IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/42043.html
   My bibliography  Save this paper

Adaptive Rolling Plans Are Good

Author

Listed:
  • Maćkowiak, Piotr

Abstract

Here we prove the goodness property of adaptive rolling plans in a multisector optimal growth model under decreasing returns in deterministic environment. Goodness is achieved as a result of fast convergence (at an asymptotically geometric rate) of the rolling plan to balanced growth path. Further on, while searching for goodness, we give a new proof of strong concavity of an indirect utility function – this result is achieved just with help of some elementary matrix algebra and differential calculus.

Suggested Citation

  • Maćkowiak, Piotr, 2009. "Adaptive Rolling Plans Are Good," MPRA Paper 42043, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:42043
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/42043/1/MPRA_paper_42043.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Benhabib, Jess & Nishimura, Kazuo, 1981. "Stability of Equilibrium in Dynamic Models of Capital Theory," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(2), pages 275-293, June.
    2. David Gale, 1967. "On Optimal Development in a Multi-Sector Economy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 34(1), pages 1-18.
    3. Venkatesh Bala & Mukul Majumdar & Tapan Mitra, 1991. "Decentralized evolutionary mechanisms for intertemporal economies: A possibility result," Journal of Economics, Springer, vol. 53(1), pages 1-29, February.
    4. Takayama,Akira, 1985. "Mathematical Economics," Cambridge Books, Cambridge University Press, number 9780521314985.
    5. Venditti, Alain, 1997. "Strong Concavity Properties of Indirect Utility Functions in Multisector Optimal Growth Models," Journal of Economic Theory, Elsevier, vol. 74(2), pages 349-367, June.
    6. Michael Kaganovich, 1998. "Decentralized Evolutionary Mechanism of Growth in a Linear Multi-sector Model," Metroeconomica, Wiley Blackwell, vol. 49(3), pages 349-363, October.
    7. Benhabib, Jess & Nishimura, Kazuo, 1979. "On the Uniqueness of Steady States in an Economy with Heterogeneous Capital Goods," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 20(1), pages 59-82, February.
    8. Jess Benhabib & Kazuo Nishimura, 2012. "The Hopf Bifurcation and Existence and Stability of Closed Orbits in Multisector Models of Optimal Economic Growth," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 51-73, Springer.
    9. Jean-Philippe Vial, 1983. "Strong and Weak Convexity of Sets and Functions," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 231-259, May.
    10. Kaganovich, Michael, 1996. "Rolling planning: Optimality and decentralization," Journal of Economic Behavior & Organization, Elsevier, vol. 29(1), pages 173-185, January.
    11. VIAL, Jean-Philippe, 1983. "Strong and weak convexity of sets and functions," LIDAM Reprints CORE 529, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Lionel W. McKenzie, 2005. "Classical General Equilibrium Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633302, December.
    13. S. M. Goldman, 1968. "Optimal Growth and Continual Planning Revision," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 145-154.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Venditti Alain, 2019. "Competitive equilibrium cycles for small discounting in discrete-time two-sector optimal growth models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 23(4), pages 1-14, September.
    2. Alain Venditti, 2012. "Weak concavity properties of indirect utility functions in multisector optimal growth models," International Journal of Economic Theory, The International Society for Economic Theory, vol. 8(1), pages 13-26, March.
    3. Venditti, Alain, 1997. "Strong Concavity Properties of Indirect Utility Functions in Multisector Optimal Growth Models," Journal of Economic Theory, Elsevier, vol. 74(2), pages 349-367, June.
    4. Drugeon, Jean-Pierre & Venditti, Alain, 2001. "Intersectoral external effects, multiplicities & indeterminacies," Journal of Economic Dynamics and Control, Elsevier, vol. 25(5), pages 765-787, May.
    5. Kaganovich, Michael, 1996. "Rolling planning: Optimality and decentralization," Journal of Economic Behavior & Organization, Elsevier, vol. 29(1), pages 173-185, January.
    6. Sorger, Gerhard, 2004. "Consistent planning under quasi-geometric discounting," Journal of Economic Theory, Elsevier, vol. 118(1), pages 118-129, September.
    7. Huynh Ngai & Nguyen Huu Tron & Nguyen Vu & Michel Théra, 2022. "Variational Analysis of Paraconvex Multifunctions," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 180-218, June.
    8. J. X. Cruz Neto & P. R. Oliveira & A. Soubeyran & J. C. O. Souza, 2020. "A generalized proximal linearized algorithm for DC functions with application to the optimal size of the firm problem," Annals of Operations Research, Springer, vol. 289(2), pages 313-339, June.
    9. T. R. Gulati & I. Ahmad & D. Agarwal, 2007. "Sufficiency and Duality in Multiobjective Programming under Generalized Type I Functions," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 411-427, December.
    10. Ali Khan, M. & Mitra, Tapan, 2008. "Growth in the Robinson-Solow-Srinivasan model: Undiscounted optimal policy with a strictly concave welfare function," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 707-732, July.
    11. D. H. Yuan & X. L. Liu & A. Chinchuluun & P. M. Pardalos, 2006. "Nondifferentiable Minimax Fractional Programming Problems with (C, α, ρ, d)-Convexity," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 185-199, April.
    12. S. Nobakhtian, 2006. "Sufficiency in Nonsmooth Multiobjective Programming Involving Generalized (Fρ)-convexity," Journal of Optimization Theory and Applications, Springer, vol. 130(2), pages 361-367, August.
    13. Ghiglino, Christian & Venditti, Alain, 2011. "Wealth distribution and output fluctuations," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2478-2509.
    14. Sorger, Gerhard, 1995. "On the sensitivity of optimal growth paths," Journal of Mathematical Economics, Elsevier, vol. 24(4), pages 353-369.
    15. Majumdar, Mukul, 2009. "Equilibrium and optimality: Some imprints of David Gale," Games and Economic Behavior, Elsevier, vol. 66(2), pages 607-626, July.
    16. A. Kabgani & F. Lara, 2022. "Strong subdifferentials: theory and applications in nonconvex optimization," Journal of Global Optimization, Springer, vol. 84(2), pages 349-368, October.
    17. Sedi Bartz & Minh N. Dao & Hung M. Phan, 2022. "Conical averagedness and convergence analysis of fixed point algorithms," Journal of Global Optimization, Springer, vol. 82(2), pages 351-373, February.
    18. Z. Y. Wu & A. M. Rubinov, 2010. "Global Optimality Conditions for Some Classes of Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 145(1), pages 164-185, April.
    19. Takahashi, Harutaka, 2010. "Global analysis of the growth and cycles of multi-sector economies with constant returns: A turnpike approach," MPRA Paper 24860, University Library of Munich, Germany, revised Jun 2010.
    20. Truman Bewley, 2010. "An Integration of Equilibrium Theory and Turnpike Theory," Levine's Working Paper Archive 1381, David K. Levine.

    More about this item

    Keywords

    indirect utility function; good plans; adaptive rolling-planning; multisector model;
    All these keywords.

    JEL classification:

    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:42043. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.