Recent Research

  • NEW Becker, Robert A. and Rincon-Zapatero, Juan P, Distinct Solutions to Koopmans' Equation for Thompson Aggregators Represent Distinct Preference Orders (June 8, 2023). Available at SSRN: https://ssrn.com/abstract=4473832

    Thompson aggregators generate recursive utility functions as solutions to Koopmans' functional equation. Multiple solutions may occur when the underlying commodity space is the positive cone of the space of bounded real-valued consumption sequences. Consider the case of extremal solutions: distinct least and greatest solutions exist. We show that these recursive utility functions represent distinct preference orders on the commodity space. We discuss the significance of this observation for uniqueness theory and optimal growth modeling with a Thompson aggregator based objective function.

  • NEW Becker, Robert A. and Rincon-Zapatero, Juan P, Recursive Utility for Thompson Aggregators: Least Fixed Point, Uniqueness, and Approximation Theories (May 22, 2023). Available at SSRN: https://ssrn.com/abstract=4456037

    We reconsider the theory of Thompson aggregators proposed by Marinacci and Montrucchio (J Econ Theory 2010). We demonstrate the Koopmans equation has a unique utility function solution given a Thompson aggregator. Uniqueness holds only on the interior of the commodity space's positive cone. We verify Du's condition (Appl Anal 1990) holds. We show iteration of the Koopmans operator with initial seed the zero function convergences uniformly to the operator's Least Fixed Point on each order interval in the commodity space's norm interior. This differs from Marinacci and Montrucchio's (J Econ Theory 2010, Math Oper Res 2019), proofs as well as proofs given by Martins-da-Rocha and Vailakis (Econometrica 2010). Those papers rely on a form of the contraction mapping theorem where the space of possibly utility functions is endowed with the topology induced by the Thompson metric. Application of Du's theory works on the possible utility function space with its norm topology. Our approach combines order and metric structures to demonstrate uniqueness differently than in the existing literature.

  • Becker, Robert A. and Rincón-Zapatero, J.P., Recursive Utility and Turnpike Theory for GMM Thompson Aggregators (January 17, 2020).
    CAEPR WORKING PAPER SERIES #2020-001. Available at SSRN: https://ssrn.com/abstract=3521498

    The existence of a unique optimum, a unique optimal stationary program, and a turnpike theorem are demonstrated for a neoclassical one sector optimal growth model. The planner's allocation problem is formulated as a discrete time deterministic, infinite horizon programming model. The production sector is subject to diminishing marginal returns to capital. The planner's objective function is derived from a Generalized Marinacci and Montrucchio (GMM) Thompson aggregator preference. A given Thompson aggregator may be associated with many intertemporal utility functions (which may not be ordinally equivalent). The choice of one of these representations over another is shown to be a matter of mathematical tractability. There is an observational equivalence between those alternative objective functions: the qualitative features of the optimal solution do not depend on the particular utility function representation of the underlying Thompson aggregator preference structure.


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    Modified: 28 September 2023
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