1. A non-linear approach to Kalecki's investment cycle.
- Author
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De Cesare, Luigi and Sportelli, Mario
- Subjects
- *
DELAY differential equations , *HOPF bifurcations , *NONLINEAR functions , *BUSINESS cycles , *DELIVERY of goods , *ECONOMIC impact - Abstract
In this paper, looking at some new contributions to the Kalecki business cycle theory, we re-examine his 1935 model concerning the gestation period between orders and deliveries of capital goods. The model gives rise to a delay differential equation (DDE) with delay dependent coefficients depending on the time delay. The model has only one equilibrium point. Proved that a unique stability switch exists, we study the emergence of the Hopf bifurcation and the direction, stability and period of the bifurcating periodic solutions. We derive an explicit formula for determining the properties of the Hopf bifurcation by using the first Lyapunov coefficient. To confirm our analytic results, we consider two types of non-linear functions, all consistent with Kalecki's hypotheses: two S-shaped functions and one fractional function. Some comments dealing with the economic implications of our analysis are also included. • Kalecki's model of the investment cycle. • Model with time delays and delay dependent coefficients. • Existence of Hopf bifurcations analyzed by choosing time delays as bifurcation parameters. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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