Handbook of Mathematical Economics, Volume 2 (Handbooks in Economics) PDF
Preview Handbook of Mathematical Economics, Volume 2 (Handbooks in Economics)
INTRODUCTION TO THE SERIES Thea imo f tHahned booiknsE conomisces riiests op roduHcaen dboofkosr variboruasn cohfee cs onomeiaccsoh,fw hicihsa d efinsiotuirvcee , reference, andt eachsiunpgp lefmoerun ste b yp rofessional anrdea sdevaarnccheedr s graduastteu deEnatcsHh.a ndboporko visdeelsf -cosnutravioenftye hsdce u rrent staotfea branocfhe conomiintc hsfe o romf c haptperresp abryel de ading spieacliosntv sa rioaussp ecotfts h ibsr ancohfe conomTihcess.se u rveys sumamrinzoeot nlrye ceirveesdub luttas l snoe wer develforpormmee cnetnst, journaarlt iacnlded si scuspsaipoenr s.o rSiogimnmeaa lt eriisaa llsi on cluded, butt hme aigno ailst op rovicdoem preheannsdai cvcee sssiubrlveeT yhse. Handboaorkesi ntentdoep dr ovindoeto nluys efruelf erveonlcuem feosr prosfieosncaoll lecbtuitao lnspsoo ssisbulpep lementarfyo arrd evaadnicnegds courfsoegrsr adusattued einnet cso nomics. CONTENTS OF THE HANDBOOK VOLUME I HistoIrnitcraold uction Par1t -MATHEMATIMCEATLH ODSI NE CONOMICS CluJpt1 er MathemaAntailcyaslai nsdC onvexwiittyAh p plicattoEi coonnso mics JERRY GREEN andWA LTER P.H ELLER Chapte2 r MathemaPtriocgarla mwmiitnAhgp pilcatitooEn cso nomics MICHAEL D. INTRILIGATOR Chapte3 r DynamiScyaslt ewmistA hp plicattoEi coonnso mics HAL R.V ARIAN CluJpt4 er ContTrhoelo wriyt Ahp plicattoEi coonnso mics DAVID KENDRICK Chapte5 r MeasuTrhee owriyt Ahp plicattoEi coonnso mics ALAN P.K IRMAN Chapte6 r TheE conomoifUc nsc ertaSienlteycT:to epdia cnsdP robbialiMsettihco ds STEVEN A.L IPPMAN andJ OHN J.M cCALL Chapte7 r GameT heoMroyd ealnsd M ethoidnPs o litEiccoanlo my MARTIN SHUBIK Chapte8 r GlobAanla lyasnidEs c onomics STEVES MALE Conteonftt hsHe a ndbook viii VOLUME II Par2t- MATHEMATICAALP PROACHTEOSM ICROECONOMIC THEORY Chapter 9 ConsumTehre ory .. ANTON P.B ARTEN andVO LKER BOHM Chapter 10 ProducTehreosr y M. ISHAQN ADIRI Chapter 11 OligoTphoeloyr y JAMES W. FRIEDMAN Chapter 12 DualAiptpyr oatcohM eisc roecoTnhoemoircy W. E.D IEWERT Chapter 13 Ont hMei croecoTnhoemoiorcfyI nvestumnedneUtrn certainty ROBERT C.M,E RTON Chapter 14 Market DeamnadEn xdc eDsesm anFdu nctions WAYNE SHAFER andHU GO SONNENSCHEIN 3 Part- MATHEMATICAALPP ROACHEST O COMPETITIVE EQUILIBRIUM Chapter 15 ExistoefnC coem petitive Equilibrium GERARD DEBREU Chapter 16 Stability FRANK HAHN Chapter 17 RegulEacro nomies EGBERT DIERKER Chapter 18 Coroefa nE conomy WERNER HILDENBRAND Conteonftt hHsea ndbook ix Chapter 19 TemporGaernye rEaqlu ilibrium Theory JEAN-MICHELG RANDMONT Chapter 20 EquiliubnrdieuUrmn certainty ROYRADNER Chapter 21 TheC omputaotfiE oqnu ilibPrriiucAmen sE :x position HERBERT E.S CARF VOLUME III Par4t- MATHEMATICAALP PROACHETSO W ELFAREE CONOMICS Chapter 22 SociCahlo iTchee ory AMARTYA SEN Chapter 23 Infoartmiaonndt hMea rket KENNETH J.A RROW Chapter 24 TheT heoorfyO ptimal Taxation J.A .M IRRLEES Chapter 25 PosiSteivceo nd-TBheesotr y EYTA N SHESHINSKI Chapter 26 OptimEaclo nomGirco watnhd T urnpTihkeeo rems LIONELW . McKENZIE Par5t -MATHEMATICAALP PROACHEST OE CONOMIC ORGANIZATIAONND PLANNING Chapter 27 OrganizDaetsiiognn THOMAS A.M ARSCHAK Chapter 28 IncienvAtes peoctfDs e centralization LEONIDH URWICZ Chapter 29 Planning GEOFFREY HEAL PREFACE TO THE HANDBOOK The fieolfmd athemateiccoanlo mics Matehmatieccaoln omiinccsl uvdaersia opupsl icoatfmi aotnhse mactoinccaelp ts andt echnitqoue ecso nompiacrst,i cuelcaornloymt ihce oTrhyi.bs r anocfh econotmircasci etossr igbiancstk ot heea rnliyn eteceenntthua rsny o,t eidnt he histoirnitcraold ubcutitith o ands,e veloped reaxptiridenrlm eyec leydn etc ades andi sc ontintuodi ons goM .a nye conomhiasvtdesi scovtehratethd le a nguage antd ooolfms a themaatrieecx st repmreoldyu citnti hvfeeu rtdheevre lopomfe nt eocnomtihce oSriym.u ltanmeaounsyml ayt,h emathiacvideai nssc ovtehraetd mathaetmiceaclo nomtihce oprryo viadnei sm portaanndit n tereasrteoiafn g appliicoaontf t hemiart hemastkiicalanllds t haetc onomhiacsgs i vreni steo somiem portnaenwmt a thematicals upcrahosg b almetemh se,o ry. Purpose The HandboookfM athematiEccaoln omiacism tsop roviad dee finsiotuirvcee , referaenndtc eea,c hsiunpgp lefmoetrnh tfe i eolfmd a theimcaaetlc onomIitc s. surveaysso ,ft hlea t1e9 70t'hsse,t aotfet haer otf m athemaetciocnaolm ics. Beariinnm gi ntdh atth ifsi eilscd o nstadnetvleyl otphiEend gi,t boerlsi tehvaet nowi sa no pporttuinmteeo t akset ocsku,m maribzoitrnhge ceirveesdua lntds newdeer velopmTehnuatsls al.u thwoerrsie n vittore edv iaenwdt oa ppratihsee cruresntta taunsdr ecednetv elopimnet nhtepsir re sentIanta idodnistt.ioi o tns use ar aesf eretnhEcede i,t hoorpste h atth iHsa ndbowoikla ls sriesste archers and stuwdoernktiisnn og n eb ranocfhm athemaetciocnaolm tiocb se come acquaiwnittoehtd h berra ncohfet sh ifsi eEladc.oh f t hceh aptcearnbs e r ead inpdeendently. Organization The Handboionkc lu2d9ce hsa ptoenvr asr itooupsii cnms a themaetciocnaolm icasr,r anignetfdoi vpea rtPasr:It t reaMattsh ematiMceatlh odsi nE conomics, icnludrienvgi oefwt shc eo nceapntdts e chnitqhuahetas v bee emno suts effuolr Prefatcote h Hea ndbook XJ1 them athematdiecvaell opomfee ncto nomtihce orPayr.t2 elaboroant es Mathematical ApptrooM aicchreose conoTmhieco ryi, nclucdoinnsgu mperro, duceorl,i gopaonlddy u,a ltihteyo Prayr.t3 treaMattsh ematical Apptroo aches CompetitEiqvuei libriinumc,l usduicnahgs peocftc so mpetietqiuviel iabsr ium existsetnacbe,iu lnicteyr,t atihcneot myp,u taotfei qouni lipbrriicuaemns dt, h e coroefa ne conoPmayr.4t coveMratsh ematiAcpaplr oacthoeW se lfarEec onom icsi,n clusdoicnigca hlo itchee oorpyt,i mtaalx atainodno ,p timeaclo nomic growtPahr.t5 t reaMattsh ematiAcpaplr oachteoEs c onomiOcr ganizaatnido n Planniingn,c luodrignagn izdaetsiiaognnndd ecentralization. Level Alolf t hteo pipcrse seanrtteer de aattae dna dvanlceevdse uli,t afboulrse be y economainsdmt ast hematwiocrikaininsntg h fei eolrbd ya dvanced graduate studeinnbt ost ehc onomaincdms a thematics. Acknowledgements Ourp rincaicpkanlo wledgaermteeo tn htaesu thoofrc sh aptientr hsHe a ndbook ofM athema[iEccaoln omiwcsh,on ootn lpyr epatrheedoi wrn c haptbeuratsl so proviaddevdio cnte h oer ganizaantdci oonnt oefnt thH ea ndboaonkdr eviewed othcehra pters. KENNETH ARROW J. StaonrfUdn iversity MICHAEL D.I NTRILIGATOR UniverosfCi atyl ifoLrnoiAsa,n geles Chpater 9 CONSUMER THEORY* ANTONP .B ART EN C.O..a Rn.CdEa thUonliisvcyieo trfL ouvBaeilng,i um and VOLKEBRO HMt UnisvieMtraiintn hFeeidRm.e, pG .e rmany Introduction 1. Thmea ionbe jctoifcvo en stuhmeeiortsr od y e tetrhmieim npoean oc bts ervable demafnocdros m moodafil ttieernasas tsiuvmoepnt t hioeobe jncsta invodent s h e beharviuoloreftas hcl eo nsaunmodent r h,ce o nstwrhiachihefn atcse s when makaid negc iTshtiero and.mi otdioeoftln h ael consumero vteark es preferences alterbnuantdtilodve eess ctrhoiejbb ceet iIvtbeses h.a vriuoclroean lso ifs ts mamxiizaotfi otpnhr eesfeeu rnednebcrue dsrag e estt wrhiiccdhte itoenr mines thter adpionsgs iTbhipelr iitnirceeissp.oua fltl th tseh ecoornyos fit shte qualiimtpaltiiocvnoae bt sieodrnevsme aodncf dh anignte hpsea ramwehtiecrhs detetrhmdeie nceio sfti hcoeon n sumer. Thhies todreivcealloo fpc moennsttuh meeiornr dyi acl aottnergsa doift ion intoeefrc eomsnitosi tnts hs eue bcjwthi,ch hau sn dersguobnsetc aonntcieaplt ual chaonvgteeisrtm oe rietpasrc efhso erAn mdt.e tasiulroveifedth y si sctaobnre y fouinKnd a tz(n17e09.r) *Wew oudl liket htaonA kn guDse atoMni,c haIenlt rilAingdarteoMura ,s -CoalnedlH lu,g o . Sonnensfcohvrea ilnu asbulgeg esatnidcor nist iOcfic somu.rw seeb ,e atrh seo lree sponsfiobarin lyi ty reamininegr r.o rs t Parotfts h piasp weerr wer itwtheinVl oel kBeorh mw asa tt hCee ntfeorOr p eratRieosnesaa rncdh Economeatnrdai ctts h Ueni versLiitbedr eeB ruxleelFsi.n anscuipapluo nrdt eFro rFdo undation Grannot7. 7 /0502i2sg r ateafcuklnlloyew dged. HanbdoookfM athemaEtcoincoacmlsi v,o l.e dibtye dA rrowa nMd. DI.nt riligator II, K.J. North-HoPlulbsalhniidCn ogm pany, © 1982 382 A.P. BaanrV.dt B eonh m Commodiatnidpe rsi ces 2. Commodciabtnedi ievsii ndgteoodo adnssd e ircvEeascc.ho mmoidcsio tmy plestpeelcbyiy if tpishe ydsc ihcaarla cittlesor ciaastntdidiao catnswte,,h iiciths avabilIlensa. t udbieehsa uvonifduo enrrc eratnaa didnitstypi eocniaoflfi cation thceh aracotafce ormimsotrdieiclttsayto t h isent ga te oocfc umnraarbytie un rge add[esAder er (o15w39 a)nD de b(r9e15u9w )h]il,ceh a dsd etsoc rotifahp et ion conticnogmemnoWtdi itsthuy ca.hne xtednesfiivonefai c toimomno tdhiet y theootfr hcyeo nssuumbesrau lmmloe rssep etchiefooircfcio enssc uhmoeoirfc e locattiroanod fiea n,nt de rtcehmoopivoctereira ma len o,df caesrptoeafci tns thteh eoofdr eyc iusnidouennrsc erFtoarimntathlyeal.sry eee q uitvT.ah lee n tradittheioornyaa lsu ssutumhaealstle yxt iahs ettfrsneieu n mibeoe cfro mmodi tiiemsp ltyhianftgi nsaip teec ioffpi hcyastciaihcroaanlc tleorciasetttiicoc.ns ,, sufficperso bfsloterum dQstui haeend ot.efi a tcciohem sm oadrmieet ays buyr ed renaulbm erAsc o.mm odibtuyn dlie,.a el .io sfrt e naulm b(ehx)rh,s= 1 .,,.e ,. inditchaqetu iannogtf ei atccyho mmocdaibnted y e,s ctrhiebreaedsf oarne e-dimevnescitoonra le) a nads p oai innet - dimeEnusciloindaela n e X= ( X1 ,.0 0, X spaRc,te h e Under perfoefacl ctlo mdmiovadinisyti ibeisl ity commodity space. renaulm ibser ip baolsseq s uaa nftoeirat ccyoh m modtihatanyty spoto hien t of e commosdpiaRtciyeas p ossciobmlmeob duintTdyhlf eei .ns ipteec ioffi cation thneu mbocefro mmoedxictlituerdsee asot sfmi etnutia wnth iicochnhast r earcis timcas�yr a cyo ntinSuusocihut sulaayrt.iii anson ena stw uarfyao,elr x amipnl e, thceo ntext ofo fcq oumamloidatinyitd nit c ehchseoo, ni tcoeeflx otc ation theorrye dawilhs etonana n cseui rtsfh aaepc per ocprriitAaestrr eei gotanhr.ed s tismpee cioffic coamtmioodenia tcmihoe dwsei,lta hni nfitnihimtoeer izon, whetihdnei rs ccroenttei tnoiurrmo eeuq,su al i arrecgsoe mrm osdpiaTtchsyeii .s altshcoea fsoer mooufdn eclesrw tiastiuhnf tfyid ciiseprneatrnlsdeyeov dme nts. Thessiet ulaetiaindao nsn atutrota hlse t wuoadfiyy n fidniimteen sional commosdpiattcyae ksae svn e cstpoaroc veteshr re e aAlpsp.l iccaabnte i ons fouinnGd a bsz(e16w89ia)cn zBd e w(l9e17y10 7,92 w)i,ta nhi nterpretation regatridaminenud gn cerMtaasil-neC(tlo17yl59.c ) o ntaanai nnaslo yqfsu iasl ity diftfiearAtesinf oaanrst. ht eh eotrhyce o onfsi ucsmo enrc mearnnoyeft d h e usuraelso uftl httesr aditthieioonanr ayfl di inmietnecs oimomnoasdlpi atcye cabnee xtetntodh ieend f diinmietnecs aiTsohensi.aus lr r veesyti rttistcoehtl esf findiitmee ncsaisoen.a l Thper icPeh o fa c ommohdh,i= lt.y,,.e i.,as r aeln umbwehrii ctshh e amopuandinit e xchfaoonrngu een o itfth e coWmimttohhde i tsyp.eo cfi fication locaatniddoa ntth ete h euosruya llyt hgaees nsecuromanelvs et nhttaihtoe n priocfael cslo mmoadriteth ioqesuseo n toeowdnt hfel oooftr he ex chfaonrg e deliavtde irfyf leorceanattni adot dn isf fdearteIentist cs. el rat hoatth er conveonrct oinosntsra urpceoti sibsaolnnemds e aniAnp grfisucyles.o t re ma Ch.C onsuTmheerory 383 9: privceecp t= o(pr 1,• ,•Pe )•c a tnh buesr eprebsyaep n otiienndEt u clidean space R•1T hvea lofuac eo mmobduintgdyil veae p nr ivceecp tio""isr=� !hpxh= p·x. 3.C onsumers Sombeu ndolfe cst ohmem osdpiatacyree ex clausd ecdo nspuomspstiiboinl ities foarc onsubmype hry soirlc oaglri ecsatlr Tihcset eiotofa n lcslo. n sumption bundwlheisac rhpe o ssiiscb alletl hecedo npstuismoeTnth .ii ssa non-empty subosfe tct ohmem osdpiatdcyee n,o teTdr abdyi tiinopniuanctl osln ys,u mp X. tiaorne debsypc orsiiqbtueiadvn eta inotdui tepsbu ynt esg aqtuiavnetT ihtiise s. ipmliienps a,r titchuaalltlal ar bc,oo rm ponoefacn otnss umbputnidxoal nre e non-poOsniet iuvasesu.sa ultmlhyeta shtc e o nsumspeXtti i csol no csoendv,e x, and boundtehldeo wbbeeorlu bonewd,i j nuigsf tibeyfd i nciotnes tornta hien ts amouonflt a baoc ro nsuimsae brlt eop erfAo rcmo.n sumer mau st choose bunfdrloehm ic so nsumspettoi roidnne e rx itsot . Givtehnse i cgonn veonnit nipoaunnt odsu tpaunatdp s r ivceecp tt,oh rve a lue xo fa b undxEl eXi nditchanete eotsua t,yil .eex.p enserse ctmesii,np us p · assocwiiatthe dt hxe.S i bnutcnhecde ol nes uimsce orn sitdote rraeiddnae markheitcs,h oiacrefesu rtrheesrt rbiytc htee dtf haatcthtv e a loufe his consumsphtoinuoolentdx cheieisdn iwteiaa(lloti rhn comem)a.by e gT ihviesn toh iimn ftohroemfa .f ixneodn -nenguamtbwie.Hvre em aya loswoan f ixed e vecotfio nri tial arv eescootftuo hrrcec o emsm osdpiatc.yIe nt hRlea tter case w, hiisn iwteiagaliltva hep n r ivceecp ti odsre fianswe= pd Thsee otfp ossible ·w . constuimopn bwuhnodvslaeel dsuo een so etx cetehiden itiaolf t hwee alth consiucmsae lrtl hebedu dsgeaetntid ds e fibnye d ,B(pw), ={ x EXpI·x�w}. (.31) Thuel timatoefa c doencsiutsmocie horon o bsuen fdarl oetm hc eo nsumption set doenph eitnsad ssat neddse siTrheeassr.ere e prebsyehi nspt rfeeedr ence raetli;:o:,wn hi icsah b inarreyl aotni oFno arn tyw bou ndxla ensyd , X. xE X,E yX, xm::ea:tnyhs xa i tas lt e aassgto oadys G .i vtehnpe r efetrheen ces conscuhmoeorams oespstr efbeurnrinde ldhe bi usd sgeeatts dhmeiasnT dhi.iss defianse d cpp(w, = ){ x ,B(Ep w,)I x E',8 (p w,)i m plxi::xe:o'sr xn::'ox:t.} (.32) Mucohf c onsutmheeroi rnpy a,r titchueela arrcl ioenrt ridbeustciroinbse, consubmeehra avsio onroe f u timlaixtiym irzaattthiheoaronn f p reference maxziamtiHiiosnt.o trhiehcraabesle leayn ldoenbgwa hteet thhweeer l l-obfe ing 384 A.P .B aratnednB oV.h m ani ndivciadbnue ma ela subryse odmr ee vaall fuuendc .Tt hireoe nlationship betwteheetnsw aeop prohaacbshe eessnt udeixetde nasfittvehefreli ryri sgto rous axiomianttirco douftc htei oconof anp creepfter reelnabctyFei r oin(s9 1c2hI6 t) . habse esnh otwhnat thn eo tiooftn hp er eferreelnacitesti homeno rbea sic concoefcp otn sumewrh tiihctsehh o errye,f orteh et askpteoanior nftata in sny g analycsoinss ubomefeh ra vTihoerr e.l atitootn hsceho inpco efap u tt ility functhioowne,va esr c,oa n venieonrta sa dnee qvuiicveaa plpernottao c h desccroinbseub meehra vcioonrs,ta im taujteoelrse moeftn htfe o duantioofn s consutmheeroT rhfyeo. l loawnianltgyh seirsie dsfi ovriebd aesdi icnattlwolo y parTthsef. i rpsatrS te,c t4i-od9nes,a wlistt hha ex iomfaotuincd aotfi ons prefetrheenaocnreudy t itlhietaoynr wdyi tthhe ex isatnebdna cseci ocn tinuity resoufcl otnss udmeemraT nhdse.e cpoanrdSt e,c t1i0o1-n5psr, e stehmneot rse classicoafdl e mratenhsdeu molartiysin nlt yhc eo ntoefdx itf ferdeenmtainadb le functions. 4. Preferences Among alctoemrnmaotbdiuivntedyi l nte hsce o nsumspetti,o nt he consumer is assutmoe dhp arveef erreepnrceebssyea bn itnerader lya ::t::,i Xoon.Fn o trw o bundxla ensdi ynX t hset atexm::e:inyrst e aads" xiaslt e agsotao ysda". s Thrbeaesa ixci aormuess uailmlpyoo snte hdpe r eferreelnawctheii aocrnohe f ten takaesnd eaf inoifart aitoinco onnasl.u mer Axi1o (mRe flexivity) Foarlx El X,x ::x:,i. aen.byu nidalsse g ooads itself. Axi2o( Tmr ansitivity) For tahnrbyeu en dxly,e,z si nX s uchx ::t:ahynayd t;:z i tt ritushe xa ::tz: . Axi3o( Cmo mpleteness) Foarn tyw bou ndlaensdi ynXx ,x :: :oyyr:: x:. A preferreelnac::te::,wi hoinsc aht itshfeitsehesra exei oimsas c omplete preorodnX ea rnwdii nblgecl a lalp eeredfr ceoenr edrTw.oo threerl actaibnoe n s deriivmemde difartoaemp l rye feorrednecre. a rtTehh ee ser oefls attriiocnt prefe>r aenntdch reee laotfii nodni fference �. Dfeini4.t1i on A bundxil ssea tiobd e s trpircetflteyor abr uendyd ,il e.x >e y . i afn odn liyf x:::aynnd o yt::x :.
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