A Closed-form Solution of the Uzawa-Lucas Model of Endogenous Growth

This paper presents a closed-form solution to the Uzawa-Lucas endogenous growth model with human and physical capital. Our result also applies if an external effect in the use of human capital in goods production occurs. Using the ``guess-and-verify' method, we determine the two value functions of the social planner in the centralized economy and of the representative agent in the decentralized case. We show that the introduction of income taxes on wages and of a subsidy on physical capital earnings helps the decentralized economy in reaching the social optimum, while keeping the policy maker's budget balanced. Finally, we derive the time-series implications of the model's solution.