MWG Microeconomic Theory Notes.pdf

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1、AdvancedMicroeconomicsKonstantinosSerfesSeptember24,2004Thesenoteshaveborrowedcontentandnotationfromthefollowingtwotextbooks:i)MicroeconomicTheorybyA.Mas-Colell,M.D.WhinstonandJ.Greenandii)AdvancedMicroeconomicTheorybyG.A.JehleandP.J.Reny.Youshouldstudythesenotesinconjuncti

2、onwiththeabovetwotextbooks.Theselecturesnotesarelikelytocontainanumberoferrors.1CONSUMERTHEORYAQUICKOVERVIEWOFCONSUMERTHEORYFormulatetheconsumers’utilitymaximizationproblemsubjecttoabudgetconstraintSolvetheconsumer’sproblemtoderivethedemandfunctionsStudythepropertiesofthedema

3、ndfunctionsTherearefourbuildingblocksinanymodelofconsumerchoice:i)theconsumptionset,ii)thepreferencerelation,iii)thefeasibleset,andiv)thebehavioralassumption.Theconsumptionsetdepictsalltheoptionsthatareavailabletotheconsumer(whethertheseoptionsarea¤ordableofnot).Thepreference

4、relationputssomestructureonhowtheconsumerranksthedi¤erentalternativesavailabletohim.Thefeasiblesetincludesalltheoptionsfromtheconsumptionsetthatarealsoa¤ordable(inasensethatwillbemadepreciselater).Finally,thebehavioralassumptionisabouthowtheconsumerchoosesamonghisalternatives

5、,givenhispreferences.Inparticular,wewillassumethattheconsumerchoosesthebestalternative.Wewillstudyeachoneofthefourbuildingblocksseparatelyandattheendwewillputthemtogethertoposetheconsumer’sconstraintmaximizationproblem.TheconsumptionsetXWeassumethatthereareLcommodities.Eachc

6、ommodity`ismeasuredinsomein…nitelydivisibleunit.Letx`2R+(non-negative)representthenumberofunitsofgood`.Wedenote1avectoroftheLgoods(consumptionbundle)byx=(x1;x2;:::;xL)2R+L:1WemakethefollowingassumptionsaboutX.1.;6=XR+L:2.Xisclosed.23.Xisconvex.34.02X:First,weassumethatthecon

7、sumptionsetisanon-empty(i.e.,itcontainsatleastoneelement)subsetofanLdimensionalEuclideanspace.Assumption2isneededfortechnicalreasonsthatwillbecomeclearlateron(R+Lforinstanceisclosed).ThethirdassumptionensuresthatXhasnoholesinitandnomissingparts(i.e.,averagesofanytwobundlesin

8、thesetalsobelongintheset).Forexample,ifthegoodswerenotperfectlydivis