Economic growth cycles driven by investment delay

Abstract

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.