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Optimal control over a continuous range of homogeneous and heterogeneous innovations with finite life-cycles

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  • Bondarev, Anton A.

Abstract

The paper presents a fully dynamic framework for simultaneous analysis of variety enhancing and quality improving innovations for the case of a single agent. There is a continuous stream of variety enhancing innovations and every new product from this stream has its own quality dimension which also may be developed. In this framework the limited life-cycles of all these new products are assumed. Then the question of how longer or shorter life-cycles may influence the innovative activity of both types is analyzed. It is demonstrated, that in the case of homogeneous products the longer is the life-cycle the more intense are innovations of both types, while in heterogeneous case the effect is more complicated. At initial stage of industry development longer life-cycles (aka patents) stimulate innovative activity, while in mature stage of development they do not. This gives foundation for limited nature of optimal length of patents solely from the considerations of the type and nature of the industry itself, without usual reference to the competition effects. The model is developed using distributed optimal control technique.

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File URL: http://mpra.ub.uni-muenchen.de/45277/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 40068.

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Date of creation: 12 May 2012
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Handle: RePEc:pra:mprapa:40068

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Keywords: Multiproduct innovations; finite life-cycles; heterogeneous production technologies; innovation incentives; distributed optimal control;

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References

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  1. Aghion, Philippe & Howitt, Peter, 1992. "A Model of Growth through Creative Destruction," Econometrica, Econometric Society, Econometric Society, vol. 60(2), pages 323-51, March.
  2. Bondarev, Anton A., 2012. "Heterogeneous product and process innovations for a multi-product monopolist under finite life-cycles of production technologies," MPRA Paper 38243, University Library of Munich, Germany.
  3. Anton Bondarev, 2010. "Product and Quality Innovations: An Optimal Control Approach," Working Papers 439, Bielefeld University, Center for Mathematical Economics.
  4. Richard Gilbert & Carl Shapiro, 1990. "Optimal Patent Length and Breadth," RAND Journal of Economics, The RAND Corporation, vol. 21(1), pages 106-112, Spring.
  5. L. Lambertini, 2008. "Optimal Product Proliferation in Monopoly: A Dynamic Analysis," Working Papers 648, Dipartimento Scienze Economiche, Universita' di Bologna.
  6. Farrell, Joseph & Shapiro, Carl, 2004. "Intellectual Property, Competition, and Information Technology," Competition Policy Center, Working Paper Series, Competition Policy Center, Institute for Business and Economic Research, UC Berkeley qt3s03932b, Competition Policy Center, Institute for Business and Economic Research, UC Berkeley.
  7. Luca Lambertini & Raimondello Orsini, 2001. "Network Externalities and the Overprovision of Quality by a Monopolist," Southern Economic Journal, Southern Economic Association, vol. 67(4), pages 969-982, April.
  8. Aghion, Philippe & Howitt, Peter, 1992. "A Model of Growth Through Creative Destruction," Scholarly Articles 12490578, Harvard University Department of Economics.
  9. Hopenhayn, Hugo A & Mitchell, Matthew F, 2001. "Innovation Variety and Patent Breadth," RAND Journal of Economics, The RAND Corporation, vol. 32(1), pages 152-66, Spring.
  10. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, 9.
  11. Herbert Dawid & Alfred Greiner & Benteng Zou, 2008. "Optimal Foreign Investment Dynamics in the Presence of Technological Spillovers," CREA Discussion Paper Series 08-07, Center for Research in Economic Analysis, University of Luxembourg.
  12. Suzanne Scotchmer, 1996. "Protecting Early Innovators: Should Second-Generation Products Be Patentable?," RAND Journal of Economics, The RAND Corporation, vol. 27(2), pages 322-331, Summer.
  13. Vincenzo Denicolo, 2002. "Sequential innovation and the patent-antitrust conflict," Oxford Economic Papers, Oxford University Press, vol. 54(4), pages 649-668, October.
  14. L. Lambertini & A. Mantovani, 2004. "Process and Product Innovation: a Differential Game Approach to Product Life Cycle," Working Papers 529, Dipartimento Scienze Economiche, Universita' di Bologna.
  15. Anton Bondarev, 2012. "The long-run dynamics of product and process innovations for a multi-product monopolist," Economics of Innovation and New Technology, Taylor & Francis Journals, vol. 21(8), pages 775-799, November.
  16. Denicolo, Vincenzo, 1996. "Patent Races and Optimal Patent Breadth and Length," Journal of Industrial Economics, Wiley Blackwell, vol. 44(3), pages 249-65, September.
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  1. Bondarev, Anton A., 2012. "Optimal control over a continuous range of homogeneous and heterogeneous innovations with finite life-cycles," MPRA Paper 40068, University Library of Munich, Germany.

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