Economic growth cycles driven by investment delay

• Published in: Economic modelling 2017-12, Vol.67, p.175-183
• Main Authors: Krawiec, Adam, Szydłowski, Marek
• Format: Article
• Language: English
• Subjects: Delay differential equations; Growth cycles; Keynesian model
• ISSN: 0264-9993; 1873-6122
• DOI: 10.1016/j.econmod.2016.11.014

We study the model of growth cycles in the framework of the Keynesian macroeconomic theory. The Kaldor–Kalecki growth model is the Kaldor business cycle model with two modifications: exponential growth introduced by Dana and Malgrange and Kaleckian investment time delay considered in this paper. This model has a form of a system of differential equations with time delay. The methods of dynamical system theory and bifurcation theory are used in the analysis of dynamics of growth cycles. Taking the time delay in investment as a bifurcation parameter we show the existence of a single Hopf bifurcation. We show that the time delay creates a limit cycle in a wider range of parameters than the model without the time delay. The time delay is the source of fluctuations which are described in a deterministic way. We carry out the numerical analysis of the model and find the limit cycle solution as well as we find that the higher the time delay parameter value the longer the period and the higher the amplitude of income and capital. We find that there is a distinguished value of growth rate parameter g=0.0147 for which the lowest value of investment time delay or the lowest value of speed of adjustment is required to obtain cyclic solutions. •The Kaldor-Kalecki growth model as a system of delay differential equations is examined.•The investment time delay plays a crucial role in the dynamics of economics growth.•The existence of a limit cycle solution due to the Hopf bifurcation with respect to time delay is proved.•The in-depth numerical analysis of the dynamics of model was carried out.•The growth rate parameter plays an important role for the existence of cycles.