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Structural analysis of optimal investment for firms with non-concave revenues

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  • Florian Wagener

Abstract

Qualitative properties of optimal investment strategies for a firm with quadratic costs and non-concave revenues are analysed. Organising information in a bifurcation diagram, it is found that the organising centre of the diagram is a so-called swallow-tail singularity. This implies the existence of threshold (or Skiba) points for positive discount factors. The parameter region for which threshold points exist is determined numerically, and for small discount factors some of its properties are derived by an approximation method.

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Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2004 with number 187.

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Date of creation: 11 Aug 2004
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Handle: RePEc:sce:scecf4:187

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Keywords: Optimal Control; Bifurcation Theory;

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References

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  1. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-39, May.
  2. Treadway, Arthur B, 1969. "On Rational Entrepreneurial Behaviour and the Demand for Investment," Review of Economic Studies, Wiley Blackwell, vol. 36(106), pages 227-39, April.
  3. Robert E. Lucas & Jr., 1967. "Adjustment Costs and the Theory of Supply," Journal of Political Economy, University of Chicago Press, vol. 75, pages 321.
  4. 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.
  5. Wagener, F. O. O., 2003. "Skiba points and heteroclinic bifurcations, with applications to the shallow lake system," Journal of Economic Dynamics and Control, Elsevier, vol. 27(9), pages 1533-1561, July.
  6. Haunschmied, Josef L. & Kort, Peter M. & Hartl, Richard F. & Feichtinger, Gustav, 2003. "A DNS-curve in a two-state capital accumulation model: a numerical analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 27(4), pages 701-716, February.
  7. Rosser Jr., J. Barkley, 2007. "The rise and fall of catastrophe theory applications in economics: Was the baby thrown out with the bathwater?," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3255-3280, October.
  8. Tobin, James, 1969. "A General Equilibrium Approach to Monetary Theory," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 1(1), pages 15-29, February.
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Cited by:
  1. Caulkins, Jonathan P. & Hartl, Richard F. & Kort, Peter M. & Feichtinger, Gustav, 2007. "Explaining fashion cycles: Imitators chasing innovators in product space," Journal of Economic Dynamics and Control, Elsevier, vol. 31(5), pages 1535-1556, May.
  2. Akao, Ken-Ichi & Kamihigashi, Takashi & Nishimura, Kazuo, 2011. "Monotonicity and continuity of the critical capital stock in the Dechert–Nishimura model," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 677-682.

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