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Equilibrium existence in a discrete-time endogenous growth model with physical and human capital

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  • Luis Alcala

Abstract

This paper studies a discrete-time version of the Lucas-Uzawa endogenous growth model with physical and human capital in the presence of externalities. Existence of an optimal equilibrium is proved using tools from dynamic programming with bounded or unbounded returns. The proofs also rely on properties of isoelastic utility and homogeneous production functions and apply well-known inequalities in real analysis, seldom used in the literature, which significantly simplify the task of verifying certain assumptions that are rather technical in nature. Some advantages of adopting a parametric family of isoelastic utility functions, instead of the ad hoc formulation typically used, are also discussed.

Suggested Citation

  • Luis Alcala, 2023. "Equilibrium existence in a discrete-time endogenous growth model with physical and human capital," Papers 2401.00342, arXiv.org, revised Feb 2025.
    • Handle: RePEc:arx:papers:2401.00342
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    References listed on IDEAS

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    1. Le Van, Cuong & Vailakis, Yiannis, 2005. "Recursive utility and optimal growth with bounded or unbounded returns," Journal of Economic Theory, Elsevier, vol. 123(2), pages 187-209, August.
    2. Le Van, Cuong & Morhaim, Lisa, 2002. "Optimal Growth Models with Bounded or Unbounded Returns: A Unifying Approach," Journal of Economic Theory, Elsevier, vol. 105(1), pages 158-187, July.
    3. Alvarez, Fernando & Stokey, Nancy L., 1998. "Dynamic Programming with Homogeneous Functions," Journal of Economic Theory, Elsevier, vol. 82(1), pages 167-189, September.
    4. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
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    More about this item

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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