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Multiple Equilibria and Thresholds Due to Relative Investment Costs

Author

Listed:
  • R. F. Hartl

    (University of Vienna)

  • P. M. Kort

    (Tilburg University
    University of Antwerp)

  • G. Feichtinger

    (Vienna University of Technology)

  • F. Wirl

    (University of Vienna)

Abstract

A dynamic model of the firm is studied in which investment costs depend on the magnitude of the investment relative to the stock of capital goods. It is shown that in general nonunique steady states can exist which can be stable or unstable. It is possible that unstable steady states occur in the concave domain of the Hamiltonian. For a particular specification, a scenario occurs with two stable steady states and one unstable steady state. The two stable steady states are long run equilibria; which one of them is reached in the long run depends on the initial state. In case the Hamiltonian is locally concave around the unstable steady state, this steady state is the threshold that separates the domain of initial conditions that each of the stable steady states attracts. The unstable steady state is a node and investment is a continuous function of the capital stock. If the unstable steady state lies in the nonconcave domain of the Hamiltonian, this steady state can either be a node or a focus. Furthermore, continuity can (but need not) be retained similarly to the concave case, a fact which has been entirely overlooked in the literature.

Suggested Citation

  • R. F. Hartl & P. M. Kort & G. Feichtinger & F. Wirl, 2004. "Multiple Equilibria and Thresholds Due to Relative Investment Costs," Journal of Optimization Theory and Applications, Springer, vol. 123(1), pages 49-82, October.
    • Handle: RePEc:spr:joptap:v:123:y:2004:i:1:d:10.1023_b:jota.0000043991.06755.af
    DOI: 10.1023/B:JOTA.0000043991.06755.af
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    References listed on IDEAS

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    3. Grüne, Lars & Semmler, Willi & Stieler, Marleen, 2015. "Using nonlinear model predictive control for dynamic decision problems in economics," Journal of Economic Dynamics and Control, Elsevier, vol. 60(C), pages 112-133.
    4. Philip L. Brock, 2009. "Collateral Constraints and Macroeconomic Adjustment in an Open Economy," Working Papers UWEC-2009-03, University of Washington, Department of Economics.
    5. Peter Funk, 2009. "History-Dependent Individual Behavior, Polarization, and Pareto-Improving Activating Welfare," Working Paper Series in Economics 43, University of Cologne, Department of Economics.
    6. Antoci, Angelo & Galeotti, Marcello & Russu, Paolo, 2011. "Poverty trap and global indeterminacy in a growth model with open-access natural resources," Journal of Economic Theory, Elsevier, vol. 146(2), pages 569-591, March.
    7. Akihiko Yanase & Ngo Van Long & Ngo Van Long, 2020. "Trade Costs and Strategic Investment in Infrastructure in a Dynamic Global Economy with Symmetric Countries," CESifo Working Paper Series 8707, CESifo.
    8. Wirl, Franz, 2009. "OPEC as a political and economical entity," European Journal of Political Economy, Elsevier, vol. 25(4), pages 399-408, December.
    9. Peter Funk, 2019. "Human Capital, Polarisation and Pareto-improving Activating Welfare," The Economic Journal, Royal Economic Society, vol. 129(619), pages 1221-1246.
    10. Y. Hossein Farzin & Ken-Ichi Akao, 2006. "When is it Optimal to Exhaust a Resource in a Finite Time?," Working Papers 2006.23, Fondazione Eni Enrico Mattei.
    11. F. Wirl, 2007. "Social Interactions within a Dynamic Competitive Economy," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 385-400, June.
    12. Feichtinger, G. & Hartl, R.F. & Kort, P.M. & Yegorov, Y.A., 2007. "A new solution property in optimal control : The lens," Other publications TiSEM c80d5d10-2f54-4c43-a949-7, Tilburg University, School of Economics and Management.
    13. Yuri Yegorov & Dieter Grass & Magda Mirescu & Gustav Feichtinger & Franz Wirl, 2020. "Growth and Collapse of Empires: A Dynamic Optimization Model," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 620-643, August.
    14. Wirl, Franz, 2004. "Thresholds in concave renewable resource models," Ecological Economics, Elsevier, vol. 48(2), pages 259-267, February.
    15. Jonathan Caulkins & Gustav Feichtinger & Richard Hartl & Peter Kort & Andreas Novak & Andrea Seidl, 2013. "Multiple equilibria and indifference-threshold points in a rational addiction model," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(3), pages 507-522, September.
    16. Ngo Van Long, 2019. "Managing, Inducing, and Preventing Regime Shifts: A Review of the Literature," CESifo Working Paper Series 7749, CESifo.
    17. Ken-Ichi Akao & Takashi Kamihigashi & Kazuo Nishimura, 2015. "Critical Capital Stock in a Continuous-Time Growth Model with a Convex-Concave Production Function," Discussion Paper Series DP2015-39, Research Institute for Economics & Business Administration, Kobe University.
    18. Wirl Franz & Novak Andreas J. & Hof Franz X., 2008. "Happiness due to Consumption and its Increases, Wealth and Status," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(4), pages 1-34, December.

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