On the dynamics of innovators and imitators

Cerqueti, Roy and Tramontanta, Fabio and Ventura, Marco (2012): On the dynamics of innovators and imitators.

Abstract

After deriving a model describing the law of evolution of innovators and imitators the article focuses on their relationships under two different scenarios: prey-predator, in which innovators are regarded as preys, and competing species. Analytic results show that among the feasible equilibria the coexistence equilibrium is the only stable equilibrium under the fi�rst scenario. We also �find conditions on the parameters allowing local stability of the coexistence equilibrium in the second scenario. Such conditions imply the existence of an inverse-U shaped relationship between innovation and imitation.

• Item Type: MPRA Paper
• Language: English
• Keywords: Imitation, innovation, intellectual property rights, Lotka-Volterra system
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling; O - Economic Development, Innovation, Technological Change, and Growth > O3 - Innovation ; Research and Development ; Technological Change ; Intellectual Property Rights > O34 - Intellectual Property and Intellectual Capital; O - Economic Development, Innovation, Technological Change, and Growth > O3 - Innovation ; Research and Development ; Technological Change ; Intellectual Property Rights > O33 - Technological Change: Choices and Consequences ; Diffusion Processes; O - Economic Development, Innovation, Technological Change, and Growth > O3 - Innovation ; Research and Development ; Technological Change ; Intellectual Property Rights > O31 - Innovation and Invention: Processes and Incentives

References

[1] Aghion P., Bloom N., Blundell R., Griffith R., Howitt P., 2005. Competition and innovation: an inverted-U relationship. Quarterly Journal of Economics 120, 701�-728.

[2] Becker G.S., 1968. Crime and Punishment: an Economic Approach, Journal of Political Economy, 76(2), 160-217.

[3] Caballero R.J., Jaffe A.B., 1993. How high are the giants� shoulders: an empirical assessment of knowledge spillovers and creative destruction in a model of economic growth. In: Blanchard, O., Fischer, S. (Eds.), NBER Macroeconomics Annual. MIT Press, Cambridge, MA.

[4] Cysne R.P., Turchick D., 2012. Intellectual property rights protection and endogenous economic growth revisited. Journal of Economic Dynamics & Control, 36, 851-861.

[5] Dixit A, Pindyck R., 1994. Investment under uncertainty. Princeton University Press.

[6] Furukawa Y., 2007. The protection of intellectual property rights and edogenous growth: is stronger always better? Journal of Economic Dynamics & Control, 31, 3644-3670.

[7] Gould D.M., Gruden, W.C., 1996. The role of intellectual property rights in economic growth. Journal of Development Economics 48, 323�-350.

[8] Goh B.S., 1976. Global Stability in Two Species Interactions, Journal of Mathematical Biology, 3, 313-318.

[9] Goh B.S., 1980. Management and analysis of biological populations, Elsevier Scienti�c Pub. Co. New York.

[10] Helpman E., 1993. Innovation, imitation, and intellectual property rights. Econometrica 61, 1247-�1280.

[11] Horii R., Iwaisako T., 2007. Economic growth with imperfect protection of intellectual property rights. Journal of Economics 90, 45�-85.

[12] Koléda G., 2005. Patents� novelty requirement and endogenous growth. Revue d'Economie Politique 114, 201�-222.

[13] Lai E.L.C., 1998. International intellectual property rights protection and the rate of product innovation. Journal of Development Economics, 55(1), 133-153.

[14] Lanjouw J.O., Pakes A., Putnam J., 1998. How to Count Patents and Value Intellectual Property: the Uses of Patent Renewal and Application Data. The Journal of Industrial Economics, 46(4), 405-432.

[15] Lotka A.J., 1956. Elements of Mathematical Biology, Dover Pub. Inc. New York.

[16] Schankerman M, 1998. How Valuable is Patent Protection? Estimates by Technology Field. Rand Journal of Economics, 29(1), 77-107.

[17] Pakes A.S., Simpson M., 1989. Patent Renewal Data, Brooking Papers on Economic Activity: Microeconomics, 331-410.

[18] Tse C. Y., 2002. The diffusion of knowledge and the productivity and appropriability of R&D investments. Journal of Economic Dynamics & Control 26, 303-331.

[19] Volterra V., 1926. Variazioni e �uttuazioni del numero d�individui in specie animali conviventi. Mem. Accad. Lincei Roma, 2, 31-113.