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Microeconomic Foundations of Representative Agent Models by Means of Ultraproducts

13 Pages Posted: 16 Jul 2014 Last revised: 5 Dec 2014

Geghard Bedrosian

Bielefeld University - Center for Mathematical Economics

Frederik Herzberg

Bielefeld University - Center for Mathematical Economics

Date Written: July 14, 2014

Abstract

This paper builds on a recent proposal for microeconomic foundations for "representative agents". Herzberg [Journal of Mathematical Economics, vol. 46, no. 6, 1115-1124 (2010)] constructed a representative utility function for infinite-dimensional social decision problems and since the decision problems of macroeconomic theory are typically infinite-dimensional, Herzberg's original result is insufficient for many applications. We therefore generalise his result by allowing the social alternatives to belong to a general reflexive Banach space and provide sufficient conditions for our new results to be satisfied in economic applications.

Keywords: microfoundation, representative agent, social choice, reflexive Banach space, convex optimisation, ultrafilter, bounded ultrapower, nonstandard analysis

JEL Classification: D71

Suggested Citation

Bedrosian, Geghard and Herzberg, Frederik, Microeconomic Foundations of Representative Agent Models by Means of Ultraproducts (July 14, 2014). Institute of Mathematical Economics Working Paper No. 514. Available at SSRN: https://ssrn.com/abstract=2466068 or http://dx.doi.org/10.2139/ssrn.2466068

Geghard Bedrosian

Bielefeld University - Center for Mathematical Economics ( email )

Postfach 10 01 31
Bielefeld, D-33501
Germany

Frederik Herzberg (Contact Author)

Bielefeld University - Center for Mathematical Economics ( email )

Postfach 10 01 31
Bielefeld, D-33501
Germany

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