Su¢ ciency Conditions and the Existence of Equilibria in the Two-Sector Endogenous Growth Model with Leisure
نویسنده
چکیده
This paper examines the existence and nature of equilibria and balanced growth paths in the Uzawa-Lucas two-sector endogenous growth model with elastic labor supply. We demonstrate that it is not possible to merely insert a labor-leisure choice into the model, as has occasionally been done in in the past the resulting rst order conditions for the representative agent violate the Pontyagrin maximum principle. We also explore di¤erent alterations to the model that introduce enough concavity to the initial optimization problem to satisfy the Arrow second order su¢ ciency conditions for optimization. Finally, we consider under what circumstances the altered models generate multiple balanced growth paths, and whether the equilibria are unique or indeterminate. JEL Classi cation Numbers: E23, J24, O41.
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