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Sustainability over sets and the business cycle

Author

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  • Lixiao Hao

    (Hebei University of Technology)

  • Vasilios I. Manousiouthakis

    (University of California at Los Angeles (UCLA))

Abstract

Many rigorous works have examined the behavior of Kaldor business cycle models. In this paper, utilizing the sustainability over sets (SOS) concept, a general theorem is proven establishing necessary and sufficient conditions for the existence and identification of rectangular sustainable sets for a general Kaldor model. These conditions can be readily verified, either in the two-dimensional space of lower and upper bounds on income, or in the one-dimensional space of upper bound on income, thus enabling identification of the region of economic sustainability for the considered Kaldor model. The Theorem’s power is illustrated with a case study of a particular Kaldor business cycle model from the literature that can exhibit rich dynamic behavior, and can give rise to economic sustainability regions that encompass multiple stable equilibrium points. Furthermore, a methodology is also presented that identifies non-rectangular sustainable sets, when the imposition of tight lower and upper bounds on one of the economic system variables (e.g., income) prevents the existence of a sustainable rectangular set.

Suggested Citation

  • Lixiao Hao & Vasilios I. Manousiouthakis, 2021. "Sustainability over sets and the business cycle," SN Business & Economics, Springer, vol. 1(6), pages 1-26, June.
    • Handle: RePEc:spr:snbeco:v:1:y:2021:i:6:d:10.1007_s43546-021-00058-5
    DOI: 10.1007/s43546-021-00058-5
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    References listed on IDEAS

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