Towards a New Mathematical Paradigm for the Development of Economic Growth Theory
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We contribute to the development of the growth theory in economics, using mathematical and statistical tools. In particular, we employ various techniques rooted in the theory of Hamiltonian systems on Poisson manifolds, jet bundles theory, calculus of variation, and statistical data analysis to study the properties of the Cobb-Douglas production function as an invariant of the one-parameter Lie group action determined by exponential growth in factors (capital and labor) and production. This approach is extended to more general models determined by logistic growth and the Lotka-Volterra type interactions between factors. The resulting new production functions are shown with the aid of statistical methods to provide a good fit to the current economic data.