Local and Global Dynamics in a Neoclassical Growth Model with Nonconcave Production Function and Nonconstant Population Growth Rate

In this paper we analyze the dynamics shown by the neoclassical one-sector growth model with differential savings as in Bohm and Kaas [J. Econom. Dynam. Control, 24 (2000), pp. 965--980] while assuming a sigmoidal production function as in [V. Capasso, R. Engbers, and D. La Torre, Nonlinear Anal., 11 (2010), pp. 3858--3876] and the labor force dynamics described by the Beverton--Holt equation (see [R. J. H. Beverton and S. J. Holt, Fishery Invest., 19 (1957), pp. 1--533]). We prove that complex features are exhibited, related both to the structure of the coexisting attractors (which can be periodic or chaotic) and to their basins (which can be simple or nonconnected). In particular we show that complexity emerges if the elasticity of substitution between production factors is low enough and shareholders save more than workers, confirming the results obtained with concave production functions. Anyway, in contrast to previous studies, the use of the S-shaped production function implies the existence of a po...

[1]  Elisabetta Michetti,et al.  Backward and forward-looking expectations in a chaotic cobweb model. , 2004, Nonlinear dynamics, psychology, and life sciences.

[2]  R. Solow.  A Contribution to the Theory of Economic Growth , 1956 .

[3]  R. Sato,et al.  Production Functions with Variable Elasticity of Factor Substitution: Some Analysis and Testing , 1968 .

[4]  J. Stiglitz.  Distribution of income and wealth among individuals , 1969 .

[5]  Laura Gardini,et al.  Endogenous cycles in discontinuous growth models , 2011, Math. Comput. Simul..

[6]  Shandelle M. Henson,et al.  Global Dynamics of Some Periodically Forced, Monotone Difference Equations , 2001 .

[7]  R. Beverton,et al.  On The Dynamics Of Exploited Fish Populations Vol-19 , 1957 .

[8]  R. Dieci.  Routes to Complexity in a Macroeconomic Model Described by a Noninvertible Triangular Map , 2003 .

[9]  Laura Gardini,et al.  Multistability and cyclic attractors in duopoly games , 2000 .

[10]  C. Mammana,et al.  Complex Dynamics in the Neoclassical Growth Model with Differential Savings and Non-Constant Labor Force Growth , 2007 .

[11]  Laura Gardini,et al.  Analysis of global bifurcations in a market share attraction model , 2000 .

[12]  Global Attractors of non-autonomous difference equations , 2008 .

[13]  C. Mammana,et al.  Variable elasticity of substituition in a discrete time Solow–Swan growth model with differential saving , 2011 .

[14]  N. Kaldor.  A Model of Economic Growth , 1957 .

[15]  F. Ramsey,et al.  THE MATHEMATICAL THEORY OF SAVING , 1928 .

[16]  Laura Gardini,et al.  Global properties of symmetric competition models with riddling and blowout phenomena , 2000 .

[17]  S. Brianzoni,et al.  Local and Global Dynamics in a Discrete Time Growth Model with Nonconcave Production Function , 2012 .

[18]  R. Vaughan.  The Pasinetti Paradox in Neoclassical and More General Models: a Correction , 1971 .

[19]  Luigi Lodovico Pasinetti,et al.  Rate of Profit and Income Distribution in Relation to the Rate of Economic Growth , 1962 .

[20]  Global attractors of quasi-linear non-autonomous difference equations: A growth model with endogenous population growth , 2013 .

[21]  John Maynard Smith.  Models in ecology , 1974 .

[22]  Christian Mira,et al.  Chaos In Discrete Dynamical Systems , 1997 .

[23]  W. Dechert.  Does optimal growth preclude chaos? A theorem on monotonicity , 1984 .

[24]  Martial Schtickzelle,et al.  Pierre-François Verhulst (1804-1849). La première découverte de la fonction logistique , 1981 .

[25]  R. A. Becker,et al.  Equilibrium Dynamics with Many Agents , 2006 .

[26]  Roy Harrod.  AN ESSAY IN DYNAMIC THEORY , 1939 .

[27]  N. S. Revankar.  A Class of Variable Elasticity of Substitution Production Functions , 1971 .

[28]  Volker Böhm,et al.  Differential savings, factor shares, and endogenous growth cycles , 2000 .

[29]  Colin W. Clark,et al.  Economically optimal policies for the utilization of biologically renewable resources , 1971 .

[30]  C. Mammana,et al.  Global attractor in Solow growth model with differential savings and endogenic labor force growth , 2008 .

[31]  Jim M Cushing,et al.  A Periodically Forced Beverton-Holt Equation , 2002 .

[32]  N. Kaldor.  Alternative theories of distribution , 1955 .

[33]  T. Swan,et al.  ECONOMIC GROWTH and CAPITAL ACCUMULATION , 1956 .

[34]  L. Gardini,et al.  Contact bifurcations related to critical sets and focal points in iterated maps of the plane , 2011 .

[35]  Ralf Engbers,et al.  On a spatial Solow model with technological diffusion and nonconcave production function , 2010 .

[36]  C. Mammana,et al.  Nonlinear dynamics in a business-cycle model with logistic population growth , 2009 .

[37]  Laura Gardini,et al.  BISTABILITY AND BORDER-COLLISION BIFURCATIONS FOR A FAMILY OF UNIMODAL PIECEWISE SMOOTH MAPS , 2005 .

[38]  中村 隆之.  ハロッド“An Essay in Dynamic Theory”（1938年草稿）をめぐるハロッド=ケインズ往復書簡の解明（2） , 2003 .