IDEAS home Printed from https://ideas.repec.org/a/eee/jeborg/v66y2008i2p420-436.html
   My bibliography  Save this article

Undiscounted optimal growth in a Leontief two-sector model with circulating capital: The case of a capital-intensive consumption good

Author

Listed:
  • Fujio, Minako

Abstract

This essay presents a complete characterization of undiscounted optimal policy in a Leontief two-sector growth model. We work with the precise technological specification used in Nishimura and Yano [Nishimura, K., Yano, M., 1995. Non-linear dynamics and chaos in optimal growth: an example. Econometrica 63, 981-1001; Nishimura, K., Yano, M., 1996. Chaotic solutions in dynamic linear programming. Chaos Solitons & Fractals 7, 1941-1953; Nishimura, K., Yano, M., 2000. Non-linear dynamics and chaos in optimal growth: a constructive exposition. In: Majumdar, M., Mitra, T. (Eds.), Optimization and Chaos. Springer-Verlag, Berlin, pp. 258-295] and employ a geometric method developed by Khan and Mitra [Khan, M.A., Mitra. T., in press. Optimal growth in a two-sector model without discounting: a geometric investigation. Japanese Economic Review]. Our analysis uncovers rich transition dynamics. Monotonic convergence emerges only under a non-negligible set of parameters with two special features; impossibility of full utilization of factors and convergence in a finite number of periods. Moving beyond this special case, full utilization is not always optimal even if it is feasible. Furthermore, with 'large enough' capital stock the optimal policy becomes a constant.

Suggested Citation

  • Fujio, Minako, 2008. "Undiscounted optimal growth in a Leontief two-sector model with circulating capital: The case of a capital-intensive consumption good," Journal of Economic Behavior & Organization, Elsevier, vol. 66(2), pages 420-436, May.
    • Handle: RePEc:eee:jeborg:v:66:y:2008:i:2:p:420-436
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-2681(06)00255-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Paul A. Samuelson & Robert M. Solow, 1956. "A Complete Capital Model Involving Heterogeneous Capital Goods," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 70(4), pages 537-562.
    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. Hirofumi Uzawa, 1964. "Optimal Growth in a Two-Sector Model of Capital Accumulation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 31(1), pages 1-24.
    4. McKenzie, Lionel W., 1983. "Turnpike theory, discounted utility, and the von Neumann facet," Journal of Economic Theory, Elsevier, vol. 30(2), pages 330-352, August.
    5. W. A. Brock, 1970. "On Existence of Weakly Maximal Programmes in a Multi-Sector Economy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 37(2), pages 275-280.
    6. Ronald W. Jones, 2018. "The Structure of Simple General Equilibrium Models," World Scientific Book Chapters, in: International Trade Theory and Competitive Models Features, Values, and Criticisms, chapter 4, pages 61-84, World Scientific Publishing Co. Pte. Ltd..
    7. Hiroshi Atsumi, 1965. "Neoclassical Growth and the Efficient Program of Capital Accumulation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 127-136.
    8. W. M. Corden, 1966. "The Two Sector Growth Model with Fixed Coefficients," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 33(3), pages 253-262.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gomes, Orlando, 2013. "Information stickiness on general equilibrium and endogenous cycles," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 7, pages 1-43.
    2. Fujio, Minako & Lei, Yan & Deng, Liuchun & Khan, M. Ali, 2021. "The miniature two-sector model of optimal growth: The neglected case of a capital-intensive investment-good sector," Journal of Economic Behavior & Organization, Elsevier, vol. 186(C), pages 662-671.
    3. Minako Fujio, 2009. "Optimal Transition Dynamics In The Leontief Two‐Sector Growth Model With Durable Capital: The Case Of Capital Intensive Consumption Goods," The Japanese Economic Review, Japanese Economic Association, vol. 60(4), pages 490-511, December.
    4. Liuchun Deng & Minako Fujio & M. Ali Khan, 2023. "On optimal extinction in the matchbox two-sector model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(2), pages 445-494, August.
    5. Khalifa, Sherif, 2013. "Undiscounted optimal growth with consumable capital and capital-intensive consumption goods," Mathematical Social Sciences, Elsevier, vol. 65(2), pages 118-135.
    6. Hiroshi Fujiu, 2021. "Business Cycles in a Two-Sided Altruism Model," Mathematics, MDPI, vol. 9(17), pages 1-12, August.
    7. Khalifa, Sherif, 2011. "Undiscounted optimal growth with consumable capital and labor-intensive consumption goods," Economic Modelling, Elsevier, vol. 28(4), pages 1673-1682, July.
    8. Ali Khan, M. & Piazza, Adriana, 2011. "Optimal cyclicity and chaos in the 2-sector RSS model: An anything-goes construction," Journal of Economic Behavior & Organization, Elsevier, vol. 80(3), pages 397-417.
    9. Liuchun Deng & Minako Fujio & M. Ali Khan, 2021. "Eventual periodicity in the two-sector RSL model: equilibrium vis-à-vis optimum growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(2), pages 615-639, September.

    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. Minako Fujio, 2009. "Optimal Transition Dynamics In The Leontief Two‐Sector Growth Model With Durable Capital: The Case Of Capital Intensive Consumption Goods," The Japanese Economic Review, Japanese Economic Association, vol. 60(4), pages 490-511, December.
    2. Khalifa, Sherif, 2011. "Undiscounted optimal growth with consumable capital and labor-intensive consumption goods," Economic Modelling, Elsevier, vol. 28(4), pages 1673-1682, July.
    3. Khalifa, Sherif, 2013. "Undiscounted optimal growth with consumable capital and capital-intensive consumption goods," Mathematical Social Sciences, Elsevier, vol. 65(2), pages 118-135.
    4. Khan, M. Ali & Zaslavski, Alexander J., 2009. "On existence of optimal programs: The RSS model without concavity assumptions on felicities," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 624-633, September.
    5. M. Khan & Alexander Zaslavski, 2007. "On a Uniform Turnpike of the Third Kind in the Robinson-Solow-Srinivasan Model," Journal of Economics, Springer, vol. 92(2), pages 137-166, October.
    6. 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.
    7. M. Ali Khan & Tapan Mitra, 2005. "On choice of technique in the Robinson–Solow–Srinivasan model," International Journal of Economic Theory, The International Society for Economic Theory, vol. 1(2), pages 83-110, June.
    8. Banerjee, Kuntal, 2017. "Suppes–Sen maximality of cyclical consumption: The neoclassical growth model," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 51-65.
    9. Jensen, Martin Kaae, 2012. "Global stability and the “turnpike” in optimal unbounded growth models," Journal of Economic Theory, Elsevier, vol. 147(2), pages 802-832.
    10. Dapeng CAI & Takashi Gyoshin NITTA, 2008. "Limit of the Solutions for the Finite Horizon Problems as the Optimal Solution to the Infinite Horizon Optimization Problems," Papers 0803.4050, arXiv.org.
    11. Banerjee, Kuntal & Mitra, Tapan, 2010. "Equivalence of utilitarian maximal and weakly maximal programs," Journal of Mathematical Economics, Elsevier, vol. 46(3), pages 279-292, May.
    12. Truman Bewley, 2010. "An Integration of Equilibrium Theory and Turnpike Theory," Levine's Working Paper Archive 1381, David K. Levine.
    13. Pedro Garcia Duarte, 2013. "A Path Through the Wilderness: Time Discounting in Growth Models," Working Papers, Department of Economics 2013_18, University of São Paulo (FEA-USP).
    14. Dapeng CAI & Takashi Gyoshin NITTA, 2008. "Constructing the Optimal Solutions to the Undiscounted Continuous-Time Infinite Horizon Optimization Problems," Papers 0803.4046, arXiv.org.
    15. Ram Dubey & Tapan Mitra, 2013. "On the nature of Suppes–Sen maximal paths in an aggregative growth model," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(1), pages 173-205, January.
    16. Alain Ayong Le Kama & Thai Ha-Huy & Cuong Le Van & Katheline Schubert, 2014. "A never-decisive and anonymous criterion for optimal growth models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(2), pages 281-306, February.
    17. Khan, M. Ali & Piazza, Adriana, 2010. "On the non-existence of optimal programs in the Robinson-Solow-Srinivasan (RSS) model," Economics Letters, Elsevier, vol. 109(2), pages 94-98, November.
    18. repec:ipg:wpaper:2013-002 is not listed on IDEAS
    19. Vassili Kolokoltsov & Wei Yang, 2012. "Turnpike Theorems for Markov Games," Dynamic Games and Applications, Springer, vol. 2(3), pages 294-312, September.
    20. Fukao Kyoji & Hamada Koichi, 1994. "International Trade and Investment under Different Rates of Time Preference," Journal of the Japanese and International Economies, Elsevier, vol. 8(1), pages 22-52, March.
    21. Zilcha, Itzhak, 1981. "Competitive Prices and Optimality in Multisector Economy with Changing Preferences," Foerder Institute for Economic Research Working Papers 275343, Tel-Aviv University > Foerder Institute for Economic Research.

    More about this item

    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:eee:jeborg:v:66:y:2008:i:2:p:420-436. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jebo .

    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.