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This work investigates the economic growth problem of establishing a relation between the elasticity of substitution between production factors, capital and output per-capita levels when dealing with a non constant elasticity of substitution production function. Starting from a discrete-time setup, some definitions of elasticity of substitution associated to an attractor are proposed and a general method to measure it is suggested. Thanks to this methodology a government may select a proper economic policy in order to reduce production costs without decreasing the capitalisation trend of the economy. The method proposed is applied to the Solow’s type growth model with differential savings using a Variable Elasticity of Substitution (VES) production function with constant returns to scale. It is found that when shareholders save more than workers or the elasticity of substitution is higher than one, a country characterised by production functions with higher elasticity of substitution experiences higher capital and output per-capita equilibrium levels. On the other hand, when the elasticity of substitution is lower than one and workers save more than shareholders, an ambiguous relation between elasticity of substitution and asymptotic dynamics is shown.

The Kaldor model describes the dynamics of economic growth over time. Many works showed that a large variety of qualitative dynamics can be produced depending on the economic assumptions. This work provides conditions to mark boundaries during boom and bust cycles, investigating how saving behaviors of workers and shareholders and elasticity of substitution between capital and labor influence the growth dynamics of non‐developed, developing and developed countries considering general and specific technologies of production. The results obtained can be used by policy‐makers to increase the lower level an economy can reach during boom and bust periods and reduce fluctuations.

This research aims at studying a general equilibrium closed economy with overlapping generations and inherited tastes (aspirations), as in de la Croix (Econ Lett 53(1):89–96, 1996). It shows that the interaction between the intensity of aspirations and the elasticity of substitution of effective consumption affects the qualitative and quantitative long-term dynamics from both local and global perspectives. The related literature is extended by showing that (1) the Neimark–Sacker bifurcation found by de la Croix (1996) does not necessarily give rise to fluctuations and (2) endogenous (long-lasting) fluctuations occur through the emergence of period-doubling bifurcations.

We analyze the dynamics produced by the neoclassical one-sector growth model with differential savings as in [3] while assuming a sigmoidal production function as in [8] and the labor force dynamics described by the Beverton Holt equation, as proposed in [2]. The resulting discrete time dynamic system is bidimensional, autonomous and triangular: we determine its invariant sets and study their local stability. We also perform a mainly numerical analysis to show that complex features are exhibited, related both to the structure of the coexixting attractors and to their basins. The study presented shows that complexity emerges if the elasticity of substitution between production factors is low enough and shareholders save more than workers, thus confirming the results obtained with concave production functions (see [6], [7] and [9]).

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...

We study the dynamics shown by the discrete time neoclassical one-sector growth model with differential savings as in Bohm and Kaas (2000) while assuming a nonconcave production function in the form given by Capasso et. al. (2010). We prove that complex features are exhibited related both to the structure of the coexixting attractors and to their basins. We also 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 while considering concave production functions (see, for instance, Brianzoni et al. (2007) (2009) and (2011)).

We study the dynamics shown by the discrete time neoclassical one-sector growth model with differential savings as in Bohm and Kaas [4] while assuming VES production function in the form given by Revankar [24] . It is shown that the model can exhibit unbounded endogenous growth despite the absence of exogenous technical change and the presence of non-reproducible factors if the elasticity of substitution is greater than one. We then consider parameters range related to non-trivial dynamics (i.e. the elasticity of substitution in less than one and shareholders save more than workers) and we focus on local and global bifurcations causing the transition to more and more complex asymptotic dynamics. In particular, as our map is non-differentiable in a subset of the states space, we show that border collision bifurcations occur. Several numerical simulations support the analysis.

We consider a discrete-time growth model of the Solow type where workers and shareholders have different but constant saving rates and the population growth dynamics is described by the logistic equation able to exhibit complicated dynamics. We show conditions for the resulting system having a compact global attractor and we describe its structure. We also perform a mainly numerical analysis using the critical lines method able to describe the strange attractor and the absorbing area, in order to show how cyclical or complex fluctuations may be produced in a business-cycle model. We study the dynamic behaviour of the model under different ranges of the main parameters, i.e. the elasticity of substitution between the two production factors and the one in the logistic equation (namely μ). We prove the existence of complex dynamics when the elasticity of substitution between production factors drops below one (so that capital income declines) or μ increases (so that the amplitude of movements in the population growth rate increases).

In this paper we analyze the dynamics shown by the neoclassical one-sector growth model with differential savings as in Bohm and Kaas (2000) while assuming CES production function and the labour force dynamic described by the Beverton Holt equation (see Beverton and Holt, 1957). The resulting dynamic system is bidimensional, autonomous and triangular: we investigate its qualitative and quantitative dynamic properties. The study herewith presented aims at confirming that the system can exhibit cycles or even a chaotic dynamic pattern, if shareholders save more than workers, when the elasticity of substitution drops below one (so that capital income declines). The analytical results are supplemented by numerical experiments.