Closed-form solutions for the Lucas-Uzawa growth model with logarithmic utility preferences via the partial Hamiltonian approach

Azam Chaudhry; Rehana Naz

doi:10.3934/dcdss.2018039

Article Contents

2018, Volume 11, Issue 4: 643-654. Doi: 10.3934/dcdss.2018039

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Closed-form solutions for the Lucas-Uzawa growth model with logarithmic utility preferences via the partial Hamiltonian approach

Azam Chaudhry^a, and
Rehana Naz^b, ,

a.
Department of Economics, Lahore School of Economics, Lahore, 53200, Pakistan
b.
Department of Mathematics and Statistical Sciences, Lahore School of Economics, Lahore, 53200, Pakistan

* Corresponding author: Rehana Naz.
* Corresponding author: Rehana Naz.

Received: November 2016

Revised: May 2017

Published: August 2018

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Abstract

In this paper, we present a dynamic picture of the two sector Lucas-Uzawa model with logarithmic utility preferences and homogeneous technology as was proposed by Bethmann [3] for a Robinson Crusoe economy. We use a newly developed partial Hamiltonian approach to derive a new set of closed-form solutions for the model with logarithmic utility preferences and homogeneous technology. Unlike the previous literature, our model yields three distinct closed-form solutions to the model. We establish the growth rates of all the variables which fully describe the dynamics of the model. Even though the first closed-form solution provides static growth rates and the other two provide dynamic growth rates, in the long run all the closed-form solutions approach the same static balanced growth path.

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Mathematics Subject Classification: 37N40, 76M60, 83C15.

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References

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