Microeconomic Foundations of Representative Agent Models by Means of Ultraproducts
13 Pages Posted: 16 Jul 2014 Last revised: 5 Dec 2014
Date Written: July 14, 2014
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
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