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Global analysis of the growth and cycles of multi-sector economies with constant returns: A turnpike approach


  • Takahashi, Harutaka


In Section 1, we explain the neoclassical optimal growth model, which includes multi capital goods, and is derived from neoclassical production functions; the transformations to the reduced model are also explained. Section 2 pertains to the explanation of the methods for proving the consumption turnpike theorem demonstrated by Scheinkman (1976) and McKenzie (1983). Also, the case in which the essentials of the von Neumann-McKenzie facet, which plays an important role in the next part, became a two-sector model and is explained using figures. In Section 3, we postulate a two-sector neoclassical optimal growth model, and the optimal path behavior in the vicinity of the optimal steady state path (modified golden rule path) are classified using the characteristics of von Neumann-McKenzie facet. Also, we will use these results to prove, based on a weaker hypothesis, that the theorem that the optimal path local stability and the optimal path attained by Benhabib and Nishimura(1985)becomes a two-term periodic solution. In Section 4, the generalization of the global asymptotic stability conclusion achieved with two divisions into a case that includes two or more types of capital goods. In Addendum, the important fundamental principles used in the main text will be defined, and a number of theorems will be proved.

Suggested Citation

  • 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.
  • Handle: RePEc:pra:mprapa:24860

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    References listed on IDEAS

    1. Basu, Susanto & Fernald, John G., 1995. "Are apparent productive spillovers a figment of specification error?," Journal of Monetary Economics, Elsevier, vol. 36(1), pages 165-188, August.
    2. 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.
    3. Basu, Susanto & Fernald, John G, 1997. "Returns to Scale in U.S. Production: Estimates and Implications," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 249-283, April.
    4. Benhabib, Jess & Nishimura, Kazuo, 1979. "The hopf bifurcation and the existence and stability of closed orbits in multisector models of optimal economic growth," Journal of Economic Theory, Elsevier, vol. 21(3), pages 421-444, December.
    5. Bartelsman, Eric J., 1995. "Of empty boxes: Returns to scale revisited," Economics Letters, Elsevier, vol. 49(1), pages 59-67, July.
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    More about this item


    multi-sector model; turnpike theory; optimal growth; the Neumann-McKednzie facet;

    JEL classification:

    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • O21 - Economic Development, Innovation, Technological Change, and Growth - - Development Planning and Policy - - - Planning Models; Planning Policy

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