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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. Casey B. Mulligan & Xavier Sala-i-Martin, 1992. "Transitional Dynamics in Two-Sector Models of Endogenous Growth," NBER Working Papers 3986, National Bureau of Economic Research, Inc.
  2. Boldrin, Michele & Montrucchio, Luigi, 1986. "On the indeterminacy of capital accumulation paths," Journal of Economic Theory, Elsevier, vol. 40(1), pages 26-39, October.
  3. Stokey, Nancy L & Rebelo, Sergio, 1995. "Growth Effects of Flat-Rate Taxes," Journal of Political Economy, University of Chicago Press, vol. 103(3), pages 519-50, June.
  4. 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.
  5. 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.
  6. Jones, Larry E. & Manuelli, Rodolfo E., 1997. "The sources of growth," Journal of Economic Dynamics and Control, Elsevier, vol. 21(1), pages 75-114, January.
  7. Jensen, Martin Kaae, 2006. "On unbounded growth with heterogenous consumers," Journal of Mathematical Economics, Elsevier, vol. 42(7-8), pages 807-826, November.
  8. James E. Rauch, 1994. "Balanced and Unbalanced Growth," NBER Working Papers 4659, National Bureau of Economic Research, Inc.
  9. Rebelo, Sergio, 1991. "Long-Run Policy Analysis and Long-Run Growth," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 500-521, June.
  10. 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.
  11. 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.
  12. Alvarez, Fernando & Stokey, Nancy L., 1998. "Dynamic Programming with Homogeneous Functions," Journal of Economic Theory, Elsevier, vol. 82(1), pages 167-189, September.
  13. Atsumi, H, 1969. "The Efficient Capital Programme for a Maintainable Utility Level," Review of Economic Studies, Wiley Blackwell, vol. 36(107), pages 263-87, July.
  14. repec:cup:cbooks:9780521443258 is not listed on IDEAS
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. Bewley, Truman, 1982. "An integration of equilibrium theory and turnpike theory," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 233-267, September.
  20. 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.
  21. Pollak, Robert A, 1971. "Additive Utility Functions and Linear Engel Curves," Review of Economic Studies, Wiley Blackwell, vol. 38(116), pages 401-14, October.
  22. Romer, Paul M, 1990. "Endogenous Technological Change," Journal of Political Economy, University of Chicago Press, vol. 98(5), pages S71-102, October.
  23. Brock, William A. & Gale, David, 1969. "Optimal growth under factor augmenting progress," Journal of Economic Theory, Elsevier, vol. 1(3), pages 229-243, October.
  24. 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.
  25. 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.
  26. 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.
  27. 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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