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2010-2011學年上學期第十三次S1授課教師Lu2010-2011學年上學期第十三次Chapter Twenty-SixFactorMarkets2010-2011學年上學期第十三次ACompetitiveFirm’sInputApurelycompetitivefirmisaprice-takerinitsoutputandinputmarkets.Itbuysadditionalunitsofinputiuntiltheextracostofextraunitexceedstheextrarevenuegeneratedbythatinputunit. MRPi(x*) Forthecompetitivefirmthemarginalrevenueofaunitofinputiis:3i)i32010-2011學年上學期第十三次AMonopolist’sDemandsforWhatifthefirmisamonopolistinitsoutputmarketwhilestillbeingaprice-takerinitsinput(Theotherextremecaseiscalledmonopsony:Asingebuyerwithinfinitesellers)42010-2011學年上學期第十三次AMonopolist’sDemandsSupposethefirmusestwoinputstoproduceasingleoutput.Thefirm’sproductionfunctiony2Sothefirm’sprofit y

252010-2011學年上學期第十三次AMonopolist’sDemandsfory 1,2 y12Theprofit- izinginputlevelsaredeterminedbyw 1 ((w 1

x2 (()y 0.2

62010-2011學年上學期第十三次AMonopolist’sDemandsThatmx*

)

)MP(x)*1 1

mx* )y )MP(x)*2 2

d(p(y)y)/dy=MR(y)<pforally>0sothemarginalrevenueproductcurveforamonopolist’sinputislowerforally>0 thanisthemarginalrevenueproductcurveforaperfectlycompetitive 2010-2011學年上學期第十三次AMonopolist’sDemandsfor$/inputpMR(y)MPi(xi i i Themonopolistdemandsfewerinputunitsthan theperfectlycompetitive2010-2011學年上學期第十三次Again,thekeytothischapteristobeabletowritedownthemonopolist’sprofitfunctionWecanusethesameprincipletostudythecaseofmonopsony.92010-2011學年上學期第十三次Chapter Twenty-SevenOligopoly2010-2011學年上學期第十三次AmonopolyisanindustryconsistingasingleAduopolyisanindustryconsistingoftwoAnoligopolyisanindustryconsistingofafewfirms.Particularly,eachfirm’sownpriceoroutputdecisionsaffectitscompetitors’profits.Howdowe yzemarketsinwhichthesupplyingindustryisoligopolistic?Considertheduopolisticcaseoftwofirmssupplying thesameproduct.2010-2011學年上學期第十三次tyAssumethatfirmscompetebychoosingoutputIffirm1producesy1unitsandfirm2producesy2unitsthentotal disy1+y2.Themarketpricewillbep(y1+y2).Thefirms’totalcostfunctionsarec1(y1)and2010-2011學年上學期第十三次tySupposefirm1takesfirm2’soutputlevelchoicey2asgiven.Thenfirm1seesitsprofitfunction 1211Giveny2,whatoutputlevel izesfirm2010-2011學年上學期第十三次tyCompetition;AnSupposethatthemarketinversedemandfunctionisT) 60andthatthefirms’totalcostfunctions y

y)15yy.

2 2010-2011學年上學期第十三次tyCompetition;AnThen,forgiveny2,firm1’sprofitfunction(y;y)(60yyyy So,giveny2,firm1’sprofit- outputlevelsolves 602yy2y

I.e.firm1’sbestresponsetoy2y R(y) 151y 42010-2011學年上學期第十三次tyCompetition;An Firm1’s“reactiony R(y) 15 1y 2010-2011學年上學期第十三次tyCompetition;AnSimilarly,giveny1,firm2’sprofitfunctiony So,giveny1,firm2’sprofit- outputlevelsolves

60

15

4I.e.firm2’sbestresponsetoy14y R(y)

45 2010-2011學年上學期第十三次tyCompetition;AnFirm2’s“reactionyR(y)

45 44 2010-2011學年上學期第十三次tyCompetition;AnAnequilibriumiswheneachfirm’soutputlevelisabestresponsetotheotherfirm’soutputlevel,forthenneitherwantstodeviatefromitsoutputApairofoutputlevels(y1*,y2*)isaCournot-Nashequilibriumif R(y

2010-2011學年上學期第十三次tyCompetition;yy yy

45yy 142*y 142

15

*

*R(y*)

14Substitutefory2*to145 y1* 15y1

4

1y11

13y2 y2

45 14

8SotheCournot-Nashequilibrium(y,y*

138). 2010-2011學年上學期第十三次tyCompetition;

Firm1’s“reaction R(y) 15 1y Firm2’s“reactiony2R2(y1)45y14 2010-2011學年上學期第十三次tyGenerally,givenfirm2’schosenoutputlevely2,firm1’sprofitfunctionis 1211andthe izingvalueofy1

yy)

2)

cy)

1(Thesolution,y1=R1(y2),isfirm1’sNashreactionto 2010-2011學年上學期第十三次tySimilarly,givenfirm1’schosenoutputlevely1,firm2’sprofitfunctionis 12 2andthe izingvalueofy2

yy)

c )

2 Thesolution,y2=R2(y1),isfirm2’sNashreactionto 2010-2011學年上學期第十三次CMPrs“reaction2

2Firm1’s“reaction

y2R2(y1).Cournot-Nashequilibriumy1*=R1(y2*)andy2*=R2(y1*)2010-2011學年上學期第十三次Iso-ProfitForfirm1,aniso-profitcurvecontainsalltheoutputpairs(y1,y2)givingfirm1thesameprofitlevel1.Whatdoiso-profitcurveslook2010-2011學年上學期第十三次Iso-ProfitCurvesforFirmWithy1fixed,firm1’sprofitincreasesasy2decreases.2010-2011學年上學期第十三次Iso-ProfitCurvesforFirmIncreasingprofitforfirm1.Iso-ProfitCurvesforFirm

2010-2011學年上學期第十三次

Q:Firm2choosesy2=y2’.Wherealongtheliney2=y2’istheoutputlevelthatizesfirm1’sprofit?A:Thepointattainingthehighestiso-profitcurveforfirm1.y1’isfirmbestresponsetoy2= Iso-ProfitCurvesforFirm

2010-2011學年上學期第十三次

Q:Firm2choosesy2=y2’.Wherealongtheliney2=y2’istheoutputlevelthatizesfirm1’sprofit?A:Thepointattainingthehighestiso-profitcurveforfirm1.y1’isfirmbestresponsetoy2= Iso-ProfitCurvesforFirm

2010-2011學年上學期第十三次

Firm1’sreactioncurvepassesthroughthe“tops”offirm1’siso-profit 2010-2011學年上學期第十三次Increasingprofitforfirm2.Iso-ProfitCurvesforFirmIncreasingprofitforfirm2.2010-2011學年上學期第十三次Iso-ProfitCurvesforFirmFirm2’sreactioncurvepassesthroughthe“tops”offirm2’siso-profity2=

2010-2011學年上學期第十三次Q:AretheCournot-Nashequilibriumprofitsthelargestthatthefirmscanearnintotal?

(y1*,y2*)istheCournot-NashArethereotheroutputlevelpairs(y1,y2)thatgivehigherprofitstobothfirms?

2010-2011學年上學期第十三次

(y1*,y2*)istheCournot-NashArethereotheroutputlevelpairs(y1,y2)thatgivehigherprofitstobothfirms?

2010-2011學年上學期第十三次

(y1*,y2*)istheCournot-NashArethereotheroutputlevelpairs(y1,y2)thatgivehigherprofitstobothfirms? 2010-2011學年上學期第十三次(y1*,y2*)istheCournot-NashHighery Higher2 2010-2011學年上學期第十三次Higher

Higher

Higher

2010-2011學年上學期第十三次(y1’,y2’)earnshigherprofitsforbothfirmsthan

doesHigher

2010-2011學年上學期第十三次Sothereareprofitincentivesforbothfirms“cooperate”byloweringtheiroutputThisisFirmsthatcolludearesaidtohaveformeda Iffirmsforma ,howshouldtheydo2010-2011學年上學期第十三次Supposethetwofirmswantto izetheirtotalprofitanddivideitbetweenthem.Theirgoalistochoosecooperativelyoutputlevelsy1andy2that m(y,y)

21)22010-2011學年上學期第十三次ThefirmscannotdoworsebycolludingsincetheycancooperativelychoosetheirCournot-NashequilibriumoutputlevelsandsoearntheirCournot-Nashequilibriumprofits.SocollusionmustprovideprofitsatleastaslargeastheirCournot-Nashequilibriumprofits.

Higher

2010-2011學年上學期第十三次(y1’,y2’)earnshigherprofitsforbothfirmsthandoes(y1*,y2*).Higher

Higher

2010-2011學年上學期第十三次(y1’,y2’)earnshigherprofitsforbothfirmsthandoes(y1*,y2*).Higher(y1”,y2”)earnsstillhigherprofitsforbothfirms.

2

2010-2011學年上學期第十三次 izesfirm1’sprofitwhileleavingfirm2’sprofitattheCournot-Nashequilibrium yy1 ~

2010-2011學年上學期第十三次_y

izesfirm1’sprofitwhileleavingfirm2’sprofitattheCournot-Nashequilibrium 22y2yy2y1

izes2’sprofitwhileleavingfirm1’sprofitattheequilibriumlevel._22

2010-2011學年上學期第十三次Thepathofoutputpairsthatizeonefirm’sprofitwhilegivingtheotherfirmatleastitsCNequilibriumprofit.Onetheseoutputpairs izethe ’sjointyy1

2010-2011學年上學期第十三次(y1m,y2m)denotestheoutputlevels izethe ’stotalprofit.y2yy1my 12010-2011學年上學期第十三次Issucha Doesonefirmhaveanincentivetocheatonthe1I.e.iffirm1continuestoproduceymunits,is12 izingforfirm2tocontinuetoproduceymunits?21Firm2’s izingresponsetoy1=ym11y2=R2(y 12010-2011學年上學期第十三次y1=R1(y2),firm1’sreaction1y2=R2(ym)isfirm1bestresponsetoR(y

1choosingy1=y1 y2y2=R2(y1),firmreactiony 12010-2011學年上學期第十三次Firm2’s izingresponsetoy1=

1m112y2=R2(ym)>y12 Firm2’sprofitincreasesifitcheatsonfirm1byincreasingitsoutputlevelfromymtoR Similarly,firm1’sprofitincreasesifitcheats12firm2byincreasingitsoutputlevelfromym12

2010-2011學年上學期第十三次y1=R1(y2),firm1’sreaction1y2=R2(ym)isfirm1bestresponseto11choosingy1=y1y2y2=R2(y1),firmreactionyy 2010-2011學年上學期第十三次Soaprofit-seekingcar inwhichfirmscooperativelysettheiroutputlevelsisfundamentallyunstable.E.g.OPEC’sbroken2010-2011學年上學期第十三次TheOrder Sofarithasbeenassumedthatfirmschoosetheiroutputlevelssimultaneously.Thecompetitionbetweenthefirmsisthenasimultaneousygameinwhichtheoutputlevelsarethestrategicvariables.Whatiffirm1choosesitsoutputlevelfirstandthenfirm2respondstothischoice?2010-2011學年上學期第十三次TheOrder Firm1isthenaleader.Firm2isaThecompetitionisasequentialgameinwhichtheoutputlevelsarethestrategicvariables.SuchgamesarevonStackelbergIsitbettertobetheOrisitbettertobethe2010-2011學年上學期第十三次StackelbergQ:Whatisthebestresponsethatfollowerfirm2canmaketothechoicey1alreadymadebytheleader,firm1?A:Choosey2=Firm1knowsthisandsoperfectlyanticipatesfirm2’sreactiontoanyy1chosenbyfirm1.2010-2011學年上學期第十三次StackelbergThismakestheleader’sprofit

y

2 1Theleaderchoosesy1 izeitsQ:WilltheleadermakeaprofitatleastaslargeasitsCournot-Nashequilibriumprofit?2010-2011學年上學期第十三次StackelbergA:Yes.TheleadercouldchooseitsCournot-Nashoutputlevel,knowingthatthefollowerwouldthenalsochooseitsC-Noutputlevel.Theleader’sprofitwouldthenbeitsC-Nprofit.Buttheleaderdoesnothavetodothis,soitsprofitmustbeatleastaslargeasitsC-Nprofit.2010-2011學年上學期第十三次StackelbergGames;AnThemarketinversedemandfunctionisp=60-Thefirms’costfunctionsarec1(y1)=y2andc2(y2)1215y2+y2Firm2isthefollower.ItsreactionfunctionyR(y)

45 442010-2011學年上學期第十三次StackelbergGames;AnTheleader’sprofitfunctioniss(y)(60 R(y))y 2 2(60y1

45y14

1y 195

7y2 Fora 195

7yy

13 2 2010-2011學年上學期第十三次StackelbergGames;AnQ:Whatisfirm2’sresponsetoleader’syy 2sR(ys 2

45134

78.TheC-Noutputlevelsare(y1*,y2*)=(13,8)sotheleaderproducesmorethanitsC-NoutputandthefollowerproducesthanitsC-Noutput.Thisistrue 2010-2011學年上學期第十三次Stackelberg(y1*,y2*)istheCournot-NashHighery Higher2 2010-2011學年上學期第十三次yAMES(y1*,y2*)istheCournot-Nashreactiony Higher2 Stackelberg

2010-2011學年上學期第十三次

(y1*,y2*)istheCournot-Nashequilibrium.(y1S,y2S)istheStackelbergequilibrium.reactionHighery2y y 2010-2011學年上學期第十三次2MES(y1*,y2*)istheCournot-equilibrium.(y1S,y2S)istheStackelbergequilibrium.reactiony2y y 2010-2011學年上學期第十三次PriceWhatiffirmscompeteusingonlyprice-settingstrategies,insteadofusingonly Gamesinwhichfirmsuseonlypricestrategies ysimultaneouslyareBertrandgames.2010-2011學年上學期第十三次BertrandEachfirm’smarginalproductioncostisconstantatc.AllfirmssimultaneouslysettheirQ:IsthereaNashA:Yes.Exactlyone.Allfirmssettheirpricesequaltothemarginalcostc.Why?2010-2011學年上學期第十三次BertrandSupposeonefirmsetsitspricehigherthananotherfirm’sprice.Thenthehigher-pricedfirmwouldhavenoHence,atanequilibrium,allfirmsmustsetthesameprice.2010-2011學年上學