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Modeling Limits to Growth

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System Dynamics Modeling with R

Part of the book series: Lecture Notes in Social Networks ((LNSN))

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Abstract

This chapter introduces system dynamics models of limits to growth. First, a one-stock model is presented, where the growth rate varies, and is influenced by the system’s carrying capacity. Second, a model of economic growth is described, which captures the law of diminishing returns, a feature of many economic systems. Third, a two-stock model of limits to growth is specified, where a growing stock consumes its carrying capacity, and this dynamic leads to growth followed by rapid decline. Before introducing the limits to growth models, an explanation of an important formulation method in system dynamics is presented. This allows modelers to construct robust equations to model the effect of one variable on another. This is useful for many system dynamics models, particularly where one system stock influences another system stock.

There will always be limits to growth. They can be self-imposed.

If they aren’t, they will be system-imposed.

Donella H. Meadows, Thinking in Systems: A Primer (2008, p. 103).

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References

  • Bacaër N (2011) Verhulst and the logistic equation (1838). In: A short history of mathematical population dynamics. Springer London, pp 35–39

    Google Scholar 

  • Meadows DH (2008) Thinking in systems: a primer. Chelsea Green Publishing

    Google Scholar 

  • Page S (2015) A model of growth. Supporting material for Coursera Model Thinking MOOC Course. https://www.coursera.org/course/modelthinking. Accessed 30 June 2015

  • Richardson GP (1991) Feedback thought in social science and systems theory. Pegasus Communications, Inc., Chicago

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  • Solow RM (1956) A contribution to the theory of economic growth. Quart J Econ 70:65–94

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  • Sterman JD (2000) Business dynamics: systems thinking and modeling for a complex world. Irwin/McGraw-Hill, Boston

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  • Verhulst P-F (1845) “Recherches mathématiques sur la loi d’accroissement de la population.” Nouv. mém. de l’Academie Royale des Sci. et Belles-Lettres de Bruxelles 18:1–41

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  • Verhulst P-F (1847) “Deuxième mémoire sur la loi d’accroissement de la population.” Mém. de l’Academie Royale des Sci., des Lettres et des Beaux-Arts de Belgique 20:1–32

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Correspondence to Jim Duggan .

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Duggan, J. (2016). Modeling Limits to Growth. In: System Dynamics Modeling with R. Lecture Notes in Social Networks. Springer, Cham. https://doi.org/10.1007/978-3-319-34043-2_3

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  • DOI: https://doi.org/10.1007/978-3-319-34043-2_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-34041-8

  • Online ISBN: 978-3-319-34043-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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