Notes on an Endogenous Growth Model with two Capital Stocks II: The Stochastic Case
AbstractThis paper extends the class of stochastic AK growth models with a closed-form solution to the case where there are two capital goods in the model. To be precise, we consider the Uzawa-Lucas model of endogenous growth with human and physical capital. The extension holds, even if an external effect in the use of human capital in goods production occurs. Using the “guess and verify” method, we determine the value function of the social planner in the centralized economy and the value function 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 is able to help the decentralized economy in reaching the social optimum, while keeping the policy maker’s budget balanced. Then the time series implications of the model’s solution are derived. In Appendix to the paper the uniqueness of the value functions is proved by using an alternative method.
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Bibliographic InfoPaper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2005-033.
Length: 25 pages
Date of creation: Jun 2005
Date of revision:
closed-form solution; value function; saddle path stability; endogenous growth;
Find related papers by JEL classification:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-10-29 (All new papers)
- NEP-DEV-2005-10-29 (Development)
- NEP-DGE-2005-10-29 (Dynamic General Equilibrium)
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