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Discrete Choice And Complex Dynamics In Deterministic Optimization Problems

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  • Kamihigashi, Takashi

Abstract

This paper shows that complex dynamics arises naturally in deterministic discrete choice problems. In particular, it shows 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 is almost always complex. These results are illustrated with various numerical examples.

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  • Kamihigashi, Takashi, 2012. "Discrete Choice And Complex Dynamics In Deterministic Optimization Problems," Macroeconomic Dynamics, Cambridge University Press, vol. 16(S1), pages 52-69, April.
  • Handle: RePEc:cup:macdyn:v:16:y:2012:i:s1:p:52-69_00
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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.

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