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

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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.

Suggested Citation

  • Florian Wagener, 2004. "Structural analysis of optimal investment for firms with non-concave revenues," Computing in Economics and Finance 2004 187, Society for Computational Economics.
    • Handle: RePEc:sce:scecf4:187
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    2. F. O. O. Wagener, 2006. "Skiba Points for Small Discount Rates," Journal of Optimization Theory and Applications, Springer, vol. 128(2), pages 261-277, February.
    3. Bondarev, Anton & Dato, Prudence & Krysiak, Frank C., 2021. "Green Technology Transitions with an Endogenous Market Structure," Working papers 2021/07, Faculty of Business and Economics - University of Basel.
    4. Kiseleva, Tatiana & Wagener, F.O.O., 2010. "Bifurcations of optimal vector fields in the shallow lake model," Journal of Economic Dynamics and Control, Elsevier, vol. 34(5), pages 825-843, May.
    5. 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.
    6. Tatiana Kiseleva & Florian Wagener, 2015. "Bifurcations of Optimal Vector Fields," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 24-55, February.
    7. 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.
    8. Akao, Ken-Ichi & Kamihigashi, Takashi & Nishimura, Kazuo, 2025. "Critical capital stock in a continuous-time growth model with a convex-concave production function," Journal of Mathematical Economics, Elsevier, vol. 119(C).

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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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