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Axiomatic choice models and duality
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I Introduction.- A The subject of the study.- 1.1 The concept of choice.- 1.2 Examples of choice problems in economics.- B The method of the study.- 1.3 Normative and descriptive theories.- 1.4 The axiomatic method.- 1.5 Deduction and induction.- II Mathematical Concepts for Choice Theory.- 2.1 Introduction.- 2.2 Ordering relations.- 2.3 Mappings and correspondences.- 2.4 Maximal elements and greatest elements.- 2.5 Utility functions.- III Choice Models.- 3.1 Introduction.- 3.2 Primitive concepts.- 3.3 The axioms of the preference model.- 3.4 Revealed preference.- 3.5 Favourability and revealed favourability.- 3.6 The logical significance of the preference model.- 3.7 A choice function model.- 3.8 The connection between the choice function model and the preference model.- 3.9 Some modifications of the choice function model.- 3.10 Summary of the connections between the models 5.- IV Mathematics for Consumer Choice Theory.- 4.1 Introduction.- 4.2 Sets in real Euclidean space.- 4.3 C.u.p. sets.- 4.4 Duality.- 4.5 A theorem on c.u.p. sets.- 4.6 Some properties of real valued functions.- V A Consumer Preference Model.- 5.1 Introduction.- 5.2 Primitive concepts.- 5.3 The axioms of the consumer preference model.- 5.4 The utility function.- 5.5 The demand function and its connection with the choice function.- 5.6 Preference sets.- 5.7 Duality in consumer choice theory.- 5.8 Preordering of the price space and the dual utility function.- 5.9 Demand functions, price functions and revealed preference relations.- VI A Demand Function Model.- 6.1 Introduction.- 6.2 Primitive concepts.- 6.3 The axioms of the demand function model.- 6.4 Reconstruction of preference sets.- 6.5 The axioms of the consumer preference model as theorems in the demand function model.- References.

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