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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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    Cited by:

    1. Jess Benhabib & 'Eric Brunet & Mildred Hager, 2020. "Innovation and imitation," Papers 2006.06315, arXiv.org, revised Aug 2020.
    2. Gomes, Orlando, 2024. "Optimal planning of technological options and productivity distribution dynamics," Economic Modelling, Elsevier, vol. 130(C).
    3. Andrea Mantovi, 2016. "Stochastic and path dependence effects in the diffusion of ideas," Working Paper series 16-12, Rimini Centre for Economic Analysis.
    4. Augusto Schianchi, 2016. "La crescita endogena: una rilettura critica," QUADERNI DI ECONOMIA DEL LAVORO, FrancoAngeli Editore, vol. 2016(106), pages 31-48.
    5. Erzo G. J. Luttmer, 2020. "Bounded Learning from Incumbent Firms," Working Papers 771, Federal Reserve Bank of Minneapolis.
    6. Jess Benhabib & Jesse Perla & Christopher Tonetti, 2021. "Reconciling Models of Diffusion and Innovation: A Theory of the Productivity Distribution and Technology Frontier," Econometrica, Econometric Society, vol. 89(5), pages 2261-2301, September.
    7. Orlando Gomes & J. C. Sprott, 2017. "Sentiment-driven limit cycles and chaos," Journal of Evolutionary Economics, Springer, vol. 27(4), pages 729-760, September.
    8. Santiago Caicedo, 2019. "Note on Idea Diffusion Models with Cohort Structures," Economica, London School of Economics and Political Science, vol. 86(342), pages 396-408, April.
    9. Erzo G. J. Luttmer, 2014. "An Assignment Model of Knowledge Diffusion and Income Inequality," Working Papers 715, Federal Reserve Bank of Minneapolis.
    10. Kishi, Keiichi & Okada, Keisuke, 2018. "Trade Liberalization, Technology Diffusion, and Productivity," MPRA Paper 88597, University Library of Munich, Germany.
    11. Kishi, Keiichi, 2019. "Technology diffusion, innovation size, and patent policy," European Economic Review, Elsevier, vol. 118(C), pages 382-410.
    12. Staley, Mark, 2015. "Firm Growth and Selection in a Finite Economy," MPRA Paper 67291, University Library of Munich, Germany.
    13. Erzo G. J. Luttmer, 2015. "Four Models of Knowledge Diffusion and Growth," Working Papers 724, Federal Reserve Bank of Minneapolis.
    14. Staley, Mark, 2018. "The Knowledge-Diffusion Bottleneck in Economic Growth and Development," MPRA Paper 87255, University Library of Munich, Germany.
    15. Olivier Gallay & Fariba Hashemi & Max-Olivier Hongler, 2019. "Imitation, Proximity, And Growth — A Collective Swarm Dynamics Approach," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 22(05), pages 1-43, August.
    16. Kishi, Keiichi & Okada, Keisuke, 2021. "The impact of trade liberalization on productivity distribution under the presence of technology diffusion and innovation," Journal of International Economics, Elsevier, vol. 128(C).

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