Closed-form solutions of Lucas-Uzawa model with externalities via partial Hamiltonian approach

TL;DR

This paper derives multiple closed-form solutions for the Lucas-Uzawa model with externalities using a partial Hamiltonian approach, revealing solution multiplicity and its implications for economic growth dynamics.

Contribution

It introduces multiple solutions for the Lucas-Uzawa model with externalities, a novel finding in the economic growth literature, and analyzes their implications.

Findings

Multiple closed-form solutions derived for the model.

Solutions enable full characterization of variable growth rates.

Potential explanation for countries overtaking each other economically.

Abstract

In this paper, we establish multiple closed-form solutions for all the variables in the Lucas-Uzawa model with externalities for the case with no parameter restrictions as well as for cases with specific parameter restrictions. These multiple solutions are derived with the help of the results derived in Naz et al (2016); Naz and Chaudhry (2017). This multiplicity of solutions is new to the economic growth literature on Lucas-Uzawa model with externalities. After finding solutions for the Lucas-Uzawa model with externalities, we use these solutions to derive the growth rates of all the variables in the system which enables us to fully describe the dynamics of the model. The multiple solutions can potentially explain why some countries economically overtake other countries even though they start from the same initial conditions.