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Equilibrium Points for Optimal Investment with Vintage Capital

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Author Info
Silvia Faggian () (Department of Applied Mathematics, University of Venice)

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Abstract

The paper concerns the study of equilibrium points, namely the stationary solutions to the closed loop equation, of an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. Sufficient conditions for existence of equilibrium points in the general case are given and later applied to the economic problem of optimal investment with vintage capital. Explicit computation of equilibria for the economic problem in some relevant examples is also provided. Indeed the challenging issue here is showing that a theoretical machinery, such as optimal control in infinite dimension, may be effectively used to compute solutions explicitly and easily, and that the same computation may be straightforwardly repeated in examples yielding the same abstract structure. No stability result is instead provided: the work here contained has to be considered as a first step in the direction of studying the behavior of optimal controls and trajectories in the long run.

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File URL: http://www.dma.unive.it/wpdma/2008wp182.pdf
File Format: application/pdf
File Function: First version, 2008
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Publisher Info
Paper provided by Department of Applied Mathematics, University of Venice in its series Working Papers with number 182.

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Length: 19 pages
Date of creation: Nov 2008
Date of revision:
Handle: RePEc:vnm:wpaper:182

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Related research
Keywords: Linear convex control; Boundary control; Hamilton–Jacobi–Bellman equations; Optimal investment problems; Vintage capital;

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Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium
E22 - Macroeconomics and Monetary Economics - - Macroeconomics: Consumption, Saving, Production, Employment, and Investment - - - Capital; Investment; Capacity

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References listed on IDEAS
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  1. Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M. & Veliov, Vladimir M., 2006. "Anticipation effects of technological progress on capital accumulation: a vintage capital approach," Journal of Economic Theory, Elsevier, vol. 126(1), pages 143-164, January. [Downloadable!] (restricted)
  2. Emilio Barucci & Fausto Gozzi, 2001. "Technology adoption and accumulation in a vintage-capital model," Journal of Economics, Springer, vol. 74(1), pages 1-38, February. [Downloadable!] (restricted)
  3. Feichtinger, G. & Hartl, R.F. & Kort, P.M., 2001. "Dynamic investment behavior taking into account ageing of the capital good," Discussion Paper 13, Tilburg University, Center for Economic Research. [Downloadable!]
  4. Fabbri, Giorgio & Gozzi, Fausto, 2006. "Vintage Capital in the AK growth model: a Dynamic Programming approach. Extended version," MPRA Paper 2863, University Library of Munich, Germany. [Downloadable!]
  5. R. Boucekkine & F. del Rio & O. Licandro & Luis A. Puch, 2000. "Vintage Capital and the Dynamics of the AK Model," Econometric Society World Congress 2000 Contributed Papers 0436, Econometric Society. [Downloadable!]
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  6. Barucci, Emilio & Gozzi, Fausto, 1998. "Investment in a vintage capital model," Research in Economics, Elsevier, vol. 52(2), pages 159-188, June. [Downloadable!] (restricted)
  7. Raouf Boucekkine & David de la Croix & Omar Licandro, 2006. "Vintage Capital," Economics Working Papers ECO2006/8, European University Institute. [Downloadable!]
    Other versions:
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