Sustainability over sets and the business cycle

Abstract

AbstractMany 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.