4,IfAMisatmaximumorminimum,thenMM=AM,OrMMcutsAMatthelatter¡¯smaximumorminimum.
Chapter1TheMarket
Theoptimizationprinciple:
Peopletrytochoosewhat¡¯sbestforthem.
Theequilibriumprinciple:
Pricesadjustuntildemandandsupplyareequal.
Thedemandcurve:
acurvethatrelatesthequantitydemandedtoprice.
Thereservationprice:
one¡¯smaximumwillingnesstopayforsomething.
Frompeople'sreservationpricestothedemandcurvebyhorizontalsummation.
Similarly,thesupplycurve.
Theirintersectionisthemarketequilibrium.（Acompetitivemarket）
Comparativestaticsisthestudyofhowtheequilibriumpriceandquantitychangewhentheunderlyingconditionschanges.Theceterisparibusprinciple.
Paretoefficiency:
aconcepttoevaluatedifferentwaysofallocatingresources.
AParetoimprovementisachangetomakesomepeoplebetteroffwithouthurtinganybodyelse.AneconomicsituationisParetoefficientorParetooptimalifthereisalreadynowaytomakeParetoimprovement.
Equilibriaintheshortrun（somefactorsareunchanged）andinthelongrun.
Chapter2BudgetConstraint
Twogoodsareoftenenoughtodiscuss.Thebudgetconstraint:
p1x1+p2x2¡Üm.
Thebudgetlineandthebudgetset（themarketopportunityset）.Fig.
Theslopeofthebudgetline:
dx2/dx1=¨Cp1/p2.
Howthebudgetlinechangeswhenincomeincreases,orwhenapriceincreases.Figs.
Rationing.It¡¯seffectsonthebudgetset.Fig.
Chapter3Preferences
Considerrationalagentsandtheirstablepreferences.
Bundlexisstrictlypreferred（s.p.）,orweaklypreferred（w.p.）,orindifferent（ind.）,toBundley.（Ifxisw.p.toyandyisw.p.tox,wesayxisindifferenttoy.）
AssumptionsaboutPreferences:
Completeness:
xisw.p.toyoryisw.p.toxforanypairofxandy.
Reflexivity:
xisw.p.toxforanybundlex.
Transitivity:
Ifxisw.p.toyandyisw.p.toz,thenxisw.p.toz.
Theindifferencesets,theindifferencecurves.Fig.Theycannotcrosseachother.
Perfectsubstitutesandperfectcomplements.Goods,bads,neutrals.Satiation.Figs.
Well-behavedpreferencesaremonotonic（meaningmoreisbetter）andconvex（meaningaveragearepreferredtoextremes）.Figs.
Themarginalrateofsubstitution（MRS）measurestheslopeoftheindifferencecurve.MRS=dx2/dx1.Itisthemarginalwillingnesstopay（howmuchtogiveupofx2toacquireonemoreofx1）.Usuallynegative.Fig.
Convexindifferencecurvesexhibitadiminishingmarginalrateofsubstitution.Fig.
Chapter4Utility,asawaytodescribepreferences
Essentialordinalutilities,versusconvenientcardinalutilityfunctions:
u（x）¡Ýu（y）ifandonlyifbundlexisw.p.tobundley.Fig.
Theindifferencecurvesaretheprojectionsofcontoursoftheu=u（x1,x2）.Fig.
Utilityfunctionsareindifferentuptoanystrictlyincreasingtransformation.
Examplesofutilityfunctions:
u（x1,x2）=x1x2;u（x1,x2）=x12x22;Fig.
u（x1,x2）=ax1+bx2（perfectsubstitutes）;Fig.
u（x1,x2）=min{ax1,bx2}（perfectcomplements）.Fig.
Quasilinearpreferences:
allindifferencecurvesarevertically（orhorizontally）shiftedcopiesofasingleone,forexampleu（x1,x2）=v（x1）+x2.Fig.
Cobb-Douglaspreferences:
u（x1,x2）=x1cx2d,oru（x1,x2）=x1ax21-awitha=c/（c+d）;andtheirlogequivalents:
u（x1,x2）=clnx1+dlnx2,oru（x1,x2）=alnx1+（1¨Ca）lnx2.Fig.
Marginalutilities,andMRSalonganindifferencecurve.
DeriveMRS=¨CMU1/MU2bytakingtotaldifferentialalonganyindifferencecurve.
Chapter5ChoiceofConsumption
Optimalchoiceisatthepointinthebudgetlinewithhighestutility.
Thetangencysolutionofanindifferencecurveandthebudgetline:
MRS=¨Cp1/p2.Fig.
Basicequations:
MU1/p1=MU2/p2andp1x1+p2x2=m.（howifnegativesolutions）
Interiorandboundary（corner）solutions.Kinkytastes.Multipletangencies.Figs.
Threeapproachestothebasicequations:
Graphical（Tangency）;As-one-variable;and*Lagrangian.
Theoptimalchoiceistheconsumer¡¯sdemandedbundle.Thedemandfunction.
Examples:
perfectsubstitutes,perfectcomplements,goods,bads,andneutrals,convexandconcavepreferences,Codd-Douglasdemandfunctions.Figs.
Chapter6Demand
Demandfunctions:
x1=x1（p1,p2,m）,x2=x2（p1,p2,m）.
Inferiorandultra-superiorgoods（byincome）;Fig.
Luxuryandnecessarygoods（byincome）.Fig.
NormalandGiffengoods（byprice）.Fig.
Theincomeexpansionpathortheincomeoffercurves（x1-x2plane）,andtheEngelcurve（m¨Cx1plane）.Figs.
Thepriceoffercurve（x1-x2plane）andthedemandcurve（p1¨Cx1plane）.Figs.
Substitutesandcomplements.Codd-Douglaspreferences.Quasilinearpreferences.
Example:
Quasilinearpreferencesleadtovertical（horizontal）incomeoffercurvesandvertical（horizontal）Engelcurves.
Chapter8SlutskyEquation
Howtheoptimummoveswhenthepriceofagoodchanges?
Decomposition:
thetotaleffect=thesubstitutioneffect+theincomeeffect.
Thepivotgivesthesubstitutioneffect,theshiftgivestheincomeeffect.
Slutskydecomposition,pivotingthebudgetlinearoundtheoriginalchoice.Fig.
Hicksdecomposition,pivotingthebudgetlinearoundtheindifferencecurve.Fig.
Thelawofdemand.Choosingtaxes.（Fig.5.9）
Chapter9BuyingandSellingforaconsumerwithanendowment¦Ø
Offercurveanddemandcurve.Afigurereview.
Laborsupply.Agraphicaldiscussion.
Chapter12Uncertainty
Utilityfunctionsandprobabilities.Expectedutilityfunctions,orvonNeumann-Morgensternutilityfunctions:
EU=¦²ipiU（si）,wherepiistheprobabilitytheeventsioccurs.
Theyareindifferentuptoanypositiveaffinetransformation.
Riskaversionandriskloving.Concavevsconvexutility.Thesecondderivative.
Chapter14Consumer¡¯sSurplus
Demandforadiscretegood.Reservationpricesandconsumer¡¯ssurplus.Fig.
Producer¡¯ssurplus.Fig.Calculatinggainsandlosses.Thewater-diamondparadox.
Chapter15MarketDemand
Addingupdemandcurves:
thehorizontalsummationprinciple.Fig.
Thepriceelasticityofdemand:
¡¡¡¡¡¡¡¡¦Å=（¦¤q/q）/（¦¤p/p）=（p/q）/（¦¤p/¦¤q）,or
¡¡¡¡¡¡¡¡¦Å=（dq/q）/（dp/p）=（p/q）/（dp/dq）.
Itisnormallynegative.So,veryoftenpeopleturntoconsideritsabsolutevalue|¦Å|.
Acommodityhasanelastic（inelastic,unit）demandif|¦Å|>1（|¦Å|<1,|¦Å|=1）.
¡¡¡¡¡¡¡¡Elasticityandrevenue.R=pq,dR=qdp+pdq,andthen
¡¡¡¡¡¡¡¡dR/dp=q[1+¦Å（p）]where¦Å（p）=（pdq）/（qdp）.Fig.
Similarly,MR=dR/dq=p（q）[1+1/¦Å（q）]where¦Å（q）=（pdq）/（qdp）.
Strikesandprofits.TheLaffercurve.
Constantelasticitydemands.Anotherwaytoexpresselasticity:
¦Å=dlnq/dlnp.
Theincomeelasticityofdemand¦Ç.Withp1x1+p2x2=m,wehave1=p1dx1/dm+p2dx2/dm=s1¦Ç1+s2¦Ç2,wheresiistheexpenditureshareofgoodi.
Thearcelasticityvsthepointelasticity.
Chapter16PartialEquilibrium
Themarketsupplycurve.Acompetitivemarket.Theequilibrium.Paretoefficiency.Fig.
Marketsurplusandmarketshortage.Fig.Shortageisnotscarcity.
Twospecialcases:
ofaverticalsupplyandofahorizontalsupply.Figs.
Algebraoftheequilibrium:
D（p）=S（p）.Comparativestatics.Shiftingbothcurves.
Taxes.DistinguishPp,thepricepaidbyconsumers,Pr,thepricereceivedbyproducers,Pl,thelistprice,andPo,theoriginalprice.
Thetwowaystoanalyzetheeffectofatax（imposedondemandorimposedonsupply）areequivalent.
Algebraoftheequilibriumwithatax:
D（pp）=S（pr）,andpp=pr+T.
Whobearstheburdenofatax?
Theonewithlesselasticitysharesmoreburden.
Passingalongatax.Thedeadweightlossofatax.Figs.
Asubsidyistheoppositeofatax.
Chapter18Technology
Thesefourchaptersfocusmainlyonresourceallocationinsiderfirms.
Inputsandoutputs.Factorsofproduction:
land,labor,capital,rawmateri
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