Risk and Uncertailt in Economics

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Introduction to the Economics of Uncertainty and Information Timothy Van Zandt INSEAD November 2006 Copyright November 2006 Preliminary and incomplete: Use only with the permission of the author. INSEAD Boulevard de Constance 77305 Fontainebleau CEDEX FRANCE Author’s address: Voice: +33 1 6072 4981 Fax: Email: WWW: +33 1 6074 6192 tvz@insead.edu faculty.insead.edu/vanzandt Table of Contents 1 Introduction to decision theory 1.1 1.2 1.3 Why individual decision theory in economics? . . . .
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  Introduction to the Economics of Uncertainty and Information TimothyVanZandtINSEAD November 2006Copyright November 2006 Preliminary and incomplete: Use only with the permission of the author. Author’s address:INSEADBoulevard de Constance77305 Fontainebleau CEDEXFRANCEVoice: +33 1 6072 4981Fax: +33 1 6074 6192Email: tvz@insead.eduWWW: aculty.insead.edu/vanzandt  TableofContents 1 Introduction todecisiontheory 1 1.1 Whyindividual decision theoryin economics? . . . . . . . . . . . . . 11.2 Descriptive, prescriptive and normative theories . . . . . . . . . . . . 11.3 A review of choice, preferencesand utility . . . . . . . . . . . . . . . 2 2 Lotteriesandobjective expected utility 7 2.1 Simple and compound lotteries . . . . . . . . . . . . . . . . . . . . . 72.2 The Independence Axiom . . . . . . . . . . . . . . . . . . . . . . . . 102.3 First-orderstochastic dominance . . . . . . . . . . . . . . . . . . . . 192.4 Continuity Axiom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.5 Expected Utility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3 Statesofnature andsubjective expected utility 31 3.1 States, actions and outcomes . . . . . . . . . . . . . . . . . . . . . . 313.2 From large worlds to small worlds . . . . . . . . . . . . . . . . . . . . 313.3 Outcomes and state-independent preferences . . . . . . . . . . . . . 353.4 Objective expected utility . . . . . . . . . . . . . . . . . . . . . . . . 373.5 Subjective expected utility . . . . . . . . . . . . . . . . . . . . . . . . 383.6 Statewise dominance . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 4 Choosingwhenthereisnew information 41 4.1 Representinginformation . . . . . . . . . . . . . . . . . . . . . . . . 414.2 Bayes’ Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.3 Independence and Exchangeability . . . . . . . . . . . . . . . . . . . 58 5 RiskPreferences 65 5.1 Money outcomes and risk aversion . . . . . . . . . . . . . . . . . . . 655.2 Comparing the risk aversion of people . . . . . . . . . . . . . . . . . 745.3 Comparing the riskiness of acts . . . . . . . . . . . . . . . . . . . . . 77 6 MarketDecisionsinthePresence ofRisk 89 6.1 Demand fora state-contingentcontract . . . . . . . . . . . . . . . . 896.2 Techniques for characterizing market decisions . . . . . . . . . . . . 946.3 Comparative statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1096.4 State-dependent utility . . . . . . . . . . . . . . . . . . . . . . . . . . 116 7 Marketsforstate-contingent contracts 121 7.1 Gains from sharing risks . . . . . . . . . . . . . . . . . . . . . . . . . 1227.2 Insurance market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Economics of Uncertainty and Information ©November 2006 imothy Van Zandt  ii EconomicsofUncertaintyandInformation 8 AssetMarkets 135 8.1 The nature of asset markets . . . . . . . . . . . . . . . . . . . . . . . 1358.2 Market equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1408.3 Complete versusincomplete markets . . . . . . . . . . . . . . . . . . 1568.4 Capital Asset Pricing Model . . . . . . . . . . . . . . . . . . . . . . . 166 9 Contracting withHiddenActions 171 9.1 Efficient contracts with moral hazard . . . . . . . . . . . . . . . . . . 1719.2 Contractsthat give one partythe gains from trade . . . . . . . . . . 172 10 Monopolisticscreening withhiddenvaluations 175 10.1 Nonlinear pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17510.2 Differentiated products . . . . . . . . . . . . . . . . . . . . . . . . . . 17510.3 Bundling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 11 Screening withadverseselection 177 11.1 The nature of adverse selection . . . . . . . . . . . . . . . . . . . . . 17711.2 Screening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18011.3 Efficient contracts with adverse selection . . . . . . . . . . . . . . . . 18911.4 The efficient contracts with zero expected profits . . . . . . . . . . . 19211.5 Monopolistic screening . . . . . . . . . . . . . . . . . . . . . . . . . 200 12 Hiddeninformationaftercontracting 205 12.1 Hidden information about health . . . . . . . . . . . . . . . . . . . . 20512.2 Coming up with amodel . . . . . . . . . . . . . . . . . . . . . . . . . 20612.3 Income redistribution . . . . . . . . . . . . . . . . . . . . . . . . . . 211 13 Signaling 215 13.1 The difference between screening andsignaling . . . . . . . . . . . . 21513.2 Signaling in labor markets . . . . . . . . . . . . . . . . . . . . . . . . 215 14 Long-termversusshort-termcontracting 217 14.1 Ex-ante versus ex-postefficiency . . . . . . . . . . . . . . . . . . . . 21714.2 Long-term and short-terminsurance contracts . . . . . . . . . . . . . 220
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