What are first-order and second-order conditions for the maximum value of a function of one variable?

Chapter 2 “Mathematics for Microeconomics” focus on topics 2.1, 2,2, and 2.3

Short Question:

1. What are first-order and second-order conditions for the maximum value of a function of one variable?

2. Describe the Young’s Theorem. Use an example to explain the theorem.

Problems:

1. Suppose a firm’s total revenues depend on the amount produced (q) according to the function:

R = 70q – q²

Total costs also depend on q:

C = q²+ 30q + 100

A. What level of output should the firm produce to maximize profits (R- C)? What will the profits be?

B. Show the second-order conditions for a maximum are satisfied at the output level found in part(A).

C. Does the solution calculated here obey the “marginal revenue equals marginal cost” rule? Explain.

Requirements: 1 DAY

MICROECONOMICTHEORYBASICPRINCIPLESANDEXTENSIONSTENTHEDITION

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MICROECONOMICTHEORYBASICPRINCIPLESANDEXTENSIONSTENTHEDITIONWalterNicholsonAmherstCollegeChristopherSnyderDartmouthCollege

VP/EditorialDirector:JackW.CalhounEditor-in-Chief:AlexvonRosenbergExecutiveEditor:MikeRocheSr.DevelopmentalEditor:SusanSmartSr.ContentProjectManager:CliffKallemeynProductionTechnologyAnalyst:AdamGrafaExecutiveMarketingManager:BrianJoynerSr.MarketingManager:JohnCareyArtDirector:MichelleKunklerSr.FirstPrintBuyer:SandeeMilewskiPrinter:WestGroupEagan,MNMicroeconomicTheoryBasicPrinciplesandExtensionsTenthEditionWalterNicholsonChristopherSnyderCOPYRIGHT©2008,2005ThomsonSouth-Western,apartofTheThomsonCorporation.Thomson,theStarlogo,andSouth-Westernaretrademarksusedhereinunderlicense.PrintedintheUnitedStatesofAmerica1234510090807ISBN13:978-0-324-42162-0ISBN10:0-324-42162-1ALLRIGHTSRESERVED.Nopartofthisworkcoveredbythecopyrighthereonmaybereproducedorusedinanyformorbyanymeans—graphic,elec-tronic,ormechanical,includingphotocopying,recording,taping,Webdistributionorinformationstorageandretrievalsystems,orinanyothermanner—withoutthewrittenpermissionofthepublisher.Forpermissiontousematerialfromthistextorproduct,submitarequestonlineathttp://www.thomsonrights.com.LibraryofCongressControlNumber:2007921464ThomsonHigherEducation5191NatorpBoulevardMason,OH45040USAFormoreinformationaboutourproducts,contactusat:ThomsonLearningAcademicResourceCenter1-800-423-0563

ToBeth,Sarah,David,Sophia,andAbbyToMaura

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AbouttheAuthorsWalterNicholsonistheWardH.PattonProfessorofEconomicsatAmherstCollege.HereceivedhisB.A.inmathematicsfromWilliamsCollegeandhisPh.D.ineconomicsfromMIT.ProfessorNicholson’sprincipalresearchinterestsareintheeconometricanalysesoflabormarketproblemsincludingunemployment,jobtraining,andtheimpactofinter-nationaltrade.Heisalsotheco-author(withChrisSnyder)ofIntermediateMicroeconomicsandItsApplication,TenthEdition(Thomson/South-Western,2007).ProfessorNicholsonandhiswife,Susan,liveinAmherst,Massachusetts,andNaples,Florida.Whatwaspreviouslyaverybusyhousehold,withfourchildreneverywhere,isnowratherempty.Butanever-increasingnumberofgrandchildrenbreathesomelifeintotheseplaceswhenevertheyvisit,whichseemsfartooseldom.ChristopherM.SnyderisaProfessorofEconomicsatDartmouthCollege.HereceivedhisB.A.ineconomicsandmathematicsfromFordhamUniversityandhisPh.D.ineconomicsfromMIT.BeforecomingtoDartmouthin2005,hetaughtatGeorgeWashingtonUniversityforoveradecade,andhehasbeenavisitingprofessorattheUniversityofChicagoandMIT.HeiscurrentlyPresidentoftheIndustrialOrganizationSocietyandAssociateEditoroftheInternationalJournalofIndustrialOrganizationandReviewofIndustrialOrganization.Hisresearchcoversvarioustheoreticalandempiricaltopicsinindustrialorganization,contracttheory,andlawandeconomics.ProfessorSnyderandhiswifeMauraDoyle(whoalsoteacheseconomicsatDartmouth)livewithinwalkingdistanceofcampusinHanover,NewHampshire,withtheirthreeelementary-school-ageddaughters.

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BriefContentsPart1IntroductionChapter1:EconomicModels3Chapter2:MathematicsforMicroeconomics19Part2ChoiceandDemandChapter3:PreferencesandUtility87Chapter4:UtilityMaximizationandChoice113Chapter5:IncomeandSubtitutionEffects141Chapter6:DemandRelationshipsamongGoods182Chapter7:UncertaintyandInformation202Chapter8:StrategyandGameTheory236Part3ProductionandSupplyChapter9:ProductionFunctions295Chapter10:CostFunctions323Chapter11:ProfitMaximization358Part4CompetitiveMarketsChapter12:ThePartialEquilibriumCompetitiveModel391Chapter13:GeneralEquilibriumandWelfare441Part5MarketPowerChapter14:Monopoly491Chapter15:ImperfectCompetition521Part6PricinginInputMarketsChapter16:LaborMarkets573Chapter17:CapitalandTime595Part7MarketFailureChapter18:AsymmetricInformation627Chapter19:ExternalitiesandPublicGoods670ix

BriefAnswerstoQueries701SolutionstoOdd-NumberedProblems711GlossaryofFrequentlyUsedTerms721Index727xBriefContents

ContentsPrefacexixPART1INTRODUCTION1CHAPTER1EconomicModels3TheoreticalModels3VerificationofEconomicModels3GeneralFeaturesofEconomicModels5DevelopmentoftheEconomicTheoryofValue8ModernDevelopments16Summary17SuggestionsforFurtherReading18CHAPTER2MathematicsforMicroeconomics19MaximizationofaFunctionofOneVariable19FunctionsofSeveralVariables23MaximizationofFunctionsofSeveralVariables28ImplicitFunctions31TheEnvelopeTheorem32ConstrainedMaximization36EnvelopeTheoreminConstrainedMaximizationProblems42InequalityConstraints43Second-OrderConditions45HomogeneousFunctions53Integration56DynamicOptimization60MathematicalStatistics64Summary74Problems75SuggestionsforFurtherReadings79Extensions:Second-OrderConditionsandMatrixAlgebra81xi

PART2CHOICEANDDEMAND85CHAPTER3PreferencesandUtility87AxiomsofRationalChoice87Utility88TradesandSubstitution91AMathematicalDerivation97UtilityFunctionsforSpecificPreferences100TheMany-GoodCase104Summary105Problems106SuggestionsforFurtherReading109Extensions:SpecialPreferences110CHAPTER4UtilityMaximizationandChoice113AnInitialSurvey114TheTwo-GoodCase:AGraphicalAnalysis114Then-GoodCase118IndirectUtilityFunction124TheLumpSumPrinciple125ExpenditureMinimization127PropertiesofExpenditureFunctions130Summary132Problems132SuggestionsforFurtherReading136Extensions:BudgetShares137CHAPTER5IncomeandSubstitutionEffects141DemandFunctions141ChangesinIncome143ChangesinaGood’sPrice144TheIndividual’sDemandCurve148CompensatedDemandCurves151AMathematicalDevelopmentofResponsetoPriceChanges155DemandElasticities158ConsumerSurplus165RevealedPreferenceandtheSubstitutionEffect169Summary172Problems173xiiContents

SuggestionsforFurtherReading176Extensions:DemandConceptsandtheEvaluationofPriceIndices178CHAPTER6DemandRelationshipsAmongGoods182TheTwo-GoodCase182SubstitutesandComplements184NetSubstitutesandComplements186SubstitutabilitywithManyGoods188CompositeCommodities188HomeProduction,AttributesofGoods,andImplicitPrices191Summary195Problems195SuggestionsforFurtherReading199Extensions:SimplifyingDemandandTwo-StageBudgeting200CHAPTER7UncertaintyandInformation202MathematicalStatistics202FairGamesandtheExpectedUtilityHypothesis203ThevonNeumann–MorgensternTheorem205RiskAversion207MeasuringRiskAversion209ThePortfolioProblem214TheState-PreferenceApproachtoChoiceunderUncertainty216TheEconomicsofInformation221PropertiesofInformation221TheValueofInformation222FlexibilityandOptionValue224AsymmetryofInformation225Summary226Problems226SuggestionsforFurtherReading231Extensions:PortfoliosofManyRiskAssets232CHAPTER8StrategyandGameTheory236BasicConcepts236Prisoners’Dilemma237NashEquilibrium240Contentsxiii

MixedStrategies247Existence251ContinuumofActions252SequentialGames255RepeatedGames259IncompleteInformation268SimultaneousBayesianGames268SignalingGames273ExperimentalGames281EvolutionaryGamesandLearning282Summary283Problems284SuggestionsforFurtherReading287Extensions:ExistenceofNashEquilibrium288PART3PRODUCTIONANDSUPPLY293CHAPTER9ProductionFunctions295MarginalProductivity295IsoquantMapsandtheRateofTechnicalSubstitution298ReturnstoScale302TheElasticityofSubstitution305FourSimpleProductionFunctions306TechnicalProgress311Summary315Problems315SuggestionsforFurtherReading319Extensions:Many-InputProductionFunctions320CHAPTER10CostFunctions323DefinitionsofCost323Cost-MinimizingInputChoices325CostFunctions330CostFunctionsandShiftsinCostCurves334Shephard’sLemmaandtheElasticityofSubstitution344Short-Run,Long-RunDistinction344Summary350Problems351xivContents

SuggestionsforFurtherReading354Extensions:TheTranslogCostFunction355CHAPTER11ProfitMaximization358TheNatureandBehaviorofFirms358ProfitMaximization359MarginalRevenue361Short-RunSupplybyaPrice-TakingFirm365ProfitFunctions369ProfitMaximizationandInputDemand374Summary380Problems381SuggestionsforFurtherReading385Extensions:ApplicationsoftheProfitFunction386PART4COMPETITIVEMARKETS389CHAPTER12ThePartialEquilibriumCompetitiveModel391MarketDemand391TimingoftheSupplyResponse395PricingintheVeryShortRun395Short-RunPriceDetermination396ShiftsinSupplyandDemandCurves:AGraphicalAnalysis401MathematicalModelofMarketEquilibrium403Long-RunAnalysis406Long-RunEquilibrium:ConstantCostCase407ShapeoftheLong-RunSupplyCurve410Long-RunElasticityofSupply412ComparativeStaticsAnalysisofLong-RunEquilibrium413ProducerSurplusintheLongRun416EconomicEfficiencyandWelfareAnalysis419PriceControlsandShortages422TaxIncidenceAnalysis423TradeRestrictions427Summary431Problems432SuggestionsforFurtherReading436Extensions:DemandAggregationandEstimation438Contentsxv

CHAPTER13GeneralEquilibriumandWelfare441PerfectlyCompetitivePriceSystem441ASimpleGraphicalModelofGeneralEquilibriumwithTwoGoods442ComparativeStaticsAnalysis451GeneralEquilibriumModelingandFactorPrices453ExistenceofGeneralEquilibriumPrices455GeneralEquilibriumModels462WelfareEconomics466EfficiencyinOutputMix469CompetitivePricesandEfficiency:TheFirstTheoremofWelfareEconomics471DepartingfromtheCompetitiveAssumptions475DistributionandtheSecondTheoremofWelfareEconomics476Summary481Problems482SuggestionsforFurtherReading486Extensions:ComputableGeneralEquilibriumModels487PART5MARKETPOWER489CHAPTER14Monopoly491BarrierstoEntry491ProfitMaximizationandOutputChoice493MonopolyandResourceAllocation497Monopoly,ProductQuality,andDurability501PriceDiscrimination503Second-DegreePriceDiscriminationthroughPriceSchedules508RegulationofMonopoly510DynamicViewsofMonopoly513Summary513Problems514SuggestionsforFurtherReading518Extensions:OptimalLinearTwo-partTariffs519CHAPTER15ImperfectCompetition521Short-RunDecisions:PricingandOutput521BertrandModel523xviContents

CournotModel524CapacityConstraints531ProductDifferentiation531TacitCollusion537Longer-RunDecisions:Investment,Entry,andExit541StrategicEntryDeterrence547Signaling551HowManyFirmsEnter?554Innovation558Summary560Problems561SuggestionsforFurtherReading565Extensions:StrategicSubstitutesandComplements566PART6PRICINGININPUTMARKETS571CHAPTER16LaborMarkets573AllocationofTime573AMathematicalAnalysisofLaborSupply576MarketSupplyCurveforLabor580LaborMarketEquilibrium581MonopsonyintheLaborMarket584LaborUnions586Summary589Problems590SuggestionsforFurtherReading594CHAPTER17CapitalandTime595CapitalandtheRateofReturn595DeterminingtheRateofReturn597TheFirm’sDemandforCapital604PresentDiscountedValueApproachtoInvestmentDecisions606NaturalResourcePricing611Summary614Problems614SuggestionsforFurtherReading618Appendix:TheMathematicsofCompoundInterest619Contentsxvii

PART7MARKETFAILURE625CHAPTER18AsymmetricInformation627ComplexContractsasaResponsetoAsymmetricInformation627Principal-AgentModel629HiddenActions630Owner-ManagerRelationship632MoralHazardinInsurance637HiddenTypes642NonlinearPricing642AdverseSelectioninInsurance650MarketSignaling657Auctions659Summary663Problems663SuggestionsforFurtherReading666Extensions:NonlinearPricingwithaContinuumofTypes667CHAPTER19ExternalitiesandPublicGoods670DefiningExternalities670ExternalitiesandAllocativeInefficiency672SolutionstotheExternalityProblem675AttributesofPublicGoods679PublicGoodsandResourceAllocation680LindahlPricingofPublicGoods684VotingandResourceAllocation687ASimplePoliticalModel690VotingMechanisms692Summary694Problems694SuggestionsforFurtherReading698Extensions:PollutionAbatement699BriefAnswerstoQueries701SolutionstoOdd-NumberedProblems711GlossaryofFrequentlyUsedTerms721Index727xviiiContents

PrefaceThe10theditionofMicroeconomicTheory:BasicPrinciplesandExtensionsrepresentsbothacontinuationofahighlysuccessfultreatmentofmicroeconomicsatarelativelyadvancedlevelandamajorchangefromthepast.Thischange,ofcourse,isthatChrisSnyderhasjoinedmeasaco-author.Hisinsightshaveimprovedallsectionsofthebook,especiallywithrespecttoitscoverageofgametheory,industrialorganization,andmodelsofimperfectinformation.Henceinmanywaysthisisanewbook,althoughonmattersofstyleandpedagogyitretainsmuchofwhathasmadeitsuccessfulformorethan35years.Thisbasicapproachistofocusonbuildingintuitionabouteconomicmodelswhileprovidingstudentswiththemathematicaltoolsneededtogofurtherintheirstudies.Thetextalsoseekstofacilitatethatlinkagebyprovidingmanynumericalexamples,advancedproblems,andextendeddiscussionsofempiricalimplementation—allofwhichareintendedtoshowstudentshowmicroeconomictheoryisusedtoday.Newdevelopmentshavemadethefieldmoreexcitingthanever,andIhopethiseditionmanagestocapturethatexcitement.NEWTOTHETENTHEDITIONTheprimarychangetothiseditionhasbeentheinclusionofthreeentirelynewchapterswrittenbyChrisSnyder:anextendedandmoreadvancedtreatmentofbasicgametheoryconcepts(Chapter8);athoroughlyreworkedandexpandedchapteronmodelsusedinindustrialorgani-zationtheory(Chapter15);andacompletelynewchapteronasymmetricinformationthatfocusesontheprincipal–agentproblemandmoderncontracttheory(Chapter18).Theimportanceoftheseadditionstotheoverallqualityofthetextcannotbeoverstated.Becausethetopicscoveredinthesenewchaptersconstitutesomeofthemostimportantgrowthareasinmicroeconomics,thebookisnowwellpositionedformanyyearsintothefuture.Severalotherchaptersofthebookhaveundergonemajorrevisionsforthisedition.Asignificantamountofmaterialhasbeenaddedtothechapteronmathematicalbackground(Chapter2);newtopicsinclude:anexpandedcoverageofintegration,basicmodelsofdynamicoptimization,andabriefintroductiontomathematicalstatistics.Thematerialonuncertaintyandriskaversionhasbeenthoroughlyrevisedandupdated(Chapter7).Muchofthetheoryofthefirm,especiallyofthefirm’sdemandsforinputs,hasbeenexpanded(Chapters9–11).xix

Thechapterongeneralequilibriummodeling(Chapter13)hasbeenthoroughlyreworkedwiththegoalofprovidingstudentswithmoredetailsabouthowcompu-tablegeneralequilibriummodelsactuallywork.Thechapteroncapitalandtime(Chapter17)hasbeensignificantlyexpandedtoincludemoreonoptimalsavingsbehaviorandonresourceallocationovertime.Numerousminorchangeshavealsobeenmadeinthecoverageandorganizationofthebooktoensurethatitcontinuestoprovideclearandup-to-datecoverageofallofthetopicsexamined.Twomodificationshavebeenmadetothetexttoenhanceitslinkagetomoregeneraleconomicliterature.First,theproblemshavebeencategorizedintotwotypes:basicproblemsandanalyticalproblems.Whereasthebasicproblemsareintendedtoreinforceconceptsfromthetext,theanalyticalproblemsareintendedtoallowthestudenttogofurtherbyshowingthemhowtoobtainresultsontheirown.Thenumberofsuchproblemshasbeensignificantlyexpandedinthisedition.Manyoftheanalyticalproblemsprovidereferencessothatstudentswhowishtopursuethetopiccanreadmore.Asecondmodificationofthetexthasbeentoexpandandrewritemanyoftheend-of-chapterExtensions.ThecommongoaloftheserevisedExtensionsistoprovidestudentsbetterlinkagebetweenthetheoreticalmaterialinthetextandthatmaterial’suseinactualempiricalapplications.Therefore,manyoftheExtensionsintroducethefunctionalformscustomarilyusedaswellassomeoftheeconometricissuesfacedbyresearcherswhenusingavailabledata.TheExtensionsarethusintendedtoshowstudentstheimportanceofjoiningmicroeconomictheoryandeconometricpractice.SUPPLEMENTSTOTHETEXTThethoroughlyrevisedancillariesforthiseditionincludethefollowing.TheSolutionsManualandTestBank(bythetextauthors).TheSolutionsManualcontainscommentsandsolutionstoallproblemsandisavailabletoalladoptinginstructorsinbothprintandelectronicversions.TheSolutionsManualandTestBankmaybedownloadedonlybyqualifiedinstructorsatthetextbooksupportWebsite(www.thomsonedu.com/economics/nicholson).PowerPointLecturePresentationSlides(byLindaGhent,EasternIllinoisUniversity).PowerPointslidesforeachchapterofthetextprovideathoroughsetofoutlinesforclassroomuseorforstudentsasastudyaid.Instructorsandstudentsmaydown-loadtheseslidesfromthebook’sWebsite(www.thomsonedu.com/economics/nicholson).ONLINERESOURCESThomsonSouth-Westernprovidesstudentsandinstructorswithasetofvaluableonlineresourcesthatareaneffectivecomplementtothistext.EachnewcopyofthebookcomeswitharegistrationcardthatprovidesaccesstoEconomicApplicationsandInfoTracCollegeEdition.EconomicApplicationsThepurchaseofthisnewtextbookincludescomplimentaryaccesstoSouth-Western’sEconomicApplications(EconApps)Website.TheEconAppsWebsiteincludesasuiteofxxPreface

regularlyupdatedWebfeaturesforeconomicsstudentsandinstructors:EconDebateOnline,EconNewsOnline,EconDataOnline,andEconLinksOnline.Theseresourcescanhelpstudentsdeepentheirunderstandingofeconomicconceptsbyanalyzingcurrentnewsstories,policydebates,andeconomicdata.EconAppscanalsohelpinstructorsdevelopassignments,casestudies,andexamplesbasedonreal-worldissues.EconDebatesOnlineprovidescurrentcoverageofeconomicspolicydebates;itincludesaprimerontheissues,linkstobackgroundinformation,andcommentaries.EconNewsOnlinesummarizesrecenteconomicsnewsstoriesandoffersquestionsforfurtherdiscussion.EconDataOnlinepresentscurrentandhistoricaleconomicdatawithaccompanyingcom-mentary,analysis,andexercises.EconLinksOnlineoffersanavigationpartnerforexploringeconomicsontheWebviaalistofkeytopiclinks.StudentsbuyingausedbookcanpurchaseaccesstotheEconAppssiteathttp://econapps.swlearning.com.InfoTracCollegeEditionThepurchaseofthisnewtextbookalsocomeswithfourmonthsofaccesstoInfoTrac.Thispowerfulandsearchableonlinedatabaseprovidesaccesstofulltextarticlesfrommorethanathousanddifferentpublicationsrangingfromthepopularpresstoscholarlyjournals.Instructorscansearchtopicsandselectreadingsforstudents,andstudentscansearcharticlesandreadingsforhomeworkassignmentsandprojects.Thepublicationscoveravarietyoftopicsandincludearticlesthatrangefromcurrenteventstotheoreticaldevelopments.InfoTracCollegeEditionoffersinstructorsandstudentstheabilitytointegratescholarshipandapplicationsofeconomicsintothelearningprocess.ACKNOWLEDGMENTSInpreparationforundertakingthisrevision,wereceivedveryhelpfulreviewsfrom:TiborBesedes,LouisianaStateUniversityElaineP.Catilina,AmericanUniversityYiDeng,SouthernMethodistUniversitySilkeForbes,UniversityofCalifornia–SanDiegoJosephP.Hughes,RutgersUniversityQihongLiu,UniversityofOklahomaRaganPetrie,GeorgiaStateUniversityWehaveusuallytriedtofollowtheirgoodadvice,butofcoursenoneoftheseindividualsbearsanyresponsibilityforthefinaloutcome.Thiseditionofthebookisthefirstthatwaswrittenwithmyco-author,ChrisSnyderofDartmouthCollege.IhavebeenverypleasedwiththeworkingrelationshipwehavedevelopedandwithChris’sfriendship.Ihopemanymoreeditionswillfollow.IamalsoindebtedtotheteamatThomsonSouth-WesternandespeciallytoSusanSmartforonceagainbringingherorganizingandcajolingskillstothisedition.Duringhertemporaryabsencefromtheproject,wewerecompletelylost.Prefacexxi

Copyeditingthismanuscriptwas,Iknow,arealchore.ThoseatNewgen-Austindidagreatjobofpenetratingourmessymanuscriptstoobtainsomethingthatactuallymakessense.ThedesignofthetextbyMichelleKunklersucceededinachievingtwoseeminglyirreconcilablegoals—makingthetextbothcompactandeasytoread.CliffKallemeyndidafinejobofkeepingtheproductionontrack;Iespeciallyappreciatedthewayhecoordinatedthecopyeditingandpageproductionprocesses.Asalways,myAmherstCollegecolleaguesandstudentsdeservesomeofthecreditforthisnewedition.FrankWesthoffhasbeenmymostfaithfuluserofthistextovermanyyears.Thistime(withhispermission,Ithink)Iactuallyliftedsomeofhisworkongeneralequilibriumtosignificantlyimprovethatportionofthetext.Tothelistofformerstudents—MarkBruni,EricBudish,AdrianDillon,DavidMacoy,TatyanaMamut,KatieMerrill,JordanMilev,DougNorton,andJeffRodman—whoseeffortsarestillevidentIcannowaddthenameofAnoopMenon,whohelpedmesolveproblemswhenIranoutofpatiencewiththealgebra.Asalways,specialthanksagaingotomywifeSusan;afterseeingtwentyeditionsofmymicroeconomicstextscomeandgo,shemustsurelyhopethateventhisgoodthingmusteventuallycometoanend.Mychildren(Kate,David,Tory,andPaul)allseemtobelivinghappyandproductivelivesdespiteaseverelackofmicroeconomiceducation.Asthenextgeneration(Beth,Sarah,David,Sophia,andAbby)growsolder,perhapstheywillseekenlightenment—atleasttotheextentofwonderingwhatthebooksdedicatedtothemareallabout.WalterNicholsonAmherst,MassachusettsJune2007ItwasaprivilegetocollaboratewithWalteronthistenthedition.IusedthistextbookinthefirstcourseIevertaught,asagraduateinstructoratMIT,andIhaveenjoyedusingitinmymicroeconomicscoursesinthethirteenyearssince.Ihavealwaysappreciatedthetext’sambitiouscoverageoftheconceptsandmethodsusedbyprofessionaleconomistsaswellasitsaccessibilitytostudents,whichisenhancedbynumerouselegantexamplestogetherwithWalter’slucidprose.Itwasachallengetomaintainthishighstandardwithmycon-tribution—althoughthiswasmadeeasierbyWalter’ssuggestions,patience,andexample,forwhichIamgrateful.Iencourageteachersandstudentstoe-mailmewithanycommentsonthetext([email protected]).IwouldliketoaddmywholeheartedthankstothosewhomWalteracknowledgedforcontributingtothebook.IalsothankGretchenOttoandhercolleaguesatNewgen–AustinaswellasMattDarnellforcarefullycopyeditingmyportionoftherevision.IthankDartmouthCollegeforprovidingtheresourcesandenvironmentthatgreatlyfacilitatedwritingthebook.Ithankmycolleaguesintheeconomicsdepartmentforhelpfuldiscussionsandunderstanding.Committingtosuchanextensiveprojectisinsomesenseafamilydecision.Iamindebtedtomywife,Maura,foraccommodatingthemanylatenightsthatwererequiredandforlisteningtomymonotonousprogressreports.Ithankmydaughters,Clare,Tess,andMeg,fortheirgoodbehavior,whichexpeditedthewritingprocess.ChristopherSnyderHanover,NewHampshireJune2007xxiiPreface

PART1IntroductionCHAPTER1EconomicModelsCHAPTER2MathematicsforMicroeconomicsThispartcontainsonlytwochapters.Chapter1examinesthegeneralphilosophyofhoweconomistsbuildmodelsofeconomicbehavior.Chapter2thenreviewssomeofthemathematicaltoolsusedintheconstructionofthesemodels.ThemathematicaltoolsfromChapter2willbeusedthroughouttheremainderofthisbook.

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CHAPTER1EconomicModelsThemaingoalofthisbookistointroduceyoutothemostimportantmodelsthateconomistsusetoexplainthebehaviorofconsumers,firms,andmarkets.Thesemodelsarecentraltothestudyofallareasofeconomics.Therefore,itisessentialtounderstandboththeneedforsuchmodelsandthebasicframeworkusedtodevelopthem.Thegoalofthischapteristobeginthisprocessbyoutliningsomeoftheconceptualissuesthatdeterminethewaysinwhicheconomistsstudypracticallyeveryquestionthatintereststhem.THEORETICALMODELSAmoderneconomyisacomplicatedentity.Thousandsoffirmsengageinproducingmillionsofdifferentgoods.Manymillionsofpeopleworkinallsortsofoccupationsandmakedecisionsaboutwhichofthesegoodstobuy.Let’susepeanutsasanexample.Peanutsmustbeharvestedattherighttimeandshippedtoprocessorswhoturnthemintopeanutbutter,peanutoil,peanutbrittle,andnumerousotherpeanutdelicacies.Theseprocessors,inturn,mustmakecertainthattheirproductsarriveatthousandsofretailoutletsintheproperquantitiestomeetdemand.Becauseitwouldbeimpossibletodescribethefeaturesofeventhesepeanutmarketsincompletedetail,economistshavechosentoabstractfromthecomplexitiesoftherealworldanddeveloprathersimplemodelsthatcapturethe“essentials.”Justasaroadmapishelpfuleventhoughitdoesnotrecordeveryhouseoreverystore,economicmodelsof,say,themarketforpeanutsarealsousefuleventhoughtheydonotrecordeveryminutefeatureofthepeanuteconomy.Inthisbookwewillstudythemostwidelyusedeconomicmodels.Wewillseethat,eventhoughthesemodelsoftenmakeheroicabstractionsfromthecomplexitiesoftherealworld,theynonethelesscaptureessentialfeaturesthatarecommontoalleconomicactivities.Theuseofmodelsiswidespreadinthephysicalandsocialsciences.Inphysics,thenotionofa“perfect”vacuumoran“ideal”gasisanabstractionthatpermitsscientiststostudyreal-worldphenomenainsimplifiedsettings.Inchemistry,theideaofanatomoramoleculeisactuallyasimplifiedmodelofthestructureofmatter.Architectsusemock-upmodelstoplanbuildings.Televisionrepairersrefertowiringdiagramstolocateproblems.Economists’modelsperformsimilarfunctions.Theyprovidesimplifiedportraitsofthewayindividualsmakedecisions,thewayfirmsbehave,andthewayinwhichthesetwogroupsinteracttoestablishmarkets.VERIFICATIONOFECONOMICMODELSOfcourse,notallmodelsprovetobe“good.”Forexample,theearth-centeredmodelofplanetarymotiondevisedbyPtolemywaseventuallydiscardedbecauseitprovedincapableofaccuratelyexplaininghowtheplanetsmovearoundthesun.Animportantpurposeofscientificinvestigationistosortoutthe“bad”modelsfromthe“good.”Twogeneralmethodshave3

beenusedforverifyingeconomicmodels:(1)adirectapproach,whichseekstoestablishthevalidityofthebasicassumptionsonwhichamodelisbased;and(2)anindirectapproach,whichattemptstoconfirmvaliditybyshowingthatasimplifiedmodelcorrectlypredictsreal-worldevents.Toillustratethebasicdifferencesbetweenthetwoapproaches,let’sbrieflyexamineamodelthatwewilluseextensivelyinlaterchaptersofthisbook—themodelofafirmthatseekstomaximizeprofits.Theprofit-maximizationmodelThemodelofafirmseekingtomaximizeprofitsisobviouslyasimplificationofreality.Itignoresthepersonalmotivationsofthefirm’smanagersanddoesnotconsiderconflictsamongthem.Itassumesthatprofitsaretheonlyrelevantgoalofthefirm;otherpossiblegoals,suchasobtainingpowerorprestige,aretreatedasunimportant.Themodelalsoassumesthatthefirmhassufficientinformationaboutitscostsandthenatureofthemarkettowhichitsellstodiscoveritsprofit-maximizingoptions.Mostreal-worldfirms,ofcourse,donothavethisinformationreadilyavailable.Yet,suchshortcomingsinthemodelarenotnecessarilyserious.Nomodelcanexactlydescribereality.Therealquestioniswhetherthissimplemodelhasanyclaimtobeingagoodone.TestingassumptionsOnetestofthemodelofaprofit-maximizingfirminvestigatesitsbasicassumption:Dofirmsreallyseekmaximumprofits?Someeconomistshaveexaminedthisquestionbysendingques-tionnairestoexecutives,askingthemtospecifythegoalstheypursue.Theresultsofsuchstudieshavebeenvaried.Businesspeopleoftenmentiongoalsotherthanprofitsorclaimtheyonlydo“thebesttheycan”toincreaseprofitsgiventheirlimitedinformation.Ontheotherhand,mostrespondentsalsomentionastrong“interest”inprofitsandexpresstheviewthatprofitmaximizationisanappropriategoal.Testingtheprofit-maximizingmodelbytestingitsassumptionshasthereforeprovidedinconclusiveresults.TestingpredictionsSomeeconomists,mostnotablyMiltonFriedman,denythatamodelcanbetestedbyinquiringintothe“reality”ofitsassumptions.1Theyarguethatalltheoreticalmodelsarebasedon“unrealistic”assumptions;theverynatureoftheorizingdemandsthatwemakecertainab-stractions.Theseeconomistsconcludethattheonlywaytodeterminethevalidityofamodelistoseewhetheritiscapableofpredictingandexplainingreal-worldevents.Theultimatetestofaneconomicmodelcomeswhenitisconfrontedwithdatafromtheeconomyitself.Friedmanprovidesanimportantillustrationofthatprinciple.Heaskswhatkindofatheoryoneshouldusetoexplaintheshotsexpertpoolplayerswillmake.Hearguesthatthelawsofvelocity,momentum,andanglesfromtheoreticalphysicswouldbeasuitablemodel.Poolplayersshootshotsasiftheyfollowtheselaws.Butmostplayersaskedwhethertheypreciselyunderstandthephysicalprinciplesbehindthegameofpoolwillundoubtedlyanswerthattheydonot.Nonetheless,Friedmanargues,thephysicallawsprovideveryaccuratepredictionsandthereforeshouldbeacceptedasappropriatetheoreticalmodelsofhowexpertsplaypool.Atestoftheprofit-maximizationmodel,then,wouldbeprovidedbypredictingthebehaviorofreal-worldfirmsbyassumingthatthesefirmsbehaveasiftheyweremaximizingprofits.(SeeExample1.1laterinthischapter.)Ifthesepredictionsarereasonablyinaccordwithreality,wemayaccepttheprofit-maximizationhypothesis.However,wewouldreject1SeeM.Friedman,EssaysinPositiveEconomics(Chicago:UniversityofChicagoPress,1953),chap.1.Foranalternativeviewstressingtheimportanceofusing“realistic”assumptions,seeH.A.Simon,“RationalDecisionMakinginBusinessOrganizations,”AmericanEconomicReview69,no.4(September1979):493–513.4Part1Introduction

themodelifreal-worlddataseeminconsistentwithit.Hence,theultimatetestofeithertheoryisitsabilitytopredictreal-worldevents.ImportanceofempiricalanalysisTheprimaryconcernofthisbookistheconstructionoftheoreticalmodels.Butthegoalofsuchmodelsisalwaystolearnsomethingabouttherealworld.Althoughtheinclusionofalengthysetofappliedexampleswouldneedlesslyexpandanalreadybulkybook,2theEx-tensionsincludedattheendofmanychaptersareintendedtoprovideatransitionbetweenthetheorypresentedhereandthewaysinwhichthattheoryisactuallyappliedinempiricalstudies.GENERALFEATURESOFECONOMICMODELSThenumberofeconomicmodelsincurrentuseis,ofcourse,verylarge.Specificassumptionsusedandthedegreeofdetailprovidedvarygreatlydependingontheproblembeingaddressed.ThemodelsemployedtoexplaintheoveralllevelofeconomicactivityintheUnitedStates,forexample,mustbeconsiderablymoreaggregatedandcomplexthanthosethatseektointerpretthepricingofArizonastrawberries.Despitethisvariety,however,practicallyalleconomicmodelsincorporatethreecommonelements:(1)theceterisparibus(otherthingsthesame)assumption;(2)thesuppositionthateconomicdecisionmakersseektooptimizesomething;and(3)acarefuldistinctionbetween“positive”and“normative”questions.Becausewewillencountertheseelementsthroughoutthisbook,itmaybehelpfulattheoutsettobrieflydescribethephilosophybehindeachofthem.TheceterisparibusassumptionAsinmostsciences,modelsusedineconomicsattempttoportrayrelativelysimplerela-tionships.Amodelofthemarketforwheat,forexample,mightseektoexplainwheatpriceswithasmallnumberofquantifiablevariables,suchaswagesoffarmworkers,rainfall,andconsumerincomes.Thisparsimonyinmodelspecificationpermitsthestudyofwheatpricinginasimplifiedsettinginwhichitispossibletounderstandhowthespecificforcesoperate.Althoughanyresearcherwillrecognizethatmany“outside”forces(presenceofwhe