The nonlinear economy (I): How resource constrains lead to business cycles

TL;DR

This paper introduces a nonlinear macroeconomic model incorporating resource constraints, showing how energy depletion and renewal can lead to stable states or sustained oscillations resembling business cycles.

Contribution

It develops a novel macroeconomic model with resource depletion, demonstrating endogenous origins of business cycles through energy and capital dynamics.

Findings

Resource constraints can produce stable or oscillatory economic states.

Endogenous business cycles emerge from resource depletion and renewal.

Conditions for coexistence of fixed points and limit cycles are identified.

Abstract

We explore the nonlinear dynamics of a macroeconomic model with resource constraints. The dynamics is derived from a production function that considers capital and a generalized form of energy as inputs. Energy, the new variable, is depleted during the production process and has to be renewed, whereas capital grows with production and decreases from depreciation. Dependent on time scales and energy related control parameters, we obtain steady states of high or low production, but also sustained oscillations that show properties of business cycles. We also find conditions for the coexistence of stable fixed points and limit cycles. Our model allows to specify investment and saving functions for Kaldor's model of business cycles. We provide evidence for an endogenous origin of business cycles if depleting resources are taken into account.