Chaos, Solitons and Fractals 113 (2018) 53–62 Contents lists available at ScienceDirect Chaos, Solitons and Fractals Nonlinear Science, and Nonequilibrium and Complex Phenomena journal homepage: www.elsevier.com/locate/chaos Frontiers Substitutability between production factors and growth. An analysis using VES production functions Francesca Grassetti ∗ , Cristiana Mammana, Elisabetta Michetti Department of Economics and Law, University of Macerata, via Crescimbeni 20, Macerata 62100, Italy a r t i c l e i n f o Article history: Received 16 November 2017 Revised 4 April 2018 Accepted 9 April 2018 JEL classification: C02 C61 E23 O41 MSC: 37C 37G 37N40 91B55 91B62 Keywords: Economic growth Elasticity of substitution VES Solow model Economic dynamics a b s t r a c t 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 defini- tions 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 or- der 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 Elas- ticity 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 char- acterised 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. © 2018 Elsevier Ltd. All rights reserved. 1. Introduction The critical relationship between economic growth and the elasticity of substitution between production factors has played a crucial role in the theory of economic growth since the Nobel Prize Robert M. Solow refuted the Harrod–Domar assumption of fixed proportions (see Harrod [1] and Domar [2]) and supposed the pos- sibility of substituting labour for capital in production (see Solow [3]). This assumption has led the way to investigations of how the elasticity of substitution affects capital and output equilibrium levels and hence economic growth. Modern growth theory often considered the Cobb–Douglas (CD) production function as implied ∗ Corresponding author. E-mail addresses: f.grassetti@unimc.it (F. Grassetti), cristiana.mammana@unimc.it (C. Mammana), elisabetta.michetti@unimc.it (E. Michetti). technology in Solow’s type [3] and Diamond [4] growth models. Given the unitary elasticity of substitution between capital and labour of the CD production function, the general conclusions have been limited. Rainer Klump and Olivier de La Grandville considered a Solow type growth model and a normalised Constant Elasticity of Substitution (CES) production function and demonstrated that an economy with higher elasticity of substitution experiences a higher level of per-capita income, both in transition and in steady state (Klump and de La Grandville [5]). They compared economies char- acterised by the same growth model and CES production function, differentiated only by the degree of elasticity of substitution.The same result was found by Klump and Preissler [6]. In line with this research Miyagiwa and Papageorgiou used the CES production function in the Diamond overlapping-generation model (see Diamond [4]) to study economic growth and its rela- tion with elasticity of substitution between production factors (see Miyagiwa and Papageorgiou [7]). Compared to the other works, https://doi.org/10.1016/j.chaos.2018.04.012 0960-0779/© 2018 Elsevier Ltd. All rights reserved.