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1、http://www.sem.tsinghua.edu.cn/ChapterNineteenProfit-MaximizationWhatDoWeDointhisChapter?Afterworkingour“producer’sbudgetsets”(productionsets),Weareworkingon“producer’schoices”Pleasepayattentiontothesimilarityanddifferencesbetween“producer’schoices”and“cons
2、umer’schoices”EconomicProfitTheeconomicprofitgeneratedby(x1,…,xm,y1,…,yn)isNotes:Forthetimebeing,werestricttothecaseofacompetitivefirm,whichisatinyrelativetothemarketsizeandtakespricesp1,…,pnw1,…,wmasgivenconstants;Short-runEconomicProfitSupposethefirmisina
3、short-runcircumstanceinwhichItsshort-runproductionfunctionisThefirm’sfixedcostis anditsprofitfunctionisShort-RunIso-ProfitLinesAniso-profitlinecontainsalltheproductionplansthatyieldthesameprofitlevel.Theequationofaniso-profitlineisI.e.Short-RunIso-ProfitLin
4、esIncreasing profityx1Short-RunProfit-Maximizationx1Increasing profityShort-RunProfit-Maximizationx1yAttheshort-runprofit-maximizingplan,theslopesoftheshort-runproductionfunctionandthemaximal iso-profitlineare equal.Short-RunProfit-Maximizationisthemarginal
5、revenueproductof input1,therateatwhichrevenueincreases withtheamountusedofinput1.Ifthenprofitincreaseswithx1.Ifthenprofitdecreaseswithx1.AMathematicalApproachtoShort-RunProfit-MaximizationMathematically,thefirm’sshortrunproblemis:MaximizeSubjectto:Thisgives
6、us:pMP1=w1Important:WehaveassumedthatMP1isdecreasinginx1ComparativeStaticsofShort-RunProfit-MaximizationWhathappenstotheshort-runprofit-maximizingproductionplanastheoutputpricepchanges?ComparativeStaticsofShort-RunProfit-MaximizationTheequationofashort-runi
7、so-profitline issoanincreaseinpcauses areductionintheslopeofthefamilyofiso-profitlinesComparativeStaticsofShort-RunProfit-Maximizationx1yComparativeStaticsofShort-RunProfit-Maximizationx1yAUsefulMath:TheEnvelopeTheoremSupposex*maximizesg(x;t),wheretisaparam
8、eter;Thenx*varieswitht,i.e,x*=x*(t);Wehavegx[x*(t),t]=0;Letg*(t)=Maxg(x,t)=g[x*(t),t]Then,thedg*(t)/dt=gx[x*(t),t]x*’(t)+gt[x*(t),t]=gt[x*(t),t]ThisiscalledtheEnvelopeTheorem.ApplyingtheEnvelopeTheorem
