arXiv subjects

Azam Chaudhry

Publications and source records attributed to Azam Chaudhry.

2 recordsLinked to original sources

arXiv2016

Comparison of Closed-form Solutions for the Lucas-Uzawa model via the Partial Hamitonian Approach and the Classical Approach

In this paper we derive the closed-form solutions for the Lucas-Uzawa growth model with the aid of the partial Hamiltonian approach and then compare our results with those derived by the classical approach \cite{chil}. The partial Hamiltonian approach provides two first integrals \cite{naz2016} in the case where there are no parameter restrictions and these two first integrals are utilized to construct three sets of closed form solutions for all the variables in the model. First two first integrals are used to find two closed form solutions, one of which is new to the literature. We then use only one of the first integrals to derive a third solution that is the same as that found in the previous literature. We also show that all three solutions converge to the same long run balance growth path.

math.OC↗

arXiv2013

A Partial Hamiltonian Approach for Current Value Hamiltonian Systems

We develop a partial Hamiltonian framework to obtain reductions and closed-form solutions via first integrals of current value Hamiltonian systems of ordinary differential equations (ODEs). The approach is algorithmic and applies to many state and costate variables of the current value Hamiltonian. However, we apply the method to models with one control, one state and one costate variable to illustrate its effectiveness. The current value Hamiltonian systems arise in economic growth theory and other economic models. We explain our approach with the help of a simple illustrative example and then apply it to two widely used economic growth models: the Ramsey model with a constant relative risk aversion (CRRA) utility function and Cobb Douglas technology and a one-sector AK model of endogenous growth are considered. We show that our newly developed systematic approach can be used to deduce results given in the literature and also to find new solutions.

math.OC↗