# American Institute of Mathematical Sciences

August  2018, 11(4): 643-654. doi: 10.3934/dcdss.2018039

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

 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.

Received  November 2016 Revised  May 2017 Published  November 2017

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.

Citation: Azam Chaudhry, Rehana Naz. Closed-form solutions for the Lucas-Uzawa growth model with logarithmic utility preferences via the partial Hamiltonian approach. Discrete & Continuous Dynamical Systems - S, 2018, 11 (4) : 643-654. doi: 10.3934/dcdss.2018039
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##### References:
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