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