The Stability Properties of Goodwin’s Growth Cycle Model with a Variable Elasticity of Substitution Production Function

This article investigates the stability properties of the well-known Goodwin’s growth cycle model, when a production function with variable elasticity of substitution is considered. It is found that the latter amounts to the introduction of a dampening effect; hence, the equilibrium becomes locally asymptotically stable. However, if we assume endogenous labour productivity growth, this is not the only possible solution; the model can exhibit converging or diverging oscillations as well as closed concentric trajectories depending on the assumed opposite effects of ‘elasticity of (factor) substitution’ and ‘endogenous labour productivity growth’.