re6rulate the l1larket fililure that

nsults from externalities l3ut Coase shows that Illarket trallSlctiollS

em solve the problel1l of externalities and get us outcome (thOtllh the actual costs involved in

precludc

Public Goods

Rebted to the question of extcrnalitie is the special ClC of Public Loods Jr( defllled in tenllS of two charlctnistilmiddots [)irs

Consider clem air I f it

lway tiOIl1 Betty Once tht good is then consulllcrs do not compete fx it everyolle can fi-ccly lise II withollt diminishing the amollllt left ft)r others Suolld we Cl1lllot control the flogt ofbcnditi tiolll plIhhc

lre IollcwlldiJc If a public goud is provided it is

provided f()r all to use If we clean the air cveryolle 1lIS c1cm lir

We canllot exclude those who hlvc llot 11lid their share A pure is one that meets these two conditiolls In most

lIe thus

ship

ecolloillists have disputed the pl1bliclll~S this list The classic textbook example of

warns all

the

evny itllll Oll

was typiCllly a

who lild not l1lY fill

next

tend to be

1Ild it

but the crux of the explanation appears (at least at first

Evell if everYOlle prdtTS having the public good to lIot having it each of us will reccive it [()l trct if S()llleOlle else pays It)r it After all the belldirs are nonexcludahle if ~lIlyone gets the

So we typically have an incentive to

pays holds back from p~lying

Thus t1w classic public good argumellt is fllr state action to fix the markets failure to generate efficient outcomes In the interests of

it is ottell said goveml11lllt Illust require everyone to

cOlltribute to the nroduction of sHch [oods While DowtTtill the

argument is not quite IS as it seelllS Three must be lIlind

For lll goods argulllent f()r sLlte action it Illust that evervone wants the lood hut that in

everyolle VlIlts the

I)r it to not hiIlg It

~ It is not the case tlut 1lllrhts lllVlT

so dlicilIltlv Suppose A1t golt wanden illtu

llls hcrvcggics lilt Blttys dog walldlls illto Ales property

his go]t 0 thlt it dOl lint gIVe 11l1lk I A [tllce would he J

ASSUllll thlt clCh would bcnefit hy would he hltln orfhllilliJllr till fellCt llolle thall lIot

tlut till other budd 1) the ()tlln

lleithlr build III meh a case SillCl lleh would prdir to pay I()r the (IHire good r1Il1er thall do virhout it the puhlic goud will be provided (lIld we sh1I1 SCl

SCttioll -+J Ollt PlOIl will pay t(lI rhl llItire good) IwviU)11 uf

do lIotlonstitlitc I llllrkct tlilurc ulltil we add ttlltlwl conditIOns such as rlLlt IJO Olle illdividuds utilitv ftlllclioll is sudl thlt It is rltiOIld tllr hllll to

leveLmiddot tilere In a Illllllhn of pl0lll (SO caell IS temptcd to

or we dn llot kllow how IlIIIlY IllOples lOOPlTllioll is

lllccssary to s((llre the good) ell As thl Illllllber ofilldIVidu11 ill(llnd IllcrlISlS the Illcd fill St)lllC sort off(l1lll11

lbollt dlocltioll of C(1lI tri hu tiolls bl(()Jlll IHCla rv

per SC but fluhlll that

lHlIllhlr ofagellts thar arc IHost Ilkllv no hy the Imrkct

) WI1lthlT puhlic good wdl he volulltlrily sllpplild alld whtthn

llllivcrsd nmtrihul()11 1S lttiulllt also deplluls 011 the nlatioll

thc goods alld individual cOlltributioll We c1l] l1htllll1I1h three hasic types of rtbtiollS

1 COlisali Rellrt1s It ( is til( totll allloullt or ill( llld ( is rhl u)lltrihutioll of allY illdividual

88 89

CHAPTER 3

then G G I + + + Gil Each individual adds to the amount of the

here is picking IIp aHer your in a public park each persons cOlltributioll helps secure the good of J clean park where 111 call walk vithOl1t feaL

b J11Ycslwld Ilt Ihc Ttl] If C is the totll amount of the and C is the contribution of mv

individual i then there exists some perSOJl k slIch

that C GI + + (1 + e (CI C2 + + + (1 + The cOlltrihutioll of individual k and those iho ttl110w her add nothing to the lmOllllt of

secured Suppose that ve all support a candidate fJr office lIld she needs 1O()()O signltlJreS to get 011 the ballot After she has obtained 1O()()O vil1id signatures additional signJtures do hef 110 good (It least fiolll a

do lIot help her get on the bll1ot

c nmsllOld III the Bottoili If C is the total illlJOUllt of the good produced and (j is the contribution of any individuill i thell there exists sOlne person k such that

2 + C l G 0 but (I + C 2 + (1 + C gt O Until the contlibution of indivlduJ k is no public good i achieved Again think of our

candidate until the 1OOOOth sih1li1ture is obt1inld no good i1t all is produced

We em identify both purl and mixed CISlS

that combine these types) We might have good that constant retllrns up to a top tllresllolll Nit tl1tn 110

more returns thereafier or which has a bottow threshold lIld COilmiddot

stant returns thereatter Illd so on Consider three interesting rasts (i) a simple case of constant returns (ii) 1 threshold at the bottom whefe the k person is also the II or last person 1I1d (iii) a case of cOllStant returns lip to a threshold at the top Will the good be provided each person maxi]l1izinl her own lltilitv or is sOllle sort of coordishynation or

(i) I silllple ((ISC (f WISllllit reflmls [n the case of COIltl11t returns each individual contribution seClIfe a bTelter level of the t)Ublic lood So AWs actioll seeuns some of the good he will incur some costs but since he NillltS the good he also secures some benefit fi0111 his contribution u(b) The

90

JII

EFFICIENCY

is that while Alfs p(() is the total costs of his share of producing the good his benefits tJ(b) are just a slllJII part of the total SOCIa benefits since everyone gallls trom his contribution

the good is nOllexclu(bble and nonrival) As 1 Dtionalecollolllic agent Alfstops contributing when his costs equal the marginal benefits 10 ililll But this will not adequately take account of the over]11 social

his contribution since all others will benefit tlom the

of the good be will provide This is a c1]ssic case where

will be underpnwided bv uncoordinated individual

A threshold at Ihe J01l01II IIICH Ihe k pcrsoll is also the n or IdSf

1)(Tsoli [n tbe second and very speri] case lICY)olles (Olitrihllfioll

ifill( good is to he s((fred (I lt11 All example is 1 crew ofl unless everyone rows the bOlt will not make

the strong current No public good is seclired ulliess everyolll colltributcs-tbe public good of reaching the destinatioll will not be achieved lIllless everyone does her Here in In illtcrestin( case whnc the public good is apt to he Khieved purely volulltary choices based silllply on individual utility maximization since no lIldividuill 11Is an incentive to over- or lI11dercolltrihutemiddoti

I (ISe (f(0IlSt1111 retllfllS lip to II tre~101d Ililhe top The third case is

illtaestlllg because here it is illclliciclIl to relluire everyolle to contribute all the tillle SUDDme at Alfs ColleQc there is 1 IaWIl

across from would prefer a nice lawll between the

two buildings to a shoddy Olle But evcryollc dso is inconvenicllced by having to walk all the way around the lILld

the walkways are) Each persoll would preftr having nice lawn alld cuUinl across diagonally I~the shortest route

-to having a nice lawn 1111

using the walkways If everyone Cllts leross the lawn will be

1() out of a 1O() peoplc do so there will be IlO

the threshold ~lt the top after the ()(Jth person

across the ]WI1 no rIlrther public good IS

COl1sider three policies 110 one crosses so we hlve iI beJlItifllllilwn but everyone is

1re

everyone crosses 1oX of the time The

91

cost As tlr lS if WC liT HOIIIO

for choosing between the

(but ifwc aSSU1lle that tlimess is part of the thml is to bc pret(rred see public IlO1iCV bJstd Oil the

EFFICIENCY CHAPTER 3

might even policy h docs) seek to ((111( 11l

frcc-riders (wIth llolicv b 1

stcond and tbird policies art Pareto illlpruvel1llnts Oil the first

Ten people can be 1Ilade better off (they (111 cut across tilt without allY additional costs to othns or tveryollc can be madt better ofF 10 of tbt time the stcond and third policics acbicvc

but at a lower

it

to ullderlnine the basic idel that uSlully

of dliciency doe Iwt necessarily seck to Clllllinlte tht hCIllfits without pping the

level of

None of this i The point is tlutthe stltc should tIX cvnyonc to secure pllblic

of sUtl IctiollWl should lw Iware that the necessity and iIlllllniilll intl-rshyto secure universal contribution is hy no IllllIlS an

thl pursuitence llOI1l the Illere existence of a puhlic good

SUMMARY

I have tried to explain the Ilotion of ettlcilIKY andIn this its rcLltion to rationality Tim ehIDter hls

bull 1)lt1111111 WII) II

ier 11I(J~~illdl rrlliolldllVllSlfllICf lIill (OlSllIlIC iI good l 0 Ihe

ltIlidl Il(r 1II1I(illltl1 ((lsls Wc hIVl a)o

scen that 1 rational producer should produce lip to the point

whert her marginal bCllefits lqud hn

1111) 111101111 (OIlSllIlIers Jlillllldk1 ((lldllg11 Illdl are Ptn1lobull illlprOIJ1lIlCllts The Edglworth Box IS expL1l1lcd

considered the rcLltioll of the contract curve to

Explaillcd tile idell of Pareto superioriry wd PUJctobull COllsidered IlilellieY tlu Pafet) prillciplc is lIililhir ltIS I IIlltlfll iilelllbull

tlH 1I0lhlll 1111 extcrnllif) 1111 ((lIsitiered IIlctl( 1111 id(albull prpcfl) 1((1111 tlwr illlcmllic 111 II( (0111 dlld hCllefls (

92

Ilriil-il) IIlakes s(I( The problclll we saw is that

lllothcr persoll negHively impacts Illy utility and this is not taken Illto ICCOtlllt ill her decision she imposes 1II nternality on

JIlL But if Illy prdirlllces 1Ie about wlut she should lIld should

not do I wdl illlpose an extcrnality Oil l1Ie simply by living her Jill 0 she secs lil This nroblt1Il of adetlllatdv ddillillg all

of the Paretu

bull Sct(J(t II( (gtOd( liI(Of(lII

bull ( olli(I((1 IIMi( yood Imil

ltlaio1l ltllId 1(li)( 0111( (llses 111(11 I 0111 II tl1 1) 11(liOIl lIil s((Ire rliClII

NOTES

Scc Anhur M (raquo)llll 111lil) 1 he

2 NlIIlCd after hlllels (1 -gt11-1 )2()) who depicted IIICfllallC

alJoclti()IlS of resource all pmslhilnics f(lf COlli nets ill this way

1 )I COllI If wc ill lIdmvlllclll dkcts (Stctioll alld Air and

a prltl-nlIcl to klC wh1I Ihcy alrtldy ILlll thcll they 11111

ILHlc We Cll] IIO l1lttlr set why llldowllll1lt dtltlIs worry

-L

he) In the very 1lllrt of

allolative from Plfer()

helHlits IS

Ut 27

socd cosl-bllllilt

93

t

CHAPTER 3

1 Rmsell Hardin makes much of the in thi~ See 1m

illld SmiddotciI) Pl 10-11

of1 Pjnrian LIberal For an

extcnded and ](ccssiblc disclIssion sec Sells amI Y

10 Sell and Rights p 211i

Ibid p 21S

12 See here HllI~llI1Il and McPhersoll FCOIOllli( (IId ivora Ihilos-Pl 71i-7)

1 See DCllnis Mucller IIiMic Choicc 1lI p 25

14 Sec (lITltt Hardin The of the (Olll 11101 IS

S Sec )lvid Schl11idtz Thc LiIIIlIS (f (OIIIIIIIICIII 111 01 the IJlhlic Coods

1( John Stuart Mill OJi 4 PI[1 1

7 Ibid Chapter 4 para 14

11 Ibid Chapter 5 para J

I) Scc ROIL]ld Coase Th ProbleIll of Social Cost

tllliows Muclkr Public Choice Ill pp 27-10

20 The Coasl theorclll Jll he applied to more realistic cases wlllre

activitls have variable costs-the Illore pllrcha~c of

the extclIlalilics SCe MIIlIIl PJlbIC Choicc III

2 ibid pp 1()Il

22 has a Will not

21 But thIS i lot to say that govclIll11clltal COC1civl actlOlI is necessary Sec

J)~tvld ScilIllidtz 1U Lilllis of (WCrJllIU111

~4 Muclkr nice OVLTvicw of tlIe cxtClll III wlmh lIllhvidual 01shy

t1mary dlOins Will seClIrl public goods alld how this result III 111111ershy11IJ1i( Chicc Ill pp IlilT TIll disClISSlOIl that t(Jllows draws ()Il

this part of Mudhr

~5 Sce ibid p 22 But see the of elK tSSULlllCl III SlliOll 4 1

2( Sec David Lyolls Till FOriIS 1IIId Liltllrs ( I JrilildlidllilII PI ()I)n~ 162f1 I havc discussed this case ill mOlT dt1I1 ill Illy SonoIIlli)sopIY PI lli2f

94

4

Game Theory

OVERVIEW

I II our lXamillatioll of utility theory ill Chaptef 2 we f(KlIscd Oil ~] fatiollal agellt as olle who has prc(erellces over outcollles and a sd

of fixed adioll optiOIlS alld who elll correiatl outcollles with lctioll shy

her nrlitnlllTs Olr outCOllllS determined hCf

J wt begall to consider how rational also arc chlracterized by [he ldditionll

interact alld eSplCillly how ration11

economic agellts wil lngal in efficiellt trallsactions 13m the

of rational intLlactioll ill Chaptcr 1 tlKtiSed

moves -middotroulhlv cases in which 1llts interests

of cOI1t1ict We gallls -a glIltTll tl1lOry of what

other ratioml aglnts lI1d especially whtn wh1t is best for not be best Jr AIr In this Chlptlr I Lmploy ollly the gellnal idea of individuals as utility lllaxillJizers the specific additional features thlt

are nquirld fiJr HOIII wllollliOlS are not cClltral to this

(Again we Slt hy it is Sll illlportlllt to distmguish [01110 ftollolllims

from rltiOllal utility maximizers ill The chlpter begins with thc sllllpiest sort of gII11C a zefO-ltlI III

gamc ill which whltevlr one person villS the other lusls This is a game or pllfe ((lllt7ia We then IllOVC on to the f~l1llOUS Irisolllrs

Dilemma and other variable-sulll games -soll1e will bc f()Cuscd

on cOIlt1ict but we will also look at glI11lS in which

will cooperate It ii illlportallt to realize that

95

Total Costs

3[i(C)]

2[1 (c)]

Idc)

utility tmnefits

CHAPTER 3

Number 01

FIG U R E 3-1 Efficient Consumption where (b) m middotn

Total Benefits

I(b)

I I (b) + [I (b)

II(b)

It will be rational f()r Air to COllSUllle two slices if the utility benefits of two slices is greater thall or equal to the utility costs or two slices~

+ 111(1)-111 21f1(r)l Because the costs are constant benefits arc decreasillg at S011le point it will be the Glse that

or as ecollomists say Illarginal (utility) benefIts that frolll sOllle slice of pizza will be less thall the marginal (utility)

costs he had to iucur ill order to get thlt slice 111 that else it would be irrationll for Homo h((lllolllims to COIlSUIlIl that additional slice of

because the preferellces he then would be satisf)llng an ranked below the prdlrellces he is fillmiddotgoing Figure 3-1 is a graphic repre sentation of a specific example of this simple choice problelll 011 the

left vertiCll axis we measure HOlllo lrollollliwss total utility costs while Oil the right vertical axis we llIeaSLIre his total utility Figure 3-1 it is rational ftlr Olll (01101111015 to purchase three slices of pizza (but no

Homo Erollolllims will conslIme up to the point whtre 1I1Il~~illill bCll~its eqllal lIIil~~illll (os This is olle definitioll of efllciency 1101110

chooses in this way not because ht values more th1I1 a ratiollal actor seeks to IIIltlximize utility

this decisi()ll is simply required rationality To choose any other

74

r

+ [JI(b)-m]

but the

benefits In

EFFICIENCY

Chicken wings for All

4 I 10

Pi128 lor 2 Betty

o I)

Chicken wings for

FIG U R E 3-2 A Simple Edgeworth Box

would be to choose a lowermiddot of course is the essellce of

over 1

is sil1lply

Pizza for AI

There is thcll a clOSt rebtioll betweell etlicicllcy and ratiollal choice to be ntionll is just to choose ill a WJY tlllt hest satistlls 01lts

as sitllations in

Chapter 4 when rationality and dli(illlcy break Ipart III many of these cases we are 1IIKLTt1II1)lIst what i the truly rational to do

that II1cans that the lIIarlinal glillS lre at least

great as the

Efficiency and Rational Exchange

Let liS 1l10Ve to a two-person case Wl will rLprCSl1lt the ell oice problelll in terms of indiHlrence curves plot olles preferences over bundles ofgoods

rates ofsubstitution between thelll (Sectioll 13 poillt Alf has four slices of pizza ~Ild Betty has eight BulEtlo chicken wings And suppose that they have pretty Illllch the sallie preferences over

which it will be dClTelsing

alld chicken so that their indiftircIIlT curves are the sallle Figure 1-2 gives their indifference llIaps Bettys (solid)

indifference curves start in the lower left Alfs curves COllle down from the upper right SllppOSC that ill this worth Box 2 Alf lI1d Betty arc at Doint PI AII has Illlir slices of plzza

and 110 wings while Betty has

75

CHAPTER 3
























76

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