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Dynamic optimization with a nonsmooth, nonconvex technology: the case of a linear objective function

Listed author(s):
  • Takashi Kamihigashi

    ()

  • Santanu Roy

    ()

This paper studies a one-sector optimal growth model with linear utility in which the production function is generally nonconvex, nondifferentiable, and discontinuous. The model also allows for a general form of irreversible investment. We show that every optimal path either converges to zero or reaches a positive steady state in finite time (and possibly jumps among different steady states afterwards). We establish conditions for extinction (convergence to zero), survival (boundedness away from zero), and the existence of a minimum safe standard of conservation. They extend the conditions known for the case of S-shaped production functions to a much large class of technologies. We also show that as the discount factor approaches one, optimal paths converge to a small neighborhood of the golden rule capital stock.
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File URL: http://hdl.handle.net/10.1007/s00199-005-0029-7
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Article provided by Springer & Society for the Advancement of Economic Theory (SAET) in its journal Economic Theory.

Volume (Year): 29 (2006)
Issue (Month): 2 (October)
Pages: 325-340

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Handle: RePEc:spr:joecth:v:29:y:2006:i:2:p:325-340
DOI: 10.1007/s00199-005-0029-7
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Web page: http://saet.uiowa.edu/

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  1. Kamihigashi, Takashi, 1999. "Chaotic dynamics in quasi-static systems: theory and applications1," Journal of Mathematical Economics, Elsevier, vol. 31(2), pages 183-214, March.
  2. Dechert, W. Davis & Nishimura, Kazuo, 1983. "A complete characterization of optimal growth paths in an aggregated model with a non-concave production function," Journal of Economic Theory, Elsevier, vol. 31(2), pages 332-354, December.
  3. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-539, May.
  4. McKenzie, Lionel W., 2005. "Optimal economic growth, turnpike theorems and comparative dynamics," Handbook of Mathematical Economics,in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 2, volume 3, chapter 26, pages 1281-1355 Elsevier.
  5. T.N. Srinivasan, 1962. "On a Two Sector Model of Growth," Cowles Foundation Discussion Papers 139R, Cowles Foundation for Research in Economics, Yale University.
  6. Costas Azariadis & Allan Drazen, 1990. "Threshold Externalities in Economic Development," The Quarterly Journal of Economics, Oxford University Press, vol. 105(2), pages 501-526.
  7. Spence, A Michael & Starrett, David, 1975. "Most Rapid Approach Paths in Accumulation Problems," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 16(2), pages 388-403, June.
  8. Majumdar, Mukul & Mitra, Tapan, 1982. "Intertemporal allocation with a non-convex technology: The aggregative framework," Journal of Economic Theory, Elsevier, vol. 27(1), pages 101-136, June.
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