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Chapter5:ProductionandCostAnalysisintheShortRun,DefiningtheProductionFunction,Q=quantityofoutput,K=quantityofcapitalinput,where,L=quantityoflaborinput,M=quantityofmaterialsinput,Theformulacanbereadas“quantityofoutputisafunctionoftheinputslistedinsidetheparentheses”,FixedInputsVersusVariableInputs,Fixedinput:quantityamanagercannotchangeduringagiventimeVariableinput:quantityamanagercanchangeduringagiventimeAmountofoutputwouldvaryasmanagersmadedecisionsregardingamountsofinput,Short-runVersusLong-runProduction,Notexpressedintermsofcalendartime,butintermsoffixedandvariableinputsShort-runproductionfunction:involvesatleastonefixedinputLong-runproductionfunction:productionprocessinwhichallinputsarevariable,Managersoperateintheshortrun,butmusthavelong-runvisionTheyneedtobeawarethatthecurrentamountoffixedinputsmaynotbeappropriateasmarketconditionschangeManagersmakemorelongruneconomicdecisions,ManagerialRuleofThumb:Short-runProductionandLong-runPlanning,ModeloftheShort-runProductionFunction,TPorQ=totalproductorquantityofoutput,where,L=quantityoflaborinput,Totalproduct:totalquantityofoutputproducedwithagivenquantityoffixedandvariableinputs,AverageProduct,AP=Theaverageproductoflabor,where,Averageproduct:amountofoutputperunitofvariableinput,MarginalProduct,MP=Themarginalproductoflabor,where,MP=TP/L=Q/L,Marginalproduct:theadditionaloutputproducedwithanadditionalunitofvariableinput,Total,Average,andMarginalProduct,HoldstrueiftheleveloftechnologyiskeptconstantThemarginalproductoradditionaloutputproducedisincreasedovertherangeofproductionAverageproductoflaboralsoincreasesinvalueasmoreunitsoflaborareemployedThus,marginalproductbecomeslessthantheaverageproduct,TotalProduct:Short-runProductionFunction,Lawofdiminishingreturnswheremarginalproducteventuallydecreases,Figure5.1a,TP:Short-runProductionFunction,TPincreasesrapidlyuptoleveloflaborinputL1thenincreasesataslowerrateaslaborinputincreasesTPcurvebecomesflatterandflatteruntilitreachesmaximumoutputlevelatL3Curveimpliesthatmarginalproductoflaborfirstincreasesrapidlythendecreases,eventuallybecomingzeroorless,APandMP:Short-runProductionFunction,Figure5.1b,BetweenzeroandL2,MPcurveliesaboveAPcurve,causingAPcurvetoincreaseBelowL2,MPcurveisbelowAPcurve,causingAPcurvetodecreaseTherefore,MPcurvemustintersectAPcurveatmaximumpointofAPcurve,APandMP:Short-runProductionFunction,EconomicExplanation,Increasingmarginalreturns:regionwhereMPcurveispositiveandincreasingLawofdiminishingreturns:regionwheremarginalproductcurveispositivebutdecreasingNegativemarginalreturns:regionwhereproductcurveisnegativesothatTPisdecreasing,LawofDiminishingReturns,OccursbecausecapitalinputandtechnologiesareheldconstantAdditionaloutputgeneratedbyadditionalunitsofvariableinput(MP)Productionbecomeslessconstrained,ProductivityChangesAcrossIndustries,where,K=capitalservices,Q=industryoutput,M=materialsuse,E=energyuse,L=laborservices,t=leveloftechnology,ModelofShort-runCostsFunctions,Costfunction:showsrelationshipbetweencostofproductionandlevelofoutputOpportunitycost:reflectsuseofresourcesinoneactivitywhileforegoinganother,ModelofShort-runCostsFunctions,Explicitcost:paymenttoanindividualthatisrecordedinanaccountingsystemImplicitcosts:valueofusingaresourcethatisnotexplicitlypaidout,isoftendifficulttomeasure,andnotrecordedinanaccountingsystem,MeasuringOpportunityCost,PricesthatafirmpaysforinputreflectsopportunitycostIfmanagersdonotrecognizeopportunitycosts,theymayhavetoomuchinvestedinbuildingsorotherassetsHistoriccost:amountofmoneyafirmpaidforaninputwhenitwaspurchased,AccountingProfitandEconomicProfit,Profit:differencebetweentotalrevenueandtotalcostofproductionAccountingprofit:differencebetweentotalrevenueandtotalexplicitcostEconomicprofit:differencebetweentotalrevenueandtotalbothimplicitandexplicit,MeasuringopportunitycostscanbedifficultbecauseaccountantsaretrainedtoexamineexplicitcostsManagersneedtodevisestrategiesforturningimplicitcostsintoexplicitcoststhataccountantscanuse,ManagerialRuleofThumb:ImportanceofOpportunityCosts,Short-runCostFunctions,Short-runcostfunction:showsrelationshipbetweenoutputandcostsbasedonunderlyingshort-runproductionfunctionItisacostfunctionforshort-runproductionprocessinwhichthereisatleastonefixedunitofproduction,Costs,Totalfixedcost:costofusingfixedinputTotalvariablecost:priceperunitoflabortimesquantityoflaborinputTotalcost:sumoftotalfixedcostplustotalvariablecosts,Costs,Averagefixedcost:totalfixedcostperunitofoutputAveragevariablecost:totalvariablecostperunitofoutputAveragetotalcost:totalcostperunitofoutputplusaveragevariablecostMarginalcost:additionalcostofproducingadditionalunitsofoutput,Total,Average,andMarginalCost,AFCdecreasescontinuouslyasmoreoutputisproducedSinceTFCisconstant,AFCmustdeclineasoutputincreasesAVCandATCfirstdecreasethenincreaseATCalwaysequalsAFCplusAVC,TC,TCV,TFCFunctions,Q,$,0,Q1,TFC,Q2,Q3,TC,TVC,Figure5.2a,MC,ATC,AVC,andAFCFunctions,AVC,AFC,ATC,MC,Figure5.2b,Short-runProductionandCost,ManagersneedtounderstandTechnologyandpricespaidforinputsofproductionDifferencebetweenvariableandfixedcostsDifferencebetweenaveragecosts(costsperunitofoutput)andmarginalcosts(additionalcostsofproducingadditionalunitsofoutput),ManagerialRuleofThumb:UnderstandingYourCosts,EconometricEstimationofCostFunctions,Deansstudiesofafurniturefactory,aleatherbeltshop,andahosierymill,1976JohnstonsstudyofBritishelectricgeneratingplants,roadpassengertransport,andfoodprocessingfirm,1960Hall,1986Blinder,etal,1990s,SummaryofKeyTerms,AccountingprofitAveragefixedcostAverageproductAveragetotalcostAveragevariablecostCostfunctionEconomicprofit,ExplicitcostFixedinputHistoriccostImplicitcostMargin

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