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Diversity of preferences in an unpredictable environment

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  • Bonneuil, Noël
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    Abstract

    The origin of preferences was viewed as related to the dominant eigenvalue of a Leslie matrix modelling reproductive strategies. In a variable environment, however, the coexistence of varying preferences no longer requires optimality, but is identified with the mathematical property of viability: a state of the population is viable if there exists at least one solution starting from it and remaining in the set of constraints until a given time horizon (or forever). The coexistence kernel of two competitors with varying preferences is computed for the case of scalar and 2 x 2 Leslie matrices, with either measurable or differentiable preferences. The homologue of indifference curves is the regulation map, the correspondence associating the set of viable preferences to a given state of the population. Among these viable trajectories, some are also optimal in the sense of dominance discounted in time. These viable optimal solutions are obtained as specific trajectories in an auxiliary dynamic system, and the associated maximal values constitute one boundary of the viability kernel of this auxiliary system (theorem). Hence, the perpetuation of varying preferences allows the diversity of economic preferences, as shown here using the example of the comparative history of fertility from mid-nineteenth century to nowadays in France and England.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Mathematical Economics.

    Volume (Year): 46 (2010)
    Issue (Month): 6 (November)
    Pages: 965-976

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    Handle: RePEc:eee:mateco:v:46:y:2010:i:6:p:965-976

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    Web page: http://www.elsevier.com/locate/jmateco

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    Keywords: Discrete time Viability theory Preferences Leslie matrix Birth fluctuations;

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    1. Bonneuil, Noel & Saint-Pierre, Patrick, 2008. "Beyond optimality: Managing children, assets, and consumption over the life cycle," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 227-241, February.
    2. Bonneuil, Noel, 1994. "Capital Accumulation, Inertia of Consumption and Norms of Reproduction," Journal of Population Economics, Springer, vol. 7(1), pages 49-62.
    3. Saint-Pierre, Patrick & Bonneuil, Noel, 2008. "Beyond Optimality : Managing Children, Assets, and Consumption over the Life Cycle," Economics Papers from University Paris Dauphine 123456789/6869, Paris Dauphine University.
    4. Larry Samuelson & Arthur J. Robson, 2007. "The Evolution of Intertemporal Preferences," American Economic Review, American Economic Association, vol. 97(2), pages 496-500, May.
    5. Hansson, Ingemar & Stuart, Charles, 1990. "Malthusian Selection of Preferences," American Economic Review, American Economic Association, vol. 80(3), pages 529-44, June.
    6. Rogers, Alan R, 1994. "Evolution of Time Preference by Natural Selection," American Economic Review, American Economic Association, vol. 84(3), pages 460-81, June.
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