管理经济学英文版最新版教学课件第5章

CHAPTER5TheProductionProcessandCostsChapterOutline•Theproductionfunction–Short-versuslong-rundecisions–Measuresofproductivity–Manager’sroleinproductionprocess–Algebraicformsoftheproductionfunctionandproductivity–Isoquantsandisocosts–Costminimizationandoptimalinputsubstitution•Thecostfunction–Short-runcosts–Averageandmarginalcosts–Relationsamongcosts–Fixedandsunkcosts–Algebraicformsofcostfunctions–Long-runcostsandeconomiesofscale•Multiple-outputcostfunctions–Economiesofscopeandcostcomplementarity5-2ChapterOverviewIntroduction•Chapter4focusedonhowconsumersadjustconsumptiondecisionsinreactiontopriceandincomechanges.Thetheorydevelopedillustratestheunderlyingprinciplesofindividualandmarketdemandcurves.•Thischapterexamineshowmanagersselecttheoptimalmixofinputsthatminimizeproductioncosts.5-3ChapterOverviewTheProductionFunction•Mathematicalfunctionthatdefinesthemaximumamountofoutputthatcanbeproducedwithagivensetofinputs.𝑄=𝐹𝐾,𝐿,where–𝑄isthelevelofoutput.–𝐾isthequantityofcapitalinput.–𝐿isthequantityoflaborinput.5-4TheProductionFunctionShort-RunversusLong-RunDecisions:FixedandVariableInputs•Short-run–Periodoftimewheresomefactorsofproduction(inputs)arefixed,andconstrainamanager’sdecisions.•Long-run–Periodoftimeoverwhichallfactorsofproduction(inputs)arevariable,andcanbeadjustedbyamanager.5-5TheProductionFunctionMeasuresofProductivity•Totalproduct(TP)–Maximumlevelofoutputthatcanbeproducedwithagivenamountofinputs.•Averageproduct(AP)–Ameasureoftheoutputproducedperunitofinput.•Averageproductoflabor:𝐴𝑃𝐿=𝑄𝐿•Averageproductofcapital:𝐴𝑃𝐾=𝑄𝐾•Marginalproduct(MP)–Thechangeintotalproduct(output)attributabletothelastunitofaninput.•Marginalproductoflabor:𝑀𝑃𝐿=∆𝑄∆𝐿•Marginalproductofcapital:𝑀𝑃𝐾=∆𝑄∆𝐾5-6TheProductionFunctionMeasuresofProductivityinAction•Considerthefollowingproductionfunctionwhen5unitsoflaborand10unitsofcapitalarecombinedproduce:𝑄=𝐹10,5=150.•Computetheaverageproductoflabor.𝐴𝑃𝐿=1505=30unitsperworker•Computetheaverageproductofcapital.𝐴𝑃𝐿=15010=15unitscapitalunit5-7TheProductionFunctionRelationbetweenProductivityMeasuresinAction5-8Laborinput(holdingcapitalconstant)0TotalproductAverageproductMarginalproductTotalproduct(TP)Averageproduct(APL)Marginalproduct(MPL)IncreasingmarginalreturnstolaborDecreasingmarginalreturnstolaborNegativemarginalreturnstolaborTheProductionFunctionTheManager’sRoleintheProductionProcess•Produceoutputontheproductionfunction.–Aligningincentivestoinducemaximumworkereffort.•Usetherightmixofinputstomaximizeprofits.–Tomaximizeprofitswhenlabororcapitalvaryintheshortrun,themanagerwillhire:•Laboruntilthevalueofthemarginalproductoflaborequalsthewagerate:𝑉𝑀𝑃𝐿=𝑤,where𝑉𝑀𝑃𝐿=𝑃×𝑀𝑃𝐿•Capitaluntilthevalueofthemarginalproductofcapitalequalstherentalrate:𝑉𝑀𝑃𝐾=𝑟,where𝑉𝑀𝑃𝐾=𝑃×𝑀𝑃𝐾5-9TheProductionFunctionManager’sRoleintheProductionProcessinAction•Supposeafirmsellsitsoutputinacompetitivemarketwhereitsoutputissoldat$5perunit.Ifworkersarealsohiredatacompetitivewageof$200,whatisthemarginalproductivityofthelastworker?•Since,𝑉𝑀𝑃𝐿=$5×𝑀𝑃𝐿and𝑤=$200,then,$5×𝑀𝑃𝐿=$200⇒𝑀𝑃𝐿=40units–Themarginalproductivityofthelastunitoflaboris40units.–Alternatively,managementshouldhirelaborsuchthatthelastunitoflaborproduces40units.5-10TheProductionFunctionAlgebraicFormsofProductionFunctions•Commonlyusedalgebraicproductionfunctionforms:–Linear:𝑄=𝐹𝐾,𝐿=𝑎𝐾+𝑏𝐿,where𝑎and𝑏areconstants.–Leontief:𝑄=𝐹𝐾,𝐿=min𝑎𝐾,𝑏𝐿,where𝑎and𝑏areconstants.–Cobb-Douglas:𝑄=𝐹𝐾,𝐿=𝐾𝑎𝐿𝑏,where𝑎and𝑏areconstants.5-11TheProductionFunctionAlgebraicFormsofProductionFunctionsinAction•Supposethatafirm’sestimatedproductionfunctionis:𝑄=3𝐾+6𝐿•Howmuchoutputisproducedwhen3unitsofcapitaland7unitsoflaborareemployed?𝑄=𝐹3,7=33+67=51units5-12TheProductionFunctionAlgebraicMeasuresofProductivity•Giventhecommonlyusedalgebraicproductionfunctionforms,wecancomputethemeasuresofproductivityasfollows:–Linear:•Marginalproducts:𝑀𝑃𝐾=𝑎and𝑀𝑃𝐿=𝑏•Averageproducts:𝐴𝑃𝐾=𝑎𝐾+𝑏𝐿𝐾and𝐴𝑃𝐿=𝑎𝐾+𝑏𝐿𝐿–Cobb-Douglas:•Marginalproducts:𝑀𝑃𝐾=𝑎𝐾𝑎−1𝐿𝑏and𝑀𝑃𝐿=𝑏𝐾𝑎−1𝐿𝑏•Averageproducts:𝐴𝑃𝐾=𝐾𝑎𝐿𝑏𝐾and𝐴𝑃𝐿=𝐾𝑎𝐿𝑏𝐿5-13TheProductionFunctionAlgebraicMeasuresofProductivityinAction•Supposethatafirmproducesoutputaccordingtotheproductionfunction𝑄=𝐹1,𝐿=114𝐿34•Whichisthefixedinput?–Capitalisthefixedinput.•Whatisthemarginalproductoflaborwhen16unitsoflaborishired?𝑀𝑃𝐿=1×34𝐿−14=1×3416−14=385-14TheProductionFunctionIsoquantsandMarginalRateofTechnicalSubstitution•Isoquantscapturethetradeoffbetweencombinationsofinputsthatyieldthesameoutputinthelongrun,whenallinputsarevariable.•Marginalrateoftechnicalsubstitutions(MRTS)–Therateatwhichaproducercansubstitutebetweentwoinputsandmaintainthesamelevelofoutput.–Absolutevalueoftheslopeoftheisoquant.𝑀𝑅𝑇𝑆𝐾𝐿=𝑀𝑃𝐿𝑀𝑃𝐾5-15TheProductionFunctionIsoquantsandMarginalRateofTechnicalSubstitutioninAction5-16LaborInput0AB𝑄𝐼=100unitsofoutput𝑄2=200unitsofoutput𝑄3=300unitsofoutputCapitalInputTheProductionFunctionDiminishingMarginalRateofTechnicalSubstitutioninAction5-