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

  • Franklin Gamboa
  • Wilfredo L. Maldonado

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.

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File URL: https://cama.crawford.anu.edu.au/pdf/working-papers/2013/382013.pdf
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Paper provided by Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University in its series CAMA Working Papers with number 2013-38.

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Length: 14 pages
Date of creation: Jun 2013
Handle: RePEc:een:camaaa:2013-38
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  1. Boucekkine, R. & Germain, M. & Licandro, O., . "Replacement echoes in the vintage capital growth model," CORE Discussion Papers RP 1275, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Raouf Boucekkine & Marc Germain & Omar Licandro & Alphonse Magnus, . "Numerical solution by iterative methods of a class on vintage capital models," Working Papers 97-26, FEDEA.
  3. Raouf Boucekkine & Omar Licandro & Luis A. Puch & Fernando del Rio, 2003. "Vintage capital and the dynamics of the AK model," Documentos de Trabajo del ICAE 0310, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
  4. 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.
  5. Goetz, Renan-Ulrich & Hritonenko, Natali & Yatsenko, Yuri, 2008. "The optimal economic lifetime of vintage capital in the presence of operating costs, technological progress, and learning," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 3032-3053, September.
  6. BOUCEKKINE, Raouf & GERMAIN, Marc & LICANDRO, Omar & MAGNUS, Alphonse, . "Creative destruction, investment volatility, and the average age of capital," CORE Discussion Papers RP 1376, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Benhabib, Jess & Rustichini, Aldo, 1990. "Vintage Capital, Investment And Growth," Working Papers 90-22, C.V. Starr Center for Applied Economics, New York University.
  8. Jovanovic, B., 1998. "Vintage Capital and Equality," Working Papers 98-16, C.V. Starr Center for Applied Economics, New York University.
  9. Cooley, T.F. & Greenwood, J. & Yorukoglu, M., 1995. "The Replacement Problem," UWO Department of Economics Working Papers 9508, University of Western Ontario, Department of Economics.
  10. Raouf Boucekkine & David de la Croix & Omar Licandro, 2006. "Vintage Capital," Economics Working Papers ECO2006/8, European University Institute.
  11. Boyan Jovanovic, 2009. "The Technology Cycle and Inequality," Review of Economic Studies, Oxford University Press, vol. 76(2), pages 707-729.
  12. repec:fth:starer:98-16 is not listed on IDEAS
  13. R. M. Solow & J. Tobin & C. C. von Weizsäcker & M. Yaari, 1966. "Neoclassical Growth with Fixed Factor Proportions," Review of Economic Studies, Oxford University Press, vol. 33(2), pages 79-115.
  14. Jovanovic, Boyan & Yatsenko, Yuri, 2012. "Investment in vintage capital," Journal of Economic Theory, Elsevier, vol. 147(2), pages 551-569.
  15. repec:fth:starer:9816 is not listed on IDEAS
  16. van Hilten, Onno, 1991. "The optimal lifetime of capital equipment," Journal of Economic Theory, Elsevier, vol. 55(2), pages 449-454, December.
  17. Fabbri, Giorgio & Gozzi, Fausto, 2008. "Solving optimal growth models with vintage capital: The dynamic programming approach," Journal of Economic Theory, Elsevier, vol. 143(1), pages 331-373, November.
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