Feasibility and Optimality of the Initial Capital Stock in the Ramsey Vintage Capital Model
AbstractUsing 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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Bibliographic InfoPaper 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.
Length: 14 pages
Date of creation: Jun 2013
Date of revision:
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Vintage capital; technological innovation; dynamic programming.;
Other versions of this item:
- Gamboa, Franklin & Maldonado, Wilfredo Leiva, 2014. "Feasibility and optimality of the initial capital stock in the Ramsey vintage capital model," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 40-45.
- 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 - - - Capital; Investment; Capacity
- O33 - Economic Development, Technological Change, and Growth - - Technological Change; Research and Development; Intellectual Property Rights - - - Technological Change: Choices and Consequences; Diffusion Processes
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