Sen, Debapriya and Stamatopoulos, Giorgos (2016): Licensing under general demand and cost functions. Published in: European Journal of Operational Research , Vol. 253, No. 3 (September 2016): pp. 673680.

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Abstract
We consider a Cournot duopoly under general demand and cost functions, where an incumbent patentee has a cost reducing technology that it can license to its rival by using combinations of royalties and upfront fees (twopart tariffs). We show that for drastic technologies: (a) licensing occurs and both firms stay active if the cost function is superadditive and (b) licensing does not occur and the patentee monopolizes the market if the cost function is additive or subadditive. For non drastic technologies, licensing takes place provided the average efficiency gain from the cost reducing technology is higher than the marginal gain computed at the licensee's reservation output. Optimal licensing policies have both royalties and fees for significantly superior technologies if the cost function is superadditive. By contrast, for additive and certain subadditive cost functions, optimal licensing policies have only royalties and no fees.
Item Type:  MPRA Paper 

Original Title:  Licensing under general demand and cost functions 
Language:  English 
Keywords:  Patent licensing; Superadditive function; Subadditive function; Royalties; Twopart tariff 
Subjects:  D  Microeconomics > D4  Market Structure, Pricing, and Design > D43  Oligopoly and Other Forms of Market Imperfection D  Microeconomics > D4  Market Structure, Pricing, and Design > D45  Rationing ; Licensing L  Industrial Organization > L1  Market Structure, Firm Strategy, and Market Performance > L13  Oligopoly and Other Imperfect Markets 
Item ID:  73980 
Depositing User:  Debapriya Sen 
Date Deposited:  24 Sep 2016 10:59 
Last Modified:  24 Sep 2016 11:00 
References:  Aczel, J. (1966). Lectures on Functional Equations and their Applications, Academic Press, New York. Arrow, K.J. (1962). Economic welfare and the allocation of resources for invention. In: R.R. Nelson (Ed.), The Rate and Direction of Inventive Activity: Economic and Social Factors, Princeton Univ. Press, pp. 609625. Avagyan V., EstebanBravo M., VidalSanz J.M. (2014). Licensing radical product innovations to speed up the diffusion. European Journal of Operational Research, 239, 542555. Beckenbach E.F. (1964). Superadditive inequalities. Pacific Journal of Mathematics, 14, 421438. Bourin JC., Hiai F. (2015). Antinorms on finite von Neumann algebras. Publications of the Research Institute for Mathematical Sciences, 51, 207235. Bruckner A.M. (1962). Tests for the superadditivity of functions. Proceedings of the American Mathematical Society, 13, 126130. Bruckner A.M. (1964). Some relations between locally superadditive functions and convex functions. Proceedings of the American Mathematical Society, 15, 6165. Choi, J.P. (2001). Technology transfer with moral hazard. International Journal of Industrial Organization, 19, 249266. Dastidar K.G. (1995). On the existence of pure strategy Bertrand equilibrium. Economic Theory, 5, 1932. Dastidar K.G. (2000). Is a unique Cournot equilibrium locally stable? Games and Economic Behavior, 32, 106218. Dixit, A. (1986). Comparative statics for oligopoly. International Economic Review, 27, 107122. FauliOller, R., Sandon'is, J. (2002). Welfare reducing licensing. Games and Economic Behavior, 41, 192205. Gaudet, G., Salant, W. (1991). Uniqueness of Cournot equilibrium: new results from old methods. Review of Economic Studies, 58, 399404. Gallini, N.T., Wright, B.D. (1990). Technology transfer under asymmetric information. RAND Journal of Economics, 21, 147160. Jensen, R. (1992). Dynamic patent licensing. International Journal of Industrial Organization, 10, 349368. Held, B., Parker J. (2011). Royalty rate and deal terms: a survey. Licensing Executives Society, Canada. Kamien, M.I., Oren, S.S., Tauman, Y. (1992). Optimal licensing of costreducing innovation. Journal of Mathematical Economics, 21, 483508. Kamien, M.I., Tauman, Y. (1984). The private value of a patent: a game theoretic analysis. Zeitschrift fur Nationalokonomie, 4 (Supplement), 93118. Kamien, M.I., Tauman, Y. (1986). Fees versus royalties and the private value of a patent. Quarterly Journal of Economics, 101, 471491. Kamien, M.I., Tauman, Y. (2002). Patent licensing: the inside story. The Manchester School, 70, 715. Katz, M.L., Shapiro, C. (1985). On the licensing of innovations. RAND Journal of Economics, 16, 504520. Katz, M.L., Shapiro, C. (1986). How to license intangible property. Quarterly Journal of Economics, 101, 567589. Marjit, S. (1990). On a noncooperative theory of technology transfer. Economics Letters, 33, 293298. Muto, S. (1993). On licensing policies in Bertrand competition. Games and Economic Behavior, 5, 257267. Saracho, A.I. (2004). The implications of intertemporal consistency for patent licensing, Working Paper. Sen, D., Tauman Y. (2007). General licensing schemes for a costreducing innovation. Games and Economic Behavior, 59, 163186. Sen, D., Stamatopoulos G. (2009). Technology transfer under returns to scale. Manchester School, 77, 337365. Wang, X.H. (1998). Fee versus royalty licensing in a Cournot duopoly model. Economics Letters 60, 5562. Vives X. (2001). Oligopoly Pricing: Old ideas and new tools, MIT Press. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/73980 