The economics of uncertainty and information by Timothy Van Zandt

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1 Introduction to decision theory 1
1.1 Whyindividualdecisiontheoryineconomics? . . . . . . . . . . . . . 1
1.2 Descriptive,prescriptiveandnormativetheories . . . . . . . . . . . . 1
1.3 Areviewofchoice,preferencesandutility . . . . . . . . . . . . . . . 2
2 Lotteries and objective expected utility 7
2.1 Simpleandcompoundlotteries . . . . . . . . . . . . . . . . . . . . . 7
2.2 TheIndependenceAxiom . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 First-orderstochasticdominance . . . . . . . . . . . . . . . . . . . . 19
2.4 ContinuityAxiom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.5 ExpectedUtility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3 States of nature and subjective expected utility 31
3.1 States,actionsandoutcomes . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Fromlargeworldstosmallworlds . . . . . . . . . . . . . . . . . . . . 31
3.3 Outcomesandstate-independentpreferences . . . . . . . . . . . . . 35
3.4 Objectiveexpectedutility . . . . . . . . . . . . . . . . . . . . . . . . 37
3.5 Subjectiveexpectedutility . . . . . . . . . . . . . . . . . . . . . . . . 38
3.6 Statewisedominance . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4 Choosing when there is new information 41
4.1 Representinginformation . . . . . . . . . . . . . . . . . . . . . . . . 41
4.2 Bayes’Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.3 IndependenceandExchangeability . . . . . . . . . . . . . . . . . . . 58
5 Risk Preferences 65
5.1 Moneyoutcomesandriskaversion . . . . . . . . . . . . . . . . . . . 65
5.2 Comparingtheriskaversionofpeople . . . . . . . . . . . . . . . . . 74
5.3 Comparingtheriskinessofacts . . . . . . . . . . . . . . . . . . . . . 77
6 Market Decisions in the Presence of Risk 89
6.1 Demandforastate-contingentcontract . . . . . . . . . . . . . . . . 89
6.2 Techniquesforcharacterizingmarketdecisions . . . . . . . . . . . . 94
6.3 Comparativestatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.4 State-dependentutility . . . . . . . . . . . . . . . . . . . . . . . . . . 116
7 Markets for state-contingent contracts 121
7.1 Gainsfromsharingrisks . . . . . . . . . . . . . . . . . . . . . . . . . 122
7.2 Insurancemarket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Economics of Uncertainty and Information ©November 2006 Timothy Van Zandt
ii Economics of Uncertainty and Information
8 Asset Markets 135
8.1 Thenatureofassetmarkets . . . . . . . . . . . . . . . . . . . . . . . 135
8.2 Marketequilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
8.3 Completeversusincompletemarkets . . . . . . . . . . . . . . . . . . 156
8.4 CapitalAssetPricingModel . . . . . . . . . . . . . . . . . . . . . . . 166
9 Contracting with Hidden Actions 171
9.1 Efficientcontractswithmoralhazard . . . . . . . . . . . . . . . . . . 171
9.2 Contractsthatgiveonepartythegainsfromtrade . . . . . . . . . . 172
10 Monopolistic screening with hidden valuations 175
10.1 Nonlinearpricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
10.2 Differentiatedproducts . . . . . . . . . . . . . . . . . . . . . . . . . . 175
10.3 Bundling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
11 Screening with adverse selection 177
11.1 Thenatureofadverseselection . . . . . . . . . . . . . . . . . . . . . 177
11.2 Screening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
11.3 Efficientcontractswithadverseselection . . . . . . . . . . . . . . . . 189
11.4 Theefficientcontractswithzeroexpectedprofits . . . . . . . . . . . 192
11.5 Monopolisticscreening . . . . . . . . . . . . . . . . . . . . . . . . . 200
12 Hidden information after contracting 205
12.1 Hiddeninformationabouthealth . . . . . . . . . . . . . . . . . . . . 205
12.2 Comingupwithamodel . . . . . . . . . . . . . . . . . . . . . . . . . 206
12.3 Incomeredistribution . . . . . . . . . . . . . . . . . . . . . . . . . . 211
13 Signaling 215
13.1 Thedifferencebetweenscreeningandsignaling . . . . . . . . . . . . 215
13.2 Signalinginlabormarkets . . . . . . . . . . . . . . . . . . . . . . . . 215
14 Long-term versus short-term contracting 217
14.1 Ex-anteversusex-postefficiency . . . . . . . . . . . . . . . . . . . . 217
14.2 Long-termandshort-terminsurancecontracts . . . . . . . . . . . . . 220


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关键词：information uncertainty Informatio formation Uncertain objective expected

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