The Hamiltonian approach to the problem of derivation of production functions in economic growth theory

TL;DR

This paper introduces a Hamiltonian framework for deriving production functions in economic growth theory, unifying existing models and proposing a new one based on Lotka-Volterra eco-dynamics.

Contribution

It presents a novel Hamiltonian approach that generalizes the derivation of production functions, including a new model within the Lotka-Volterra system.

Findings

Unified Hamiltonian framework for production functions

Derivation of existing models as special cases

Proposal of a new eco-dynamic based production model

Abstract

We introduce a general Hamiltonian framework that appears to be a natural setting for the derivation of various production functions in economic growth theory, starting with the celebrated Cobb-Douglas function. Employing our method, we investigate some existing models and propose a new one as special cases of the general $n$-dimensional Lotka-Volterra system of eco-dynamics.