NONLINEAR DYNAMICS AND ECONOMIC GROWTH. THE INFLUENCE OF ELASTICITY OF SUBSTITUTION BETWEEN INPUT FACTORS AND DIFFERENTIAL SAVINGS PROPENSITIES.

This thesis investigates the qualitative and quantitative dynamics of the Solow-Swan growth model with differential saving considering different production functions in order to analyse how the long run behaviour of the economy is influenced by the elasticity of substitution between production factors and by different savings propensity between workers and shareholders. In the first chapter the economic growth problem of establishing a relation between the elasticity of substitution, capital and output per-capita levels when dealing with a non constant elasticity of substitution production function is discussed. Starting from a discrete-time setup, some definitions of elasticity of substitution associated to an attractor are proposed and a method to measure it is suggested. The main goal is to compare dynamic growth models with VES, sigmoidal and CES production functions. To this end, the method proposed is applied to the Kaldor’s model using a VES production function with constant returns to scale. It is found that when simple dynamics are exhibited, a country characterized by production functions with higher elasticity of substitution experiences higher capital and output per-capita equilibrium levels. On the other hand, when the long term dynamics consist of cycles or more complex features, then an ambiguous relation between elasticity of substitution and asymptotic dynamics is shown. In the second chapter the Kaldor growth model is analysed, assuming the Shifted Cobb-Douglas (SCD) production function, a technology that - differently from CES and VES one - allow to consider the dynamics of non developed and developing countries as well as that of developed economies. The resulting model is a discontinuous map generating a poverty trap. Furthermore multistability phenomena may emerge: next to the ”vicious circle of poverty”, long run behaviours may include boom and bust period (fluctuations may arise when the elasticity of substitution is lower then one) and convergence to a positive level of capital per-capita. In the last chapter the discrete tme neoclassical one-sector growth model with differential savings is studied assuming the Kadiyala production function which shows a variable elasticity of substitution symmetric with respect to capital and labor. It is shown 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. 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. Moreover, multistability phenomena may occur so that the model is able to explain co-existence of under-developed, developing and developed economies. Fluctuations and complex dynamics may arise when the elasticity of substitution between production factors is lower than one and shareholders save more than workers.