中国航空工业第一集团公司在2000年8月决定今后民用飞机

1Chapter4TheTheoryofOptimizationInthischapterwewillgiveyouthekeytothekingdomofeconomicdecisionmaking:marginalanalysis.2Virtuallyallofmicroeconomicsinvolvessolutionstooptimizationproblems.Themostinterestingandchallengingproblemsfacingamanagerinvolvetryingeithertomaximizeortominimizeparticularobjectivefunctions.Regardlessofwhethertheoptimizationinvolvesmaximizationorminimization,orconstrainedorunconstrainedchoicevariables,alloptimizationproblemsaresolvedbyusingmarginalanalysis.3Webegintheanalysisofoptimizationtheorybyexplainingsometerminology.thenderivetworulesformakingoptimaldecisions.44.1CONCEPTSANDTERMINOLOGYobjectivefunctionThefunctionthedecisionmakerseekstomaximizeorminimize.maximizationproblemAnoptimizationproblemthatinvolvesmaximizingtheobjectivefunction.minimizationproblemAnoptimizationproblemthatinvolvesminimizingtheobjectivefunction.5ActivitiesorChoiceVariablesactivitiesorchoicevariablesDeterminethevalueoftheobjectivefunction.discretechoicevariableAchoicevariablethatcantakeonlyspecificintegervalues.continuouschoicevariableAchoicevariablethatcantakeonanyvaluebetweentwoendpoints.6unconstrainedandconstrainedoptimizationunconstrainedoptimizationAnoptimizationprobleminwhichthedecisionmakercanchoosethelevelofactivityfromanunrestrictedsetofvalues.constrainedoptimizationAnoptimizationprobleminwhichthedecisionmakerchoosesvaluesforthechoicevariablesfromarestrictedsetofvalues.7constrainedmaximizationAmaximizationproblemwheretheactivitiesmustbechosentosatisfyasideconstraintthatthetotalcostoftheactivitiesbeheldtoaspecificamount.constrainedminimizationAminimizationproblemwheretheactivitiesmustbechosentosatisfyasideconstraintthatthetotalbenefitoftheactivitiesbeheldtoaspecificamount.8marginalanalysisAnanalyticaltoolforsolvingoptimizationproblemsthatinvolveschangingthevalue(s)ofthechoicevariable(s)byasmallamounttoseeiftheobjectivefunctioncanbefurtherincreased(formaximizationproblems)orfurtherdecreased(forminimizationproblems).94.2unconstrainedmaximizationTheresultsofthischapterfallneatlyintotwocategories:thesolutiontounconstrainedandthesolutiontoconstrainedoptimizationproblems.10Whenthevaluesofthechoicevariablesarenotrestrictedbyconstraintssuchaslimitedincome,limitedexpenditures,orlimitedtime,theoptimizationproblemissaidtobeunconstrained.Oneofthemostimportantunconstrainedoptimizationproblemsfacingmanagersisselectingthesetofvariablesthatwillmaximizetheprofitofthefirm.11Thisproblemandallotherunconstrainedmaximizationproblemscanbesolvedbyfollowingthissimplerule:Tomaximizeanobjectivefunction,thevalueofwhichdependsoncertainactivitiesorchoicevariables,eachactivityiscarriedoutuntilthemarginalbenefitfromanincreaseintheactivityequalsthemarginalcostoftheincreasedactivity:12MBA=MCA,MBB=MCB,…..,MBZ=MCZoptimalleveloftheactivityThelevelofactivitythatmaximizesnetbenefit.marginalbenefit(MB)Theadditiontototalbenefitattributabletoincreasingtheactivitybyasmallamount.marginalcost(MC)Theadditiontototalcostattributabletoincreasingtheactivitybyasmallamount.1314Whenthechoicevariablesarenotcontinuousbutdiscrete,itmaynotbepossibletopreciselyequatebenefitandcostatthemargin.Fordiscretechoicevariables,thedecisionmakersimplycarriesouttheactivityuptothepointwhereanyfurtherincreasesintheactivityresultinmarginalcostexceedingmarginalbenefit.15SunkcostsandfixedcostsareirrelevantsunkcostsCoststhathavepreviouslybeenpaidandcannotberecovered.fixedcostsCoststhatareconstantandmustbepaidnomatterwhatleveloftheactivityischosen.16中国航空工业第一集团公司在2000年8月决定今后民用飞机不再发展干线飞机，而转向发展支线飞机。这一决策立时引起广泛争议和反弹。许多人反对干线飞机项目下马的一个重要理由就是，该项目已经投入数十亿元巨资，上万人倾力奉献，耗时六载，在终尝胜果之际下马造成的损失实在太大了。这种痛苦的心情可以理解，但丝毫不构成该项目应该上马的理由，因为不管该项目已经投入了多少人力、物力、财力，对于上下马的决策而言，其实都是无法挽回的沉没成本。17事实上，干线项目下马完全是“前景堪忧”使然。从销路看，原打算生产150架飞机，到1992年首次签约时定为40架，后又于1994年降至20架，并约定由中方认购。但民航只同意购买5架，其余15架没有着落。可想而知，在没有市场的情况下，继续进行该项目会有怎样的未来收益？18沉没成本与人生态度经济学中有许多概念不仅有利于经营企业，而且对于认识人生也是有益的。沉没成本这个概念是其中之一。当一项业已发生的成本，无论如何努力也无法收回的时候，这种成本就构成了沉没成本。面对这种无法收回的沉没成本，明智的投资者会视其为没有发生。举个例子来说，你花了10块钱买了一张今晚的电影票，准备晚上去电影院看电影，不想临出门时天空突然下起了大雨。这时你该怎么办？194.3constrainedoptimizationInmanyinstances,managersfacelimitationsontherangeofvaluesthatthechoicevariablescantake.Forexample,budgetsmaylimittheamountoflaborandcapitalmanagersmaypurchase.Timeconstraintsmaylimitthenumberofhoursmanagerscanallocatetocertainactivities.Suchconstraintsarecommonandrequiremodifyingthesolutiontooptimizationproblems.20Tomaximizeorminimizeanobjectivefunctionsubjecttoaconstraint,theratiosofthemarginalbenefittopricemustbeequalforallactivities,MBA/PA=MBB/PB=……MBZ/PZ21andthevaluesofthechoicevariablesmustmeettheconstraint.Oneofthemostimportantconstrainedoptimizationproblemsfacingamanageristhetaskofproducingagivenoutputattheleastpossibletotalcost.22CasestudyIscost-benefitanalysisreallyuseful?(pp134)?Findtheanswerstoquestion