北京大学中级微观经济学课件Ch27-Oligopoly

ChapterTwenty-SevenOligopolyOligopolyAmonopolyisanindustryconsistingasinglefirm.Aduopolyisanindustryconsistingoftwofirms.Anoligopolyisanindustryconsistingofafewfirms.Particularly,eachfirm’sownpriceoroutputdecisionsaffectitscompetitors’profits.OligopolyHowdoweanalyzemarketsinwhichthesupplyingindustryisoligopolistic?Considertheduopolisticcaseoftwofirmssupplyingthesameproduct.QuantityCompetitionAssumethatfirmscompetebychoosingoutputlevels.Iffirm1producesy1unitsandfirm2producesy2unitsthentotalquantitysuppliedisy1+y2.Themarketpricewillbep(y1+y2).Thefirms’totalcostfunctionsarec1(y1)andc2(y2).QuantityCompetitionSupposefirm1takesfirm2’soutputlevelchoicey2asgiven.Thenfirm1seesitsprofitfunctionasGiveny2,whatoutputlevely1maximizesfirm1’sprofit?11212111(;)()().yypyyycyQuantityCompetition;AnExampleSupposethatthemarketinversedemandfunctionisandthatthefirms’totalcostfunctionsarepyyTT()60cyy1112()cyyy2222215().andQuantityCompetition;AnExample(;)().yyyyyy121211260Then,forgiveny2,firm1’sprofitfunctionisQuantityCompetition;AnExample(;)().yyyyyy121211260Then,forgiveny2,firm1’sprofitfunctionisSo,giveny2,firm1’sprofit-maximizingoutputlevelsolvesyyyy112160220.QuantityCompetition;AnExample(;)().yyyyyy121211260Then,forgiveny2,firm1’sprofitfunctionisSo,giveny2,firm1’sprofit-maximizingoutputlevelsolvesyyyy112160220.I.e.firm1’sbestresponsetoy2isyRyy11221514().QuantityCompetition;AnExampley2y16015Firm1’s“reactioncurve”yRyy11221514().QuantityCompetition;AnExample(;)().yyyyyyy211222226015Similarly,giveny1,firm2’sprofitfunctionisQuantityCompetition;AnExample(;)().yyyyyyy211222226015Similarly,giveny1,firm2’sprofitfunctionisSo,giveny1,firm2’sprofit-maximizingoutputlevelsolvesyyyy21226021520.QuantityCompetition;AnExample(;)().yyyyyyy211222226015Similarly,giveny1,firm2’sprofitfunctionisSo,giveny1,firm2’sprofit-maximizingoutputlevelsolvesyyyy21226021520.I.e.firm1’sbestresponsetoy2isyRyy2211454().QuantityCompetition;AnExampley2y1Firm2’s“reactioncurve”yRyy2211454().45/445QuantityCompetition;AnExampleAnequilibriumiswheneachfirm’soutputlevelisabestresponsetotheotherfirm’soutputlevel,forthenneitherwantstodeviatefromitsoutputlevel.Apairofoutputlevels(y1*,y2*)isaCournot-NashequilibriumifyRy221**().yRy112**()andQuantityCompetition;AnExampleyRyy11221514***()yRyy2211454***().andQuantityCompetition;AnExampleyRyy11221514***()yRyy2211454***().andSubstitutefory2*togetyy111514454**QuantityCompetition;AnExampleyRyy11221514***()yRyy2211454***().andSubstitutefory2*togetyyy111151445413***QuantityCompetition;AnExampleyRyy11221514***()yRyy2211454***().andSubstitutefory2*togetyyy111151445413***Hencey2451348*.QuantityCompetition;AnExampleyRyy11221514***()yRyy2211454***().andSubstitutefory2*togetyyy111151445413***Hencey2451348*.SotheCournot-Nashequilibriumis(,)(,).**yy12138QuantityCompetition;AnExampley2y1Firm2’s“reactioncurve”6015Firm1’s“reactioncurve”yRyy11221514().yRyy2211454().45/445QuantityCompetition;AnExampley2y1Firm2’s“reactioncurve”4860Firm1’s“reactioncurve”yRyy11221514().813Cournot-Nashequilibriumyy12138**,,.yRyy2211454().QuantityCompetition11212111(;)()()yypyyycy11121121110ypyyypyyycy()()().Generally,givenfirm2’schosenoutputlevely2,firm1’sprofitfunctionisandtheprofit-maximizingvalueofy1solvesThesolution,y1=R1(y2),isfirm1’sCournot-Nashreactiontoy2.QuantityCompetition22112222(;)()()yypyyycy22122122220ypyyypyyycy()()().Similarly,givenfirm1’schosenoutputlevely1,firm2’sprofitfunctionisandtheprofit-maximizingvalueofy2solvesThesolution,y2=R2(y1),isfirm2’sCournot-Nashreactiontoy1.QuantityCompetitiony2y1Firm1’s“reactioncurve”Firm1’s“reactioncurve”yRy112().Cournot-Nashequilibriumy1*=R1(y2*)andy2*=R2(y1*)y2*yRy221().y1*Iso-ProfitCurvesForfirm1,aniso-profitcurvecontainsalltheoutputpairs(y1,y2)givingfirm1thesameprofitlevel1.Whatdoiso-profitcurveslooklike?y2y1Iso-ProfitCurvesforFirm1Withy1fixed,firm1’sprofitincreasesasy2decreases.y2y1Increasingprofitforfirm1.Iso-ProfitCurvesforFirm1y2y1Iso-ProfitCurvesforFirm1Q:Firm2choosesy2=y2’.Wherealongtheliney2=y2’istheoutputlevelthatmaximizesfirm1’sprofit?y2’y2y1Iso-ProfitCurvesforFirm1Q:Firm2choosesy2=y2’.Wherealongtheliney2=y2’istheoutputlevelthatmaximizesfirm1’sprofit?A:Thepointattainingthehighestiso-profitcurveforfirm1.y2’y1’y2y1Iso-ProfitCurvesforFirm1Q:Firm2choosesy2=y2’.Wherealongtheliney2=y2’istheoutputlevelthatmaximizesfirm1’sprofit?A:Thepointattainingthehighestiso-profitcurveforfirm1.y1’isfirm1’sbestresponsetoy2=y2’.y2’y1’y2y1Iso-ProfitCurvesforFirm1Q:Firm2choosesy2=y2’.Wherealongtheliney2=y2’istheoutputlevelthatmaximizesfirm1’sprofit?A:Thepointattainingthehighestiso-profitcurveforfirm1.y1’isfirm1’sbestresponsetoy2=y2’.y2’R1(y2’)y2y1y2’R1(y2’)y2”R1(y2”)Iso-ProfitCurvesforFirm1y2y1y2’y2”R1(y2”)R1(y2’)Firm1’sreactioncurvepassesthroughthe“tops”offirm1’siso-profitcurves.Iso-ProfitCurve