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Global stability and the “turnpike” in optimal unbounded growth models

  • Jensen, Martin Kaae

This study proves various global stability results for unbounded optimal growth models. The main theorem states that any optimal path will eventually be in the neighborhood of a balanced growth path if future utility is sufficiently weakly discounted. The assumptions allow for non-smooth technologies, joint production, and production in independent sectors. Hence, the results form the integration of new growth and turnpike theory sought by McKenzie (1998) [31] in his Ely lecture. The applicability of the results is exemplified by means of a number of cases from growth theory and other areas of economics.

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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 147 (2012)
Issue (Month): 2 ()
Pages: 802-832

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Handle: RePEc:eee:jetheo:v:147:y:2012:i:2:p:802-832
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. Jensen, Martin Kaae, 2006. "On unbounded growth with heterogenous consumers," Journal of Mathematical Economics, Elsevier, vol. 42(7-8), pages 807-826, November.
  2. Robert A. Pollak, 1971. "Additive Utility Functions and Linear Engel Curves," Review of Economic Studies, Oxford University Press, vol. 38(4), pages 401-414.
  3. Nancy L. Stokey & Sergio Rebelo, 1993. "Growth Effects of Flat-Rate Taxes," NBER Working Papers 4426, National Bureau of Economic Research, Inc.
  4. Rauch, James E., 1997. "Balanced and unbalanced growth," Journal of Development Economics, Elsevier, vol. 53(1), pages 41-66, June.
  5. Larry E. Jones & Rodolfo E. Manuelli, 1994. "The Sources of Growth," Macroeconomics 9411002, EconWPA, revised 05 Mar 1999.
  6. Boldrin, Michele & Montrucchio, Luigi, 1986. "On the indeterminacy of capital accumulation paths," Journal of Economic Theory, Elsevier, vol. 40(1), pages 26-39, October.
  7. Yano, Makoto, 1985. "Competitive Equilibria on Turnpikes in a McKenzie Economy, II: An Asymptotic Turnpike Theorem," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(3), pages 661-69, October.
  8. Bewley, Truman, 1982. "An integration of equilibrium theory and turnpike theory," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 233-267, September.
  9. H. Atsumi, 1969. "The Efficient Capital Programme for a Maintainable Utility Level," Review of Economic Studies, Oxford University Press, vol. 36(3), pages 263-287.
  10. Boldrin, Michele & Nishimura, Kazuo & Shigoka, Tadashi & Yano, Makoto, 2001. "Chaotic Equilibrium Dynamics in Endogenous Growth Models," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 97-132, January.
  11. Kurz,Heinz D. & Salvadori,Neri, 1995. "Theory of Production," Cambridge Books, Cambridge University Press, number 9780521443258, June.
  12. Romer, Paul M, 1990. "Endogenous Technological Change," Journal of Political Economy, University of Chicago Press, vol. 98(5), pages S71-102, October.
  13. Kaganovich, Michael, 1998. "Sustained endogenous growth with decreasing returns and heterogeneous capital," Journal of Economic Dynamics and Control, Elsevier, vol. 22(10), pages 1575-1603, August.
  14. Sergio T. Rebelo, 1990. "Long Run Policy Analysis and Long Run Growth," NBER Working Papers 3325, National Bureau of Economic Research, Inc.
  15. J. Tsukui, 1967. "The Consumption and the Output Turnpike Theorems in a von Neumann Type of Model—A Finite Term Problem," Review of Economic Studies, Oxford University Press, vol. 34(1), pages 85-93.
  16. Alvarez, Fernando & Stokey, Nancy L., 1998. "Dynamic Programming with Homogeneous Functions," Journal of Economic Theory, Elsevier, vol. 82(1), pages 167-189, September.
  17. M. Morishima, 1961. "Prices and the Turnpike: II. Proof of a Turnpike Theorem: The "No Joint Production" Case," Review of Economic Studies, Oxford University Press, vol. 28(2), pages 89-97.
  18. Yano, Makoto, 1984. "Competitive Equilibria on Turnpikes in a McKenzie Economy, I: A Neighborhood Turnpike Theorem," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(3), pages 695-717, October.
  19. 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.
  20. Jones, Larry E & Manuelli, Rodolfo E, 1990. "A Convex Model of Equilibrium Growth: Theory and Policy Implications," Journal of Political Economy, University of Chicago Press, vol. 98(5), pages 1008-38, October.
  21. Cass, David & Shell, Karl, 1976. "The structure and stability of competitive dynamical systems," Journal of Economic Theory, Elsevier, vol. 12(1), pages 31-70, February.
  22. Casey B. Mulligan & Xavier Sala-i-Martin, 1993. "Transitional Dynamics in Two-Sector Models of Endogenous Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 108(3), pages 739-773.
  23. Dasgupta, Swapan & Mitra, Tapan, 1988. "Intertemporal optimality in a closed linear model of production," Journal of Economic Theory, Elsevier, vol. 45(2), pages 288-315, August.
  24. Dolmas, Jim, 1996. "Endogenous Growth in Multisector Ramsey Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(2), pages 403-21, May.
  25. Makoto Yano, 1998. "On the Dual Stability of a von Neumann Facet and the Inefficacy of Temporary Fiscal Policy," Econometrica, Econometric Society, vol. 66(2), pages 427-452, March.
  26. Alexandre Scheinkman, Jose, 1976. "On optimal steady states of n-sector growth models when utility is discounted," Journal of Economic Theory, Elsevier, vol. 12(1), pages 11-30, February.
  27. Gantz, Donald T, 1980. "A Strong Turnpike Theorem for a Nonstationary von Neumann-Gale Production Model," Econometrica, Econometric Society, vol. 48(7), pages 1777-90, November.
  28. Brock, William A. & Gale, David, 1969. "Optimal growth under factor augmenting progress," Journal of Economic Theory, Elsevier, vol. 1(3), pages 229-243, October.
  29. J. v. Neumann, 1945. "A Model of General Economic Equilibrium," Review of Economic Studies, Oxford University Press, vol. 13(1), pages 1-9.
  30. Lucas, Robert E, Jr, 1990. "Supply-Side Economics: An Analytical Review," Oxford Economic Papers, Oxford University Press, vol. 42(2), pages 293-316, April.
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