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Discrete Choice and Complex Dynamics in Deterministic Optimization Problems

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  • Takashi Kamihigashi

    (Research Institute for Economics & Business Administration (RIEB), Kobe University, Japan)

Abstract

This papers shows that complex dynamics arise naturally in deterministic discrete choice problems. In particular, we show that if the objective function of a maximization problem can be written as a function of a sequence of discrete variables, and if the (maximized) value function is strictly increasing in an exogenous variable, then for almost all values of the exogenous variable, any optimal path exhibits aperiodic dynamics. This result is applied to a maximization problem with indivisible durable goods as well as to a Ramsey model with an indivisible consumption good. In each model, it is shown that optimal dynamics are almost always complex. These results are illustrated with various numerical examples.

Suggested Citation

  • Takashi Kamihigashi, 2011. "Discrete Choice and Complex Dynamics in Deterministic Optimization Problems," Discussion Paper Series DP2011-19, Research Institute for Economics & Business Administration, Kobe University, revised Jul 2011.
    • Handle: RePEc:kob:dpaper:dp2011-19
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    File URL: https://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/DP2011-19.pdf
    File Function: Revised version, 2011
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    Cited by:

    1. Takashi Kamihigashi, 2013. "Ergodic chaos and aggregate stability: A deterministic discrete-choice model of wealth distribution dynamics," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(1), pages 45-56, March.

    More about this item

    Keywords

    Discrete choice; Complex dynamics; Chaos; Indivisible goods;
    All these keywords.

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