Microeconomic foundations of representative agent models by means of ultraproducts - Geghard Bedrosian; Frederik Herzberg (Bielefeld University, Center for Mathematical Economics (IMW), 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: D71; 330; microfoundation; representative agent; social choice; reflexive Banach space; convex optimisation; ultrafilter; bounded ultrapower; nonstandard analysis