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Growth and the diffusion of ideas

  • Staley, Mark

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.

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Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 47 (2011)
Issue (Month): 4-5 ()
Pages: 470-478

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Handle: RePEc:eee:mateco:v:47:y:2011:i:4:p:470-478
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  1. Mark Staley, 2010. "Innovation, diffusion and the distribution of income in a Malthusian economy," Journal of Evolutionary Economics, Springer, vol. 20(5), pages 689-714, October.
  2. Robert E. Lucas, Jr., 2008. "Ideas and Growth," NBER Working Papers 14133, National Bureau of Economic Research, Inc.
    • Robert E. Lucas, 2009. "Ideas and Growth," Economica, London School of Economics and Political Science, vol. 76(301), pages 1-19, 02.
  3. Susanto Basu & David N. Weil, 1998. "Appropriate Technology And Growth," The Quarterly Journal of Economics, MIT Press, vol. 113(4), pages 1025-1054, November.
  4. Charles I. Jones, . "Growth: With or Without Scale Effects?," Working Papers 99001, Stanford University, Department of Economics.
  5. Barro, Robert J & Sala-i-Martin, Xavier, 1997. " Technological Diffusion, Convergence, and Growth," Journal of Economic Growth, Springer, vol. 2(1), pages 1-26, March.
  6. Aghion, Philippe & Howitt, Peter, 1992. "A Model of Growth Through Creative Destruction," Scholarly Articles 12490578, Harvard University Department of Economics.
  7. Gene M. Grossman & Elhanan Helpman, 1989. "Quality Ladders in the Theory of Growth," NBER Working Papers 3099, National Bureau of Economic Research, Inc.
  8. Aghion, P. & Howitt, P., 1989. "A Model Of Growth Through Creative Destruction," UWO Department of Economics Working Papers 8904, University of Western Ontario, Department of Economics.
  9. Parente, Stephen L & Prescott, Edward C, 1994. "Barriers to Technology Adoption and Development," Journal of Political Economy, University of Chicago Press, vol. 102(2), pages 298-321, April.
  10. Segerstrom, P.S., 1990. "Innovation, Imitation And Economic Growth," Papers 8818, Michigan State - Econometrics and Economic Theory.
  11. Jones, Charles I, 1995. "Time Series Tests of Endogenous Growth Models," The Quarterly Journal of Economics, MIT Press, vol. 110(2), pages 495-525, May.
  12. Harris, Christopher & Howitt, Peter & Vickers, John & Aghion, Philippe, 2001. "Competition, Imitation and Growth with Step-by-Step Innovation," Scholarly Articles 12375013, Harvard University Department of Economics.
  13. Iwai, Katsuhito, 1984. "Schumpeterian dynamics : An evolutionary model of innovation and imitation," Journal of Economic Behavior & Organization, Elsevier, vol. 5(2), pages 159-190, June.
  14. Eaton, Jonathan & Kortum, Samuel, 1999. "International Technology Diffusion: Theory and Measurement," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(3), pages 537-70, August.
  15. Mukoyama, Toshihiko, 2003. "Innovation, imitation, and growth with cumulative technology," Journal of Monetary Economics, Elsevier, vol. 50(2), pages 361-380, March.
  16. Staley, Mark, 2008. "Innovation, Diffusion and the Distribution of Income in a Malthusian Economy," MPRA Paper 9849, University Library of Munich, Germany.
  17. Iwai, Katsuhito, 1984. "Schumpeterian dynamics, Part II : Technological progress, firm growth and `economic selection'," Journal of Economic Behavior & Organization, Elsevier, vol. 5(3-4), pages 321-351.
  18. Romer, Paul M, 1990. "Endogenous Technological Change," Journal of Political Economy, University of Chicago Press, vol. 98(5), pages S71-102, October.
  19. Liam Brunt, 2003. "Mechanical innovation in the industrial revolution: the case of plough design," Economic History Review, Economic History Society, vol. 56(3), pages 444-477, 08.
  20. Stephen L. Parente & Edward C. Prescott, 2002. "Barriers to Riches," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262661306, June.
  21. Allen, Robert C., 1983. "Collective invention," Journal of Economic Behavior & Organization, Elsevier, vol. 4(1), pages 1-24, March.
  22. Fernando E. Alvarez & Francisco J. Buera & Robert E. Lucas, Jr., 2008. "Models of Idea Flows," NBER Working Papers 14135, National Bureau of Economic Research, Inc.
  23. Kremer, Michael, 1993. "Population Growth and Technological Change: One Million B.C. to 1990," The Quarterly Journal of Economics, MIT Press, vol. 108(3), pages 681-716, August.
  24. Jan Eeckhout & Boyan Jovanovic, 2002. "Knowledge Spillovers and Inequality," American Economic Review, American Economic Association, vol. 92(5), pages 1290-1307, December.
  25. Samuel S. Kortum, 1997. "Research, Patenting, and Technological Change," Econometrica, Econometric Society, vol. 65(6), pages 1389-1420, November.
  26. Aghion, Philippe, et al, 2001. "Competition, Imitation and Growth with Step-by-Step Innovation," Review of Economic Studies, Wiley Blackwell, vol. 68(3), pages 467-92, July.
  27. Jovanovic, Boyan & Rob, Rafael, 1989. "The Growth and Diffusion of Knowledge," Review of Economic Studies, Wiley Blackwell, vol. 56(4), pages 569-82, October.
  28. P. Taylor & L. Jonker, 2010. "Evolutionarily Stable Strategies and Game Dynamics," Levine's Working Paper Archive 457, David K. Levine.
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