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1、ChapterOptimizationwithEqualityConstraintsChapter11presentedagenera!methodforfindingtherelativeextremaofanobjectivefunctionoftwoormorechoicevariables.Oneimportantfeatureafthatdiscussionisthatallthechoicevariablesareindependentofoncanother,inthesensethatthedecisionmadereg
2、ardingonevariabledoesnotimpingeuponthechoicesQftheremainingvariables,Forinstance,atwoMproducttlm1canchooseanyvalueforQIandanyvaluefor':'2itwishes,withoutthet'ovochoiceslimitingeachother.Ifthesaidfirmissomehowrequiredtoobservearestriction(sucha5aproductionquota)intheformo
3、fQI+Q2;;;;;950,ho.....ever,theindependencebetweenthechoicevariableswillbelost.Inthatevent,thefirm'sprolit~maximizing~lUtputlevelsQfandQ;willbenotonlysimultaneousbutalsodependent,becausethchighcrQjis,thelowerQimustcorre•spondinglybe.inordertostayI},.'ithinthecombinedquota
4、of950.Thenevoptimumsatis•fyingtheproductionquotaconstitutesaconslIuinedoptimum,vhich,ingeneral.maybeexpectedtodifferfromthefreeoptimumdiscuHscdinChap.!1.Arestriction,suchastheproductionquotamentionedbefore,establishesarelationshipbetweenthetwovariablesintheirrolesascho
5、icevariabtc.s,butthis~houldbedistinguishedfromothertypesofrelationshipsthatmaylinkthevariablestogether.Forinstance,inEx•ample2ofSeG.11.6,thenvoproductsofthefinnarerelatedinconsumption(substitute~)aswellasinproduction(asisreflectedinthecostilHlction),butthaIfactdocsnotqua
6、lifytheproblemasoncofconstrainedoptimization,sincethet~ooutputvariablesan~stillin•dependentascluneevariables.Onlythedependenceofthevariablesquachoicevariablesgivc~risctoacon~traincdoptimum.Tnthcprescntchapter,weshallconsiderequalityconstraintsonly,~uehasQI+Q2:::::950.Our
7、primaryc~mccrnwillbewithrelativeconstrainedextrema,althoughah.m{uteoneswillalsobediscuss.edinSec.12.4.12.1EffectsofaConstraintTheprimarypurposeofimposingaconstraintistogiveduccllgnizancctocertainlimitingfactorspresentintheoptimizationproblemunderdiscussion.347348PartFour
8、OplimizaliollProb/elllsWehavealreadyseenthelimitationonoutputchoicesthatresultfromaproductionquota,Forf
