IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/73677.html
   My bibliography  Save this paper

Back to the Sixties: A Note on Multi-Primary-Factor Linear Models with Homogeneous Capital

Author

Listed:
  • Freni, Giuseppe

Abstract

This paper extends Bruno's (1967) one capital good two-sector growth model with discrete technology by allowing multiple primary factors of production. While the existence of an optimal steady state is established for any positive rate of discount, an example in which three "modified golden rules" exist shows that the optimal steady state is non necessarily unique. The extended model provides a simple exemplification of the more general principle that the presence of multiple primary factors of production into homogeneous capital models can definitively result into the same complications that arise when there is joint production.

Suggested Citation

  • Freni, Giuseppe, 2016. "Back to the Sixties: A Note on Multi-Primary-Factor Linear Models with Homogeneous Capital," MPRA Paper 73677, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:73677
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/73677/1/MPRA_paper_73677.pdf
    File Function: original version
    Download Restriction: no

    File URL: https://mpra.ub.uni-muenchen.de/77617/8/MPRA_paper_77617.pdf
    File Function: revised version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Maria Dolores Guillo & Fidel Perez-Sebastian, 2015. "Convergence in a Dynamic Heckscher–Ohlin Model with Land," Review of Development Economics, Wiley Blackwell, vol. 19(3), pages 725-734, August.
    2. Brock, William A, 1973. "Some Results on the Uniqueness of Steady States in Multisector Models of Optimum Growth when Future Utilities are Discounted," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(3), pages 535-559, October.
    3. Kazuo Nishimura & Alain Venditti & Makoto Yano, 2006. "Endogenous Fluctuations In Two‐Country Models," The Japanese Economic Review, Japanese Economic Association, vol. 57(4), pages 516-532, December.
    4. Edwin Burmeister & Ngo Van Long, 1977. "On Some Unresolved Questions in Capital Theory: An Application of Samuelson's Correspondence Principle," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 91(2), pages 289-314.
    5. Neri Salvadori (ed.), 2003. "The Theory of Economic Growth," Books, Edward Elgar Publishing, number 2741.
    6. Dantzig, George B. & Manne, Alan S., 1974. "A complementarity algorithm for an optimal capital path with invariant proportions," Journal of Economic Theory, Elsevier, vol. 9(3), pages 312-323, November.
    7. Luigi L. Pasinetti, 1960. "A Mathematical Formulation of the Ricardian System," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 27(2), pages 78-98.
    8. Burmeister, Edwin & Turnovsky, Stephen J, 1972. "Capital Deepening Response in an Economy with Heterogeneous Capital Goods," American Economic Review, American Economic Association, vol. 62(5), pages 842-853, December.
    9. Giuseppe Freni, 1997. "Equilibrio dinamico di produzione e prezzi in un modello unisettoriale," Economia politica, Società editrice il Mulino, issue 3, pages 399-438.
    10. Burmeister, Edwin, 1981. "On the Uniqueness of Dynamically Efficient Steady States," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(1), pages 211-219, February.
    11. Brock, William A & Burmeister, Edwin, 1976. "Regular Economies and Conditions for Uniqueness of Steady States in Optimal Multi-Sector Economic Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(1), pages 105-120, February.
    12. Liviatan, Nissan & Samuelson, Paul A., 1969. "Notes on Turnpikes: Stable and unstable," Journal of Economic Theory, Elsevier, vol. 1(4), pages 454-475, December.
    13. Samuelson, Paul A. & Etula, Erkko M., 2006. "Complete work-up of the one-sector scalar-capital theory of interest rate: Third installment auditing Sraffa's never-completed "Critique of Modern Economic Theory"," Japan and the World Economy, Elsevier, vol. 18(3), pages 331-356, August.
    14. Erkko Etula, 2008. "The Two‐Sector Von Thünen Original Marginal Productivity Model Of Capital; And Beyond," Metroeconomica, Wiley Blackwell, vol. 59(1), pages 85-104, February.
    15. Arie Leizarowitz, 1985. "Existence of Overtaking Optimal Trajectories for Problems with Convex Integrands," Mathematics of Operations Research, INFORMS, vol. 10(3), pages 450-461, August.
    16. Giuseppe Freni & Fausto Gozzi & Neri Salvadori, 2006. "Existence of optimal strategies in linear multisector models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 25-48, September.
    17. Burmeister, Edwin, 1975. "Many Primary Factors in Non-Joint Production Economies," The Economic Record, The Economic Society of Australia, vol. 51(136), pages 486-512, December.
    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. Freni, Giuseppe & Gozzi, Fausto & Pignotti, Cristina, 2008. "Optimal strategies in linear multisector models: Value function and optimality conditions," Journal of Mathematical Economics, Elsevier, vol. 44(1), pages 55-86, January.
    2. 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.
    3. Neri Salvadori & Rodolfo Signorino, 2017. "From endogenous growth to stationary state: The world economy in the mathematical formulation of the Ricardian system," The European Journal of the History of Economic Thought, Taylor & Francis Journals, vol. 24(3), pages 507-527, May.
    4. W. A. Brock, 1977. "Applications of Recent Results on the Asymptotic Stability of Optimal Control to the Problem of Comparing Long Run Equilibria," Discussion Papers 274, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Murray Brown, 1980. "The Measurement of Capital Aggregates: A Postreswitching Problem," NBER Chapters, in: The Measurement of Capital, pages 377-432, National Bureau of Economic Research, Inc.
    6. Ariel Dvoskin & Saverio M. Fratini, 2016. "On the Samuelson–Etula Master Function and the capital controversy," The European Journal of the History of Economic Thought, Taylor & Francis Journals, vol. 23(6), pages 1032-1058, November.
    7. Bellino, Enrico & Nerozzi, Sebastiano, 2013. "Causality and interdependence in Pasinetti's works and in the modern classical approach," MPRA Paper 52179, University Library of Munich, Germany.
    8. Fabbri, Giorgio & Faggian, Silvia & Freni, Giuseppe, 2017. "Non-existence of optimal programs for undiscounted growth models in continuous time," Economics Letters, Elsevier, vol. 152(C), pages 57-61.
    9. Azam, Jean-Paul, 2023. "Was Lucifer a Gambler? A Rational-Choice Hermeneutic of Peter Olivi’s Treatise on Demons," TSE Working Papers 23-1483, Toulouse School of Economics (TSE).
    10. Alain Raybaut, 2018. "Coupling and synchronization dynamics in endogenous business cycles models," Post-Print halshs-01941339, HAL.
    11. Heinz D. Kurz, 2011. "The Contributions of Two Eminent Japanese Scholars to the Development of Economic Theory: Michio Morishima and Takashi Negishi," Chapters, in: Heinz D. Kurz & Tamotsu Nishizawa & Keith Tribe (ed.), The Dissemination of Economic Ideas, chapter 13, Edward Elgar Publishing.
    12. Bilancini Ennio & D'Alessandro Simone, 2008. "Functional Distribution, Land Ownership and Industrial Takeoff: The Role of Effective Demand," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 8(1), pages 1-36, August.
    13. Erzo Luttmer, 2017. "Slow Convergence in Economies with Organization Capital," 2017 Meeting Papers 1117, Society for Economic Dynamics.
    14. Freni, Giuseppe & Salvadori, Neri, 2016. "Ricardo on Machinery: A Textual Analysis," MPRA Paper 73427, University Library of Munich, Germany.
    15. Stavroula DIMKOU & George MAKRIS, 2017. "Financial Sector And Growth Process In South-Eastern Europe'S Former Socialist Countries: Could A Kaldorian Cumulative Causation Approach Help To Better Understand The Links Between Them?," Scientific Bulletin - Economic Sciences, University of Pitesti, vol. 16(1), pages 60-73.
    16. Fabbri, Giorgio & Faggian, Silvia & Freni, Giuseppe, 0. "On competition for spatially distributed resources in networks," Theoretical Economics, Econometric Society.
    17. Jonathan F. Cogliano & Roberto Veneziani, 2023. "Classical Competition and Equilibrium: An Agent-Based Analysis," Working Papers 977, Queen Mary University of London, School of Economics and Finance.
    18. Thomas F. RUTHERFORD & Miles K. LIGHT & Gustavo Adolfo HERNANDEZ, 2002. "A dynamic general equilibrium model for tax policy analysis in Colombia," Archivos de Economía 1910, Departamento Nacional de Planeación.
    19. Nazim Kadri Ekinci, 2009. "Consumption And Growth From A Ricardian Perspective," Metroeconomica, Wiley Blackwell, vol. 60(4), pages 638-659, November.
    20. Luigi L. Pasinetti, 2000. "Critique of the neoclassical theory of growth and distribution," BNL Quarterly Review, Banca Nazionale del Lavoro, vol. 53(215), pages 383-431.

    More about this item

    Keywords

    Homogeneous capital; Multiple primary factors; Linear activity models; Duality.;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

    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:73677. 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.