Cycles and chaos in the one-sector growth model with elastic labor supply

Gerhard Sorger

doi:10.1007/s00199-016-1005-0

Abstract

It is shown that the discrete-time version of the neoclassical one-sector optimal growth model with elastic labor supply and standard monotonicity and convexity assumptions on technology and preferences can have periodic solutions of any period as well as chaotic solutions. The optimality of these non-monotonic solutions is traced back to strong income effects. When technology and preferences are parameterized as it is commonly done in quantitative macroeconomic studies, these phenomena cannot occur.

Highlights

The neoclassical one-sector growth model with infinitely lived households has been widely used to study the causes and consequences of long-run growth and business cycles
It is shown that the discrete-time version of the neoclassical one-sector optimal growth model with elastic labor supply and standard monotonicity and convexity assumptions on technology and preferences can have periodic solutions of any period as well as chaotic solutions
Whereas the deterministic version of this model with inelastic labor supply has the property that all solutions converge monotonically to a unique interior steady state, this is not necessarily the case when labor supply is elastic and time is modeled as a discrete variable

Summary

Introduction

The neoclassical one-sector growth model with infinitely lived households has been widely used to study the causes and consequences of long-run growth and business cycles. De Hek (1998) provides both an example in which there exist multiple interior steady states and an example in which the optimal solution displays periodic oscillations He concludes his paper by posing the question of “whether this model. The purpose of the present paper is to conduct a similar systematic analysis of period-2 cycles and to provide an affirmative answer to the question by De Hek (1998) regarding more complicated dynamics To this end, we first extend the results from De Hek (1998) by proving that, for any time-preference factor between 0 and 1, there exist a production function and an instantaneous utility function—both satisfying standard monotonicity and convexity assumptions—such that the resulting model admits a locally asymptotically stable optimal solution which is periodic with period 2.

The model

The results and their implications

Findings

Compliance with ethical standards