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On knife-edge conditions with unbounded growth

Author

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  • Bugajewski, Dariusz
  • Maćkowiak, Piotr

Abstract

Imagine an economic process modeled with help of ordinary differential equations with some fixed initial conditions and suppose that a solution to the system under consideration, for some reason, should enjoy desired conditions. It appears that small changes in the system describing the modeled process may have devastating effect on the fulfillment of the desired conditions by solutions of the perturbed system. Such a feature of a system is called a knife-edge condition in the literature on economic growth and it has recently found some deeper interest in that literature. However, the available results seem to be unclear and not correct – this paper shows how to correct and improve these results, creating consistent mathematical foundations of that theory. The main contribution of the paper is that knife-edge conditions are present whenever long-term unbounded growth of an economic variable is required as (or implied by) a desired regularity condition.

Suggested Citation

  • Bugajewski, Dariusz & Maćkowiak, Piotr, 2015. "On knife-edge conditions with unbounded growth," Journal of Macroeconomics, Elsevier, vol. 45(C), pages 274-283.
    • Handle: RePEc:eee:jmacro:v:45:y:2015:i:c:p:274-283
    DOI: 10.1016/j.jmacro.2015.05.005
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    References listed on IDEAS

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    1. Jakub Growiec, 2007. "Beyond the Linearity Critique: The Knife-edge Assumption of Steady-state Growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(3), pages 489-499, June.
    2. Jones, Charles I., 2005. "Growth and Ideas," Handbook of Economic Growth, in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 1, chapter 16, pages 1063-1111, Elsevier.
    3. Robert M. Solow, 1994. "Perspectives on Growth Theory," Journal of Economic Perspectives, American Economic Association, vol. 8(1), pages 45-54, Winter.
    4. Christian Groth & Karl-Josef Koch & Thomas Steger, 2010. "When economic growth is less than exponential," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(2), pages 213-242, August.
    5. Growiec, Jakub, 2010. "Knife-edge conditions in the modeling of long-run growth regularities," Journal of Macroeconomics, Elsevier, vol. 32(4), pages 1143-1154, December.
    6. Christiaans, Thomas, 2004. "Types of balanced growth," Economics Letters, Elsevier, vol. 82(2), pages 253-258, February.
    7. Turnovsky, Stephen J., 2002. "Knife-Edge Conditions And The Macrodynamics Of Small Open Economies," Macroeconomic Dynamics, Cambridge University Press, vol. 6(02), pages 307-335, April.
    8. Jonathan Temple, 2003. "The Long‐Run implications of Growth Theories," Journal of Economic Surveys, Wiley Blackwell, vol. 17(3), pages 497-510, July.
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    Cited by:

    1. Sriket, Hongsilp & Suen, Richard M.H., 2022. "Sources of economic growth in models with non-renewable resources," Journal of Macroeconomics, Elsevier, vol. 72(C).

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    More about this item

    Keywords

    Knife-edge condition; Long-term growth; Perturbation of system of differential equations; Regular growth;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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