Stability and Hopf-Bifurcation of a growth model considering autonomous consumption and employment effects

João Gabriel de Araujo Oliveira, Beatriz Estulano Vieira and Maurilio Boaventura

Chapter 8 in Income Distribution, Economic Growth and Unemployment, 2025, pp 156-186 from Edward Elgar Publishing

Abstract: Our main objective in this chapter is to present the effects of employment on the capacity utilization and investment of a macrodynamic 3D system. Here, we rewrite the income function and derive a dynamic model of capacity-utilization rate, investment-share, and the desirable level of employment. After that, we use the Routh-Hurwitz criteria to prove stability, which guarantees the necessary conditions for our numerical simulation and avoids Harrodian instability. We also find a bifurcation in the proposed model by considering the Hopf technique. This tool provides insight into model behavior in chaos and includes a switching mechanism between different policies: either raising labor levels or the amount of autonomous consumption, but not both simultaneously. Finally, we present a numerical exercise from a computational simulation using the Finite-Difference Time-Domain Method to demonstrate our model's efficiency. We conclude that the level of employment affects the system in two ways: first, it will disappear with the effects of autonomous consumption if the sum of the growth rates of wages and employment is greater than the growth rate of the autonomous component, thereby increasing both profit and wages in the economy. Second, if the growth rate of the autonomous component is higher, in this case, employment tends to zero and harms the incomes of the economy.

Keywords: Sraffian Supermultiplier; Employment; Stability; Hopf-Bifurcation (search for similar items in EconPapers)
Date: 2025
ISBN: 9781035342556
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