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

Bondarev, Anton A. (2012): Optimal control over a continuous range of homogeneous and heterogeneous innovations with finite life-cycles.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Multiproduct innovations, finite life-cycles, heterogeneous production technologies, innovation incentives, distributed optimal control
• Subjects: C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods; 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; L - Industrial Organization > L0 - General > L00 - General

References

Aghion, P. and P. Howitt (1992). A model of growth through creative destruction. Econometrica 60 (2), 323-351.

Bondarev, A. (2010). Product and quality innovations: An optimal control approach. Working Papers 439, Bielefeld University, Institute of Mathematical Economics.

Bondarev, A. (2012a). The long run dynamics of heterogeneous product and process innovations for a multi product monopolist. Economics of Innovations and New Technology (forthcoming).

Bondarev, A. (2012b). 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.

Chang, H. (1995). Patent scope, antitrust policy, and cumulative innovation. The RAND Journal of Economics 26 (3), 671-688.

Cornelli, F. and M. Schankerman (1999). Patent renewals and r&d incentives. The RAND Journal of Economics 30 (2), 197-213.

Dawid, H., A. Greiner, and B. Zou (2010). Optimal foreign investment dynamics in the presence of technological spillovers. Journal of Economic Dynamics and Control 34 (3), 296 - 313.

Dockner, E., S. Jorgensen, N. Long, and G. Sorger (2000). Differential Games in Economics and Management Sciences. Cambridge University Press,/Cambridge.

Grossman, G. M. and E. Helpman (1993). Endogenous innovation in the theory of growth. working paper 4527, National Bureau of Economic Research.

Lambertini, L. (2009). Optimal product proliferation in a monopoly: A dynamic analysis. Review of Economic Analysis 1, 28-46.

Lambertini, L. and A. Mantovani (2010). Process and product innovation: A differential game approach to product life cycle. International Journal of Economic Theory 6 (2), 227-252.

Lambertini, L. and R. Orsini (2001). Network externalities and the overprovision of quality by a monopolist. Southern Economic Journal 67 (2), 969-982.

Lin, P. (2004). Process and product r&d by a multiproduct monopolist. Oxford Economic Papers (56), 735-743.

Nordhaus, W. D. (1967). The optimal life of a patent. Cowles Foundation Discussion Papers 241, Cowles Foundation for Research in Economics, Yale University.

Scotchmer, S. (1996). Protecting early innovators:should second-generation products be patentable? Journal of Industrial Economics N/A(27), 322-331.