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Feasibility and Optimality of the Initial Capital Stock in the Ramsey Vintage Capital Model

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  • Franklin Gamboa
  • Wilfredo L. Maldonado

Abstract

Using a discrete version of the Ramsey Vintage Capital Model we provide a characterization of the initial capital stocks compatible with a predefined scrapping time and a level of technical progress which generate feasible capital paths. From that characterization, it is proved that for a given level of technological progress there exists a minimum scrapping time for the machines which allows a sustainable growth path. Moreover, we reduce the infinite horizon dynamic programming problem to one of finite dimension and we show how this reduction allows us to find the optimal structure of the initial capital stock as well as the optimal scrapping time. A numerical example shows that, in accordance with the infinite horizon approach, the greater the technological progress, the lower the optimal scrapping time.

Suggested Citation

  • Franklin Gamboa & Wilfredo L. Maldonado, 2013. "Feasibility and Optimality of the Initial Capital Stock in the Ramsey Vintage Capital Model," CAMA Working Papers 2013-38, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  • Handle: RePEc:een:camaaa:2013-38
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    File URL: https://cama.crawford.anu.edu.au/sites/default/files/publication/cama_crawford_anu_edu_au/2017-02/38_2013_gamboa_maldonado.pdf
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    References listed on IDEAS

    as
    1. Malcomson, James M., 1975. "Replacement and the rental value of capital equipment subject to obsolescence," Journal of Economic Theory, Elsevier, vol. 10(1), pages 24-41, February.
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    4. Raouf Boucekkine & David de la Croix & Omar Licandro, 2006. "Vintage Capital," Economics Working Papers ECO2006/8, European University Institute.
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    6. Boucekkine, Raouf & Licandro, Omar & Puch, Luis A. & del Rio, Fernando, 2005. "Vintage capital and the dynamics of the AK model," Journal of Economic Theory, Elsevier, vol. 120(1), pages 39-72, January.
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    More about this item

    Keywords

    Vintage capital; technological innovation; dynamic programming.;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity
    • O33 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Technological Change: Choices and Consequences; Diffusion Processes

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