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Licensing under general demand and cost functions

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  • Sen, Debapriya
  • Stamatopoulos, Giorgos

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 (two-part 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.

Suggested Citation

  • Sen, Debapriya & Stamatopoulos, Giorgos, 2016. "Licensing under general demand and cost functions," MPRA Paper 73980, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:73980
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    Cited by:

    1. Masahiko Hattori & Yasuhito Tanaka, 2018. "License and Entry Strategies for an Outside Innovator Under Duopoly with Combination of Royalty and Fixed Fee," Journal of Industry, Competition and Trade, Springer, vol. 18(4), pages 485-502, December.
    2. Masahiko Hattori & Yasuhito Tanaka, 2018. "Negative Royalty in Duopoly and Definition of License Fee: General Demand and Cost Functions," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 17(2), pages 163-178, September.
    3. Stefano Colombo & Luigi Filippini & Debapriya Sen, 2023. "Patent Licensing and Capacity in a Cournot Model," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 62(1), pages 45-62, February.
    4. Liu Yao & Mukherjee Arijit, 2024. "Lobbying for Tariff Protection, International Technology Licensing and Consumer Surplus," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 24(1), pages 117-139, January.
    5. Luca Sandrini, 2023. "Price vs Market Share with Royalty Licensing: Incomplete Adoption of a Superior Technology with Heterogeneous Firms," Discussion Papers 2302, Budapest University of Technology and Economics, Quantitative Social and Management Sciences.
    6. Sen, Debapriya & Tauman, Yair, 2018. "Patent licensing in a Cournot oligopoly: General results," Mathematical Social Sciences, Elsevier, vol. 96(C), pages 37-48.
    7. Wu, Cheng-Han, 2018. "Price competition and technology licensing in a dynamic duopoly," European Journal of Operational Research, Elsevier, vol. 267(2), pages 570-584.
    8. Zhang, Qiao & Zhang, Jianxiong & Zaccour, Georges & Tang, Wansheng, 2018. "Strategic technology licensing in a supply chain," European Journal of Operational Research, Elsevier, vol. 267(1), pages 162-175.
    9. Colombo, Stefano & Filippini, Luigi & Sen, Debapriya, 2020. "Licensing with capacity constraint," MPRA Paper 102653, University Library of Munich, Germany.
    10. Hattori, Masahiko & Tanaka, Yasuhito, 2017. "Robustness of subsidy in licensing under vertical differentiation: General distribution and cost functions," MPRA Paper 78857, University Library of Munich, Germany.
    11. Wu, Cheng-Han & Kao, Yi-Jhe, 2018. "Cooperation regarding technology development in a closed-loop supply chain," European Journal of Operational Research, Elsevier, vol. 267(2), pages 523-539.
    12. Siyu Ma & Debapriya Sen & Yair Tauman, 2024. "Optimal patent licensing: from three to two part tariffs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(4), pages 1233-1273, December.
    13. Tanaka, Yasuhito & Hattori, Masahiko, 2017. "Convexity, concavity, super-additivity, and sub-additivity of cost function without fixed cost," MPRA Paper 80502, University Library of Munich, Germany.
    14. Tanaka, Yasuhito & Hattori, Masahiko, 2017. "On a strictly convex and strictly sub-additive cost function with positive fixed cost," MPRA Paper 80579, University Library of Munich, Germany.
    15. Hattori, Masahiko & Tanaka, Yasuhito, 2017. "License and entry strategies for an outside innovator in duopoly with combination of royalty and fixed fee under vertical differentiation," MPRA Paper 78856, University Library of Munich, Germany.
    16. Ma, Siyu & Sen, Debapriya & Tauman, Yair, 2022. "Optimal patent licensing: from three to two part tariffs," MPRA Paper 111624, University Library of Munich, Germany.
    17. Qiao, Haike & Su, Qin, 2021. "Distribution channel and licensing strategy choice considering consumer online reviews in a closed-loop supply chain," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 151(C).
    18. Huang, Yanting & Wang, Zongjun, 2017. "Information sharing in a closed-loop supply chain with technology licensing," International Journal of Production Economics, Elsevier, vol. 191(C), pages 113-127.
    19. Ramon Fauli‐Oller & Joel Sandonís, 2022. "Fee versus royalty licensing in a Cournot duopoly with increasing marginal costs," Manchester School, University of Manchester, vol. 90(4), pages 439-452, July.

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    More about this item

    Keywords

    Patent licensing; Superadditive function; Subadditive function; Royalties; Two-part tariff;
    All these keywords.

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D45 - Microeconomics - - Market Structure, Pricing, and Design - - - Rationing; Licensing
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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