microeconomic theory uncertainty

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1、CHAPTERSEVENUncertaintyInthischapterweexploresomeofthebasicelementsofthetheoryofindividualbehaviorinuncertainsituations.Wediscusswhyindividualsdonotlikeriskandthevariousmeth-ods(buyinginsurance,acquiringmoreinformation,andpreservingoptions)theymayadopttoreduceit.Moregenerally,thechapterisintendedtop

2、rovideabriefintroductiontoissuesraisedbythepossibilitythatinformationmaybeimperfectwhenindividualsmakeutility-maximizingdecisions.TheExtensionssectionprovidesadetailedapplicationoftheconceptsinthischaptertotheportfolioproblem,acentralprobleminfinancialeco-nomics.Whetherawell-informedpersoncantakeadva

3、ntageofapoorlyinformedpersoninamarkettransaction(asymmetricinformation)isaquestionputoffuntilChapter18.MathematicalStatisticsManyoftheformaltoolsformodelinguncertaintyineconomicsituationswereoriginallydevelopedinthefieldofmathematicalstatistics.SomeofthesetoolswerereviewedinChapter2,andinthischapterw

4、ewillmakeagreatdealofuseoftheconceptsintroducedthere.Specifically,fourstatisticalideaswillrecurthroughoutthischapter.•Randomvariable:Arandomvariableisavariablethatrecords,innumericalform,1thepossibleoutcomesfromsomerandomevent.•Probabilitydensityfunction(PDF):Afunctionf(x)thatshowstheprobabilitiesass

5、ociatedwiththepossibleoutcomesfromarandomvariable.•Expectedvalueofarandomvariable:Theoutcomeofarandomvariablethatwilloccur‘‘onaverage.’’TheexpectedvalueisdenotedbyE(x).IfxisadiscreterandomPnvariablewithnoutcomes,thenREðxÞ¼i¼1xifðxiÞ.Ifxisacontinuousrandomþ1variable,thenEðxÞ¼xfðxÞdx.%1•Varianceandsta

6、ndarddeviationofarandomvariable:Theseconceptsmeasurethedispersionofarandomvariableaboutitsexpectedvalue.Inthediscretecase,2Pn22VarRðxÞ¼rx¼i¼1½xi%EðxÞfðxiÞ;inthecontinuouscase,VarðxÞ¼rx¼þ12½x%EðxÞfðxÞdx.Thestandarddeviationisthesquarerootofthevariance.%1Asweshallsee,alltheseconceptswillcomeintoplaywh

7、enwebeginlookingatthedeci-sion-makingprocessofapersonfacedwithanumberofuncertainoutcomesthatcanbeconceptuallyrepresentedbyarandomvariable.1~Whenitisnecessarytodistinguishbetweenrandomvariablesandnonra