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

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  • 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.

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  • 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
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    1. Ronald W. Jones, 1965. "The Structure of Simple General Equilibrium Models," Journal of Political Economy, University of Chicago Press, vol. 73, pages 557-557.
    2. W. M. Corden, 1966. "The Two Sector Growth Model with Fixed Coefficients," Review of Economic Studies, Oxford University Press, vol. 33(3), pages 253-262.
    3. 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.
    4. W. A. Brock, 1970. "On Existence of Weakly Maximal Programmes in a Multi-Sector Economy," Review of Economic Studies, Oxford University Press, vol. 37(2), pages 275-280.
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    Cited by:

    1. Gomes, Orlando, 2013. "Information stickiness on general equilibrium and endogenous cycles," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy (IfW), vol. 7, pages 1-43.
    2. Khalifa, Sherif, 2013. "Undiscounted optimal growth with consumable capital and capital-intensive consumption goods," Mathematical Social Sciences, Elsevier, vol. 65(2), pages 118-135.
    3. Khalifa, Sherif, 2011. "Undiscounted optimal growth with consumable capital and labor-intensive consumption goods," Economic Modelling, Elsevier, vol. 28(4), pages 1673-1682, July.
    4. 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.
    5. 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.

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