Bedrosian, Geghard: Ultraproduct construction of representative utility functions with infinite-dimensional domain. 2015
Inhalt
- Acknowledgements
- Contents
- 1 Introduction
- 2 Mathematical methodology
- 2.1 Boolean algebra
- 2.2 Predicate Logic
- 2.3 Ultraproducts
- 2.4 An ultrapower construction of a nonstandard model of the real numbers
- 2.5 Superstructures and bounded ultrapowers
- 2.6 Nonstandard universe
- 2.7 Saturation and topology
- 3 Theorem on microeconomic foundations of representative agent models
- 3.1 The model and formulation
- 3.2 Kirman-Sondermann correspondence
- 3.3 Assumptions
- 3.4 Socially acceptable and representative utility functions
- 4 Illustration: Possible macroeconomic applications
- 5 Generalisation to the case of weak compactness
- 5.1 Nonstandard characterisation of weak compactness
- 5.1.1 Pseudo-norms and nonstandard hulls
- 5.1.2 Nonstandard hull with respect to the weak topology
- 5.1.3 Weak compactness
- 5.2 Existence of a representative utility function w.r.t. the weak topology
- 6 Extension: Kirman-Sondermann correspondence for vote abstention
- 6.1 Arrow-rational aggregators
- 6.2 Generalised ultraproduct construction
- 6.3 Generalised Kirman-Sondermann correspondence
- 7 Conclusion
- Bibliography