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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. [ABSTRACT FROM AUTHOR]

We study the discrete time neoclassical one-sector growth model with differential savings while assuming Kadiyala production function which shows a variable elasticity of substitution symmetric with respect to capital and labor. We show that, if workers save more than shareholders, then the growth path is bounded from above and the boundary is independent from the savings rate of shareholders. Moreover, the growth path for non-developed countries is influenced only by the savings rate of shareholders while level of capital per capita of developed economies is influenced by the savings rate of workers. We also show that multistability phenomena may occur so that the model is able to explain co-existence of under-developed, developing and developed economies. We prove that fluctuations and complex dynamics may arise when the elasticity of substitution between production factors is lower than one and shareholders save more than workers. [ABSTRACT FROM AUTHOR]