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## On sufficiency issues, first integrals and exact solutions of Uzawa-Lucas model with unskilled labor

 Centre for Mathematics and Statistical Sciences, Lahore School of Economics, Lahore, 53200, Pakistan

* Corresponding author: Rehana Naz

Received  January 2019 Revised  May 2019 Published  December 2019

In this article, the sufficiency issues, first integrals and exact solutions for the Uzawa-Lucas model with unskilled labor are investigated. The sufficient conditions are established by utilizing Arrow's Sufficiency theorem. The non-negativeness conditions for the balanced growth path (BGP) are provided and growth rate is explicitly given in terms of parameters of the model. The first integrals are established by the partial Hamiltonian approach. Then first integrals are utilized to construct the exact solutions for all the variables. The growth rates of all variables and graphical representation of exact solutions are provided for the special case when the inverse of the intertemporal elasticity of substitution is the same as the share of physical capital.

Citation: Rehana Naz. On sufficiency issues, first integrals and exact solutions of Uzawa-Lucas model with unskilled labor. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020170
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##### References:
Evolution over time of $c(t), \;u(t), \; k(t)$ and $h(t)$
Effect of change of $\beta$ on evolution over time of $c(t), \;u(t), \; k(t)$ and $h(t)$
Parameters values
 $\theta=\alpha$ $\beta$ $\rho$ $\nu$ $n$ $m$ $k_0$ $h_0$ $0.33$ $0.25$ $0.05$ $0.1$ $0.04$ $0.01$ $40$ $10$
 $\theta=\alpha$ $\beta$ $\rho$ $\nu$ $n$ $m$ $k_0$ $h_0$ $0.33$ $0.25$ $0.05$ $0.1$ $0.04$ $0.01$ $40$ $10$
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