Exact solutions for a Solow-Swan model with non-constant returns to scale
Nicol\`o Cangiotti, Mattia Sensi
TL;DR
This paper derives exact solutions for the Solow-Swan growth model incorporating non-constant returns to scale, providing a general solution approach and specific solutions for Cobb-Douglas and von Bertalanffy functions, supported by numerical simulations.
Contribution
It introduces a general solution strategy for the Solow-Swan model with non-constant returns to scale and computes exact solutions for specific production functions.
Findings
Exact solutions for Cobb-Douglas and von Bertalanffy models obtained
Numerical simulations validate the analytical solutions
General solution strategy applicable to non-constant returns to scale
Abstract
The Solow-Swan model is shortly reviewed from a mathematical point of view. By considering non-constant returns to scale, we obtain a general solution strategy. We then compute the exact solution for the Cobb-Douglas production function, for both the classical model and the von Bertalanffy model. Numerical simulations are provided.
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