Polterovich, Victor and Henkin, Gennadi (1989): An Evolutionary Model with Interaction between Development and Adoption of New Technologies. Published in: Matekon , Vol. 26, No. 1 (1989): pp. 3-19.
Download (3MB) | Preview
We propose a difference-differential equation that reflects interactions between innovation and imitation processes to describe the evolution of the distribution curve of firms by efficiency levels. An explicit solution of this equation is obtained for arbitrary finite initial conditions. It is shown that this equation admits one-parametric family of logistic waves, and that arbitrary solution exponentially converges to one of the waves. This result explains two stylized empirical facts: the "logistic" shape of diffusion curves and the stable form of production capacities distribution by efficiency levels. Possible generalizations, modifications and applications are discussed.
|Item Type:||MPRA Paper|
|Original Title:||An Evolutionary Model with Interaction between Development and Adoption of New Technologies|
|Keywords:||innovation; imitation; diffusion; logistic distribution; efficiency; wave solution; stability; Burgers equation|
|Subjects:||O - Economic Development, Technological Change, and Growth > O4 - Economic Growth and Aggregate Productivity > O41 - One, Two, and Multisector Growth Models
O - Economic Development, Technological Change, and Growth > O3 - Technological Change; Research and Development; Intellectual Property Rights > O33 - Technological Change: Choices and Consequences; Diffusion Processes
|Depositing User:||Victor Polterovich|
|Date Deposited:||08. May 2010 06:39|
|Last Modified:||13. Feb 2013 12:49|
S.P. Aukutsionek, "O teoriiakh neravnomernosti tekhnicheskogo progressa", Ekonomika i matematicheskie metody, 1986, vol. 27, no. 5.
E. Mansfield, The Economics of Innovation [Russian translation], Progress Publishers, Moscow (1970).
D. Sahal, Technological Innovation: Concepts, Models, Estimates [Russian translation], Finansy i Statistika Publishers, Moscow (1985).
A. Romeo, "Interindustry and interfirm differences in the rate of diffusion of an innovation", Rev. Econ. Stat., 1975, vol. 57, no. 3.
T.H. Hannan and J.M. McDowell, "Market concentration and the diffusion of new technology in the banking industry," Rev. Econ. Stat., 1984, vol. 66, no. 4.
S. Davies, The Diffusion of Process Innovations, Cambridge (1979).
A.E. Varshavskiy Nauchno-tekhnicheskxi progress v modeliakh ekonomicheskogo razvitiia, Finansy i Statistika Publishers, Moscow (1984).
R. Jensen, "Adoption and diffusion of an innovation of uncertain profitability," J. Econ. Theor., 1982, vol. 27, no. 1.
L. Johansen, Production Functions, Amsterdam-London (1972).
K. Sato, Production Functions and Aggregation, Amsterdam (1975).
A.A. Petrov and I.G. Pospelov, "Sistemnyi analiz razvivaiushcheisia ekonomiki: k teorii proizvodstvennykh funktsii, I," Izv.ANSSSR, Tekhn. kibernet., 1979, No. 2.
A.A. Shananin, "Issledovanie odnogo klassa proizvodstvennykh funktsii, voznikaiushchikh pri makroopisanii ekonomicheskikh sistem," Zh. vych. Mat. i Mat. Fiz, 1984, vol. 24, no. 12.
K. Iwai, "Schumpeterian dynamics. Part I: An evolutionary model of innovation and imitation," J. Econ. Behavior and Organization, 1984, vol. 5, no. 2.
K. Iwai, "Schurapeterian dynamics. Part II: Technological progress, firm growth and ‘economic selection’," J. Econ. Behavior and Organization, 1984, vol. 5, no. 3-4.
V.L. Makarov and A.P. Torzhevskii, Vliianie sdvigov v tekhnicheskikh urovniakh proizvodstva na makropokazateli rzvitiia ekonomiki, Preprint, TsEMI AN SSSR, Moscow (1986).
V.L. Makarov, "O dinamicheskikh modeliakh ekonomiki i razvitii idei L.V. Kantorovicha", Ekonomika i matematicheskie metody, 1987, vol. 23, no. 1.
J. Whitham, Linear and Nonlinear Waves [Russian translation], Mir Publishers, Moscow (1977).
J. Murray, Nonlinear Differential Equations in Biology. Lectures on Models [Russian translation], Mir Publishers, Moscow (1983).
D. Levi, O. Ranisco, and M. Bruschi, "Continuous and discrete matrix Burgers hierarchies", Nuovo Cimento, 1983, vol. 748, no. 1.