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Innovation, Diffusion and the Distribution of Income in a Malthusian Economy

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  • Staley, Mark

Abstract

Between 5000 BCE and 1800, the population of the world grew 120-fold despite constraints on the total amount of land available for production. This paper develops a model linking population growth to increasing productivity driven by random innovation and diffusion. People are endowed with a set of skills obtained from their parents or neighbours, but those skills are imperfectly applied during their lifetimes. The resulting variation in productivity leads to a distribution of income and to a process of diffusion whereby high-income activities spread at the expense of low-income activities. An analytic formula is derived for the steady-state distribution of income. The model predicts that the rate of growth of population approaches an asymptotic limit, whereupon there are no scale effects. The model also predicts that if the rate of diffusion of knowledge is increased, the growth rate will increase.

Suggested Citation

  • Staley, Mark, 2008. "Innovation, Diffusion and the Distribution of Income in a Malthusian Economy," MPRA Paper 9849, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:9849
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    File URL: https://mpra.ub.uni-muenchen.de/9849/1/MPRA_paper_9849.pdf
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    References listed on IDEAS

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    1. Oded Galor & Omer Moav, 2002. "Natural Selection and the Origin of Economic Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 117(4), pages 1133-1191.
    2. Quamrul Ashraf & Oded Galor, 2011. "Dynamics and Stagnation in the Malthusian Epoch," American Economic Review, American Economic Association, vol. 101(5), pages 2003-2041, August.
    3. Charles I. Jones, 1995. "Time Series Tests of Endogenous Growth Models," The Quarterly Journal of Economics, Oxford University Press, vol. 110(2), pages 495-525.
    4. Galor, Oded, 2005. "From Stagnation to Growth: Unified Growth Theory," Handbook of Economic Growth,in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 1, chapter 4, pages 171-293 Elsevier.
    5. Gary D. Hansen & Edward C. Prescott, 2002. "Malthus to Solow," American Economic Review, American Economic Association, vol. 92(4), pages 1205-1217, September.
    6. Clark, Gregory & Hamilton, Gillian, 2006. "Survival of the Richest: The Malthusian Mechanism in Pre-Industrial England," The Journal of Economic History, Cambridge University Press, vol. 66(03), pages 707-736, September.
    7. Robert C. Merton, 1975. "An Asymptotic Theory of Growth Under Uncertainty," Review of Economic Studies, Oxford University Press, vol. 42(3), pages 375-393.
    8. Bourguignon, Francois, 1974. "A particular class of continuous-time stochastic growth models," Journal of Economic Theory, Elsevier, vol. 9(2), pages 141-158, October.
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    Cited by:

    1. Staley, Mark, 2011. "Growth and the diffusion of ideas," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 470-478.

    More about this item

    Keywords

    Selection; Malthusian; Diffusion; Innovation;

    JEL classification:

    • O30 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - General
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • N00 - Economic History - - General - - - General
    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General

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