Recursive Utility and Thompson Aggregators, I: Constructive Existence Theory for the Koopmans Equation

Robert Becker and Juan Pablo Rincón-Zapatero

No 2018-006, CAEPR Working Papers from Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington

Abstract: We reconsider the theory of Thompson aggregators proposed by Marinacci and Montrucchio [34]. We prove a variant of their Recovery Theorem establishing the existence of extremal solutions to the Koopmans equation. We apply the constructive Tarski-Kantorovich Fixed Point Theorem rather than the nonconstructive Tarski Theorem employed in [34]. We also obtain additional properties of the extremal solutions. The Koopmans operator possesses two distinct order continuity properties. Each is sufficient for the application of the Tarski-Kantorovich Theorem. One version builds on the order properties of the underlying vector spaces for utility functions and commodities. The second form is topological. The Koopmans operator is continuous in Scott's [40] induced topology. The least fixed point is constructed with either continuity hypothesis by the partial sum method. This solution is a concave function whenever the Thompson aggregator is concave and also norm continuous on the interior of its effective domain.

Keywords: Recursive Utility; Thompson Aggregators; Koopmans Equation; Koopmans operator; Order Continuity; Tarski-Kantorovich Fixed (search for similar items in EconPapers)
JEL-codes: D10 D15 D50 E21 (search for similar items in EconPapers)
Pages: 41 pages
Date: 2018-07
New Economics Papers: this item is included in nep-upt
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Citations: View citations in EconPapers (2)

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