上财中级微观经济学课件

ChapterNineteenProfit-Maximization2025/5/221EconomicProfitAfirmusesinputsj=1…,mtomakeproductsi=1,…n.Outputlevelsarey1,…,yn.Inputlevelsarex1,…,xm.Productpricesarep1,…,pn.Inputpricesarew1,…,wm.

2025/5/222TheCompetitiveFirmThecompetitivefirmtakesalloutputpricesp1,…,pnandallinputpricesw1,…,wmasgivenconstants.2025/5/223EconomicProfitTheeconomicprofitgeneratedbytheproductionplan(x1,…,xm,y1,…,yn)is2025/5/224EconomicProfitOutputandinputlevelsaretypicallyflows.E.g.x1mightbethenumberoflaborunitsusedperhour.Andy3mightbethenumberofcarsproducedperhour.Consequently,profitistypicallyaflowalso;e.g.thenumberofdollarsofprofitearnedperhour.2025/5/225EconomicProfitHowdowevalueafirm?Supposethefirm’sstreamofperiodiceconomicprofitsisP0,P1,P2,…andristherateofinterest.Thenthepresent-valueofthefirm’seconomicprofitstreamis2025/5/226EconomicProfitAcompetitivefirmseekstomaximizeitspresent-value.How?2025/5/227EconomicProfitSupposethefirmisinashort-runcircumstanceinwhichItsshort-runproductionfunctionis2025/5/228EconomicProfitSupposethefirmisinashort-runcircumstanceinwhichItsshort-runproductionfunctionis

Thefirm’sfixedcostis

anditsprofitfunctionis2025/5/229Short-RunIso-ProfitLinesA$P

iso-profitlinecontainsalltheproductionplansthatprovideaprofitlevel$P.A$Piso-profitline’sequationis

2025/5/2210Short-RunIso-ProfitLinesA$P

iso-profitlinecontainsalltheproductionplansthatyieldaprofitlevelof$P.Theequationofa$Piso-profitlineis

I.e.2025/5/2211Short-RunIso-ProfitLineshasaslopeofandaverticalinterceptof2025/5/2212Short-RunIso-ProfitLinesIncreasing

profityx12025/5/2213Short-RunProfit-MaximizationThefirm’sproblemistolocatetheproductionplanthatattainsthehighestpossibleiso-profitline,giventhefirm’sconstraintonchoicesofproductionplans.Q:Whatisthisconstraint?2025/5/2214Short-RunProfit-MaximizationThefirm’sproblemistolocatetheproductionplanthatattainsthehighestpossibleiso-profitline,giventhefirm’sconstraintonchoicesofproductionplans.Q:Whatisthisconstraint?A:Theproductionfunction.2025/5/2215Short-RunProfit-Maximizationx1Technically

inefficient

plansyTheshort-runproductionfunctionand

technologysetfor2025/5/2216Short-RunProfit-Maximizationx1Increasing

profity2025/5/2217Short-RunProfit-Maximizationx1y2025/5/2218Short-RunProfit-Maximizationx1yGivenp,w1andtheshort-run

profit-maximizingplanis2025/5/2219Short-RunProfit-Maximizationx1yGivenp,w1andtheshort-run

profit-maximizingplanis

Andthemaximum

possibleprofit

is2025/5/2220Short-RunProfit-Maximizationx1yAttheshort-runprofit-maximizingplan,theslopesoftheshort-runproductionfunctionandthemaximal

iso-profitlineare

equal.2025/5/2221Short-RunProfit-Maximizationx1yAttheshort-runprofit-maximizingplan,theslopesoftheshort-runproductionfunctionandthemaximal

iso-profitlineare

equal.2025/5/2222Short-RunProfit-Maximization

isthemarginalrevenueproductof

input1,therateatwhichrevenueincreases

withtheamountusedofinput1.Ifthenprofitincreaseswithx1.Ifthenprofitdecreaseswithx1.

2025/5/2223Short-RunProfit-Maximization;ACobb-DouglasExampleSupposetheshort-runproduction

functionisThemarginalproductofthevariable

input1isTheprofit-maximizingconditionis2025/5/2224Short-RunProfit-Maximization;ACobb-DouglasExampleSolvingforx1gives2025/5/2225Short-RunProfit-Maximization;ACobb-DouglasExampleSolvingforx1givesThatis,2025/5/2226Short-RunProfit-Maximization;ACobb-DouglasExampleSolvingforx1givesThatis,so2025/5/2227Short-RunProfit-Maximization;ACobb-DouglasExampleisthefirm’s

short-rundemandforinput1whenthelevelofinput2isfixedatunits.2025/5/2228Short-RunProfit-Maximization;ACobb-DouglasExampleisthefirm’s

short-rundemandforinput1whenthelevelofinput2isfixedatunits.Thefirm’sshort-runoutputlevelisthus2025/5/2229ComparativeStaticsofShort-RunProfit-MaximizationWhathappenstotheshort-runprofit-maximizingproductionplanastheoutputpricepchanges?2025/5/2230ComparativeStaticsofShort-RunProfit-MaximizationTheequationofashort-runiso-profitline

issoanincreaseinpcauses

--areductionintheslope,and--areductionintheverticalintercept.2025/5/2231ComparativeStaticsofShort-RunProfit-Maximizationx1y2025/5/2232ComparativeStaticsofShort-RunProfit-Maximizationx1y2025/5/2233ComparativeStaticsofShort-RunProfit-Maximizationx1y2025/5/2234ComparativeStaticsofShort-RunProfit-MaximizationAnincreaseinp,thepriceofthefirm’soutput,causesanincreaseinthefirm’soutputlevel(thefirm’ssupplycurveslopesupward),andanincreaseinthelevelofthefirm’svariableinput(thefirm’sdemandcurveforitsvariableinputshiftsoutward).2025/5/2235ComparativeStaticsofShort-RunProfit-MaximizationTheCobb-Douglasexample:When

thenthefirm’sshort-run

demandforitsvariableinput1isanditsshort-run

supplyis2025/5/2236ComparativeStaticsofShort-RunProfit-MaximizationTheCobb-Douglasexample:When

thenthefirm’sshort-run

demandforitsvariableinput1isincreasesaspincreases.anditsshort-run

supplyis2025/5/2237ComparativeStaticsofShort-RunProfit-MaximizationTheCobb-Douglasexample:When

thenthefirm’sshort-run

demandforitsvariableinput1isincreasesaspincreases.anditsshort-run

supplyisincreasesaspincreases.2025/5/2238ComparativeStaticsofShort-RunProfit-MaximizationWhathappenstotheshort-runprofit-maximizingproductionplanasthevariableinputpricew1changes?2025/5/2239ComparativeStaticsofShort-RunProfit-MaximizationTheequationofashort-runiso-profitline

issoanincreaseinw1causes

--anincreaseintheslope,and--nochangetotheverticalintercept.2025/5/2240ComparativeStaticsofShort-RunProfit-Maximizationx1y2025/5/2241ComparativeStaticsofShort-RunProfit-Maximizationx1y2025/5/2242ComparativeStaticsofShort-RunProfit-Maximizationx1y2025/5/2243ComparativeStaticsofShort-RunProfit-MaximizationAnincreaseinw1,thepriceofthefirm’svariableinput,causesadecreaseinthefirm’soutputlevel(thefirm’ssupplycurveshiftsinward),andadecreaseinthelevelofthefirm’svariableinput(thefirm’sdemandcurveforitsvariableinputslopesdownward).2025/5/2244ComparativeStaticsofShort-RunProfit-MaximizationTheCobb-Douglasexample:When

thenthefirm’sshort-run

demandforitsvariableinput1isanditsshort-run

supplyis2025/5/2245ComparativeStaticsofShort-RunProfit-MaximizationTheCobb-Douglasexample:When

thenthefirm’sshort-run

demandforitsvariableinput1isdecreasesasw1increases.anditsshort-run

supplyis2025/5/2246ComparativeStaticsofShort-RunProfit-MaximizationTheCobb-Douglasexample:When

thenthefirm’sshort-run

demandforitsvariableinput1isdecreasesasw1increases.decreasesasw1increases.anditsshort-run

supplyis2025/5/2247Long-RunProfit-MaximizationNowallowthefirmtovarybothinputlevels.Sincenoinputlevelisfixed,therearenofixedcosts.2025/5/2248Long-RunProfit-MaximizationBothx1andx2arevariable.Thinkofthefirmaschoosingtheproductionplanthatmaximizesprofitsforagivenvalueofx2,andthenvaryingx2tofindthelargestpossibleprofitlevel.2025/5/2249Long-RunProfit-MaximizationTheequationofalong-runiso-profitline

issoanincreaseinx2causes

--nochangetotheslope,and--anincreaseintheverticalintercept.2025/5/2250Long-RunProfit-Maximizationx1y2025/5/2251Long-RunProfit-Maximizationx1yLargerlevelsofinput2increasethe

productivityofinput1.2025/5/2252Long-RunProfit-Maximizationx1yLargerlevelsofinput2increasethe

productivityofinput1.Themarginalproduct

ofinput2is

diminishing.2025/5/2253Long-RunProfit-Maximizationx1yLargerlevelsofinput2increasethe

productivityofinput1.Themarginalproduct

ofinput2is

diminishing.2025/5/2254Long-RunProfit-Maximizationx1y

foreachshort-run

productionplan.2025/5/2255Long-RunProfit-Maximizationx1yThemarginalproduct

ofinput2is

diminishingso...

foreachshort-run

productionplan.2025/5/2256Long-RunProfit-Maximizationx1ythemarginalprofit

ofinput2is

diminishing.

foreachshort-run

productionplan.2025/5/2257Long-RunProfit-MaximizationProfitwillincreaseasx2increasessolongasthemarginalprofitofinput2

Theprofit-maximizinglevelofinput2thereforesatisfies2025/5/2258Long-RunProfit-MaximizationProfitwillincreaseasx2increasessolongasthemarginalprofitofinput2

Theprofit-maximizinglevelofinput2thereforesatisfies

Andissatisfiedinanyshort-run,so...2025/5/2259Long-RunProfit-MaximizationTheinputlevelsofthelong-runprofit-maximizingplansatisfy

Thatis,marginalrevenueequalsmarginalcostforallinputs.and2025/5/2260Long-RunProfit-MaximizationTheCobb-Douglasexample:When

thenthefirm’sshort-run

demandforitsvariableinput1isanditsshort-run

supplyisShort-runprofitistherefore…2025/5/2261Long-RunProfit-Maximization2025/5/2262Long-RunProfit-Maximization2025/5/2263Long-RunProfit-Maximization2025/5/2264Long-RunProfit-Maximization2025/5/2265Long-RunProfit-MaximizationWhatisthelong-runprofit-maximizing

levelofinput2?Solvetoget2025/5/2266Long-RunProfit-MaximizationWhatisthelong-runprofit-maximizing

input1level?Substituteintotoget2025/5/2267Long-RunProfit-MaximizationWhatisthelong-runprofit-maximizing

input1level?Substituteintotoget2025/5/2268Long-RunProfit-MaximizationWhatisthelong-runprofit-maximizing

outputlevel?Substituteintotoget2025/5/2269Long-RunProfit-MaximizationWhatisthelong-runprofit-maximizing

outputlevel?Substituteintotoget2025/5/2270Long-RunProfit-MaximizationSogiventhepricesp,w1andw2,and

theproductionfunctionthelong-runprofit-maximizingproduction

planis2025/5/2271Returns-to-ScaleandProfit-MaximizationIfacompetitivefirm’stechnologyexhibitsdecreasingreturns-to-scalethenthefirmhasasinglelong-runprofit-maximizingproductionplan.2025/5/2272Returns-toScaleandProfit-Maximizationxyy*x*Decreasing

returns-to-scale2025/5/2273Returns-to-ScaleandProfit-MaximizationIfacompetitivefirm’stechnologyexhibitsincreasingreturns-to-scalethenthefirmdoesnothaveaprofit-maximizingplan.2025/5/2274Returns-toScaleandProfit-Maximizationxyy〞x’Increasing

returns-to-scaley’x〞Increasing

profit2025/5/2275Returns-to-ScaleandProfit-MaximizationSoanincreasingreturns-to-scaletechnologyisinconsistentwithfirmsbeingperfectlycompetitive.2025/5/2276Returns-to-ScaleandProfit-MaximizationWhatifthecompetitivefirm’stechnologyexhibitsconstantreturns-to-scale?2025/5/2277Returns-toScaleandProfit-Maximizationxyy〞x’Constant

returns-to-scaley’x〞Increasing

profit2025/5/2278Returns-toScaleandProfit-MaximizationSoifanyproductionplanearnsapositiveprofit,thefirmcandoubleupallinputstoproducetwicetheoriginaloutputandearntwicetheoriginalprofit.2025/5/2279Returns-toScaleandProfit-MaximizationTherefore,whenafirm’stechnologyexhibitsconstantreturns-to-scale,earningapositiveeconomicprofitisinconsistentwithfirmsbeingperfectlycompetitive.Henceconstantreturns-to-scalerequiresthatcompetitivefirmsearneconomicprofitsofzero.2025/5/2280Returns-toScaleandProfit-Maximizationxyy〞x’Constant

returns-to-scaley’x〞P=02025/5/2281RevealedProfitabilityConsideracompetitivefirmwithatechnologythatexhibitsdecreasingreturns-to-scale.Foravarietyofoutputandinputpricesweobservethefirm’schoicesofproductionplans.Whatcanwelearnfromourobservations?2025/5/2282RevealedProfitabilityIfaproductionplan(x’,y’)ischosenatprices(w’,p’)wededucethattheplan(x’,y’)isrevealedtobeprofit-maximizingfortheprices(w’,p’).2025/5/2283RevealedProfitabilityxy

ischosenatprices2025/5/2284RevealedProfitabilityxy

ischosenatpricesso

isprofit-maximizingattheseprices.2025/5/2285RevealedProfitabilityxy

ischosenatpricesso

isprofit-maximizingattheseprices.

wouldgivehigher

profits,sowhyisitnot

chosen?2025/5/2286RevealedProfitabilityxy

ischosenatpricesso

isprofit-maximizingattheseprices.

wouldgivehigher

profits,sowhyisitnot

chosen?Becauseitis

notafeasibleplan.2025/5/2287RevealedProfitabilityxy

ischosenatpricesso

isprofit-maximizingattheseprices.

wouldgivehigher

profits,sowhyisitnot

chosen?Becauseitis

notafeasibleplan.Sothefirm’stechnologysetmustlieunderthe

iso-profitline.2025/5/2288RevealedProfitabilityxy

ischosenatpricesso

isprofit-maximizingattheseprices.Sothefirm’stechnologysetmustlieunderthe

iso-profitline.Thetechnology

setissomewhere

inhere2025/5/2289RevealedProfitabilityxy

ischosenatpricesso

maximizesprofitattheseprices.

wouldprovidehigher

profitbutitisnotchosen2025/5/2290RevealedProfitabilityxy

ischosenatpricesso

maximizesprofitattheseprices.

wouldprovidehigher

profitbutitisnotchosen

becauseitisnotfeasible2025/5/2291RevealedProfitabilityxy

ischosenatpricesso

maximizesprofitattheseprices.

wouldprovidehigher

profitbutitisnotchosen

becauseitisnotfeasibleso

thetechnologysetliesunder

theiso-profitline.2025/5/2292RevealedProfitabilityxy

ischosenatpricesso

maximizesprofitattheseprices.Thetechnologysetis

alsosomewherein

here.2025/5/2293RevealedProfitabilityxyThefirm’stechnologysetmustlieunder

bothiso-profitlines2025/5/2294RevealedProfitabilityx