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Growth and the diffusion of ideas

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  • Staley, Mark

Abstract

In a recent model of growth developed by Lucas (Lucas, R., 2009. Ideas and growth. Economica 76, 1–19), a continuum of people interact in a random manner and copy each other’s productive ideas when it is economically beneficial to do so. This paper extends the Lucas model by assuming that each person’s productivity also experiences random shocks due to individual discovery. A nonlinear partial differential equation is derived for the distribution of income, which admits a traveling wave solution representing a growing economy. The growth rate is an increasing function of the rate of imitation. The growth rate is also an increasing but concave function of population size and reaches a plateau in the continuum limit. Hence the scale effect is bounded. The model is extended to account for a nonzero cost of imitation, with similar results. The mathematical tools presented in this paper should prove useful in developing idea-based models of growth.

Suggested Citation

  • Staley, Mark, 2011. "Growth and the diffusion of ideas," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 470-478.
  • Handle: RePEc:eee:mateco:v:47:y:2011:i:4:p:470-478
    DOI: 10.1016/j.jmateco.2011.06.006
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. A. Mantovi, 2016. "Stochastic and path dependence effects in the diffusion of ideas," Economics Department Working Papers 2016-EP02, Department of Economics, Parma University (Italy).
    2. Augusto Schianchi, 2016. "La crescita endogena: una rilettura critica," QUADERNI DI ECONOMIA DEL LAVORO, FrancoAngeli Editore, vol. 2016(106), pages 31-48.
    3. Luttmer, Erzo G. J., 2014. "An Assignment Model of Knowledge Diffusion and Income Inequality," Working Papers 715, Federal Reserve Bank of Minneapolis.
    4. repec:spr:joevec:v:27:y:2017:i:4:d:10.1007_s00191-017-0497-5 is not listed on IDEAS
    5. Staley, Mark, 2015. "Firm Growth and Selection in a Finite Economy," MPRA Paper 67291, University Library of Munich, Germany.
    6. Luttmer, Erzo G. J., 2015. "Four Models of Knowledge Diffusion and Growth," Working Papers 724, Federal Reserve Bank of Minneapolis.
    7. A. Mantovi, 2016. "Stochastic and path dependence effects in the diffusion of ideas," Economics Department Working Papers 2016-EP02, Department of Economics, Parma University (Italy).

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