# On the Solutions of the Lucas-Uzawa Model

## TL;DR

This paper critically examines recent solutions to the Lucas-Uzawa model, demonstrating that purported new solutions are not fundamentally different from existing ones through rigorous mathematical proof.

## Contribution

It clarifies the validity of solutions to the Lucas-Uzawa model, showing that claimed new solutions are not genuinely novel using the existence and uniqueness theorem.

## Key findings

- The second solution is not fundamentally different from the known solution.
- The paper confirms the uniqueness of the existing solution.
- It corrects misconceptions about the solution space of the model.

## Abstract

In a recent paper, Naz and Chaudry provided two solutions for the model of Lucas-Uzawa, via the Partial Hamiltonian Approach. The first one of these solutions coincides exactly with that determined by Chilarescu. For the second one, they claim that this is a new solution, fundamentally different than that obtained by Chilarescu. We will prove in this paper, using the existence and uniqueness theorem of nonlinear differential equations, that this is not at all true.