IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/80579.html
   My bibliography  Save this paper

On a strictly convex and strictly sub-additive cost function with positive fixed cost

Author

Listed:
  • Tanaka, Yasuhito
  • Hattori, Masahiko

Abstract

We investigate the existence of a strictly convex and strictly sub-additive cost function with positive fixed cost. If there is a positive fixed cost, any cost function can not be super-additive, and concavity (including linearity) of cost function implies strict sub-additivity. Then, does there exist a strictly convex and strictly sub-additive cost function? We will present such a cost function. It is close to a linear function although it is strictly convex.

Suggested Citation

  • 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.
    • Handle: RePEc:pra:mprapa:80579
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/80579/1/MPRA_paper_80579.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Sen, Debapriya & Stamatopoulos, Giorgos, 2016. "Licensing under general demand and cost functions," European Journal of Operational Research, Elsevier, vol. 253(3), pages 673-680.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. 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).
    4. Sen, Debapriya & Tauman, Yair, 2018. "Patent licensing in a Cournot oligopoly: General results," Mathematical Social Sciences, Elsevier, vol. 96(C), pages 37-48.
    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. 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.
    7. 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.
    8. Colombo, Stefano & Filippini, Luigi & Sen, Debapriya, 2020. "Licensing with capacity constraint," MPRA Paper 102653, University Library of Munich, Germany.
    9. 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.
    10. 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.
    11. Ma, Siyu & Sen, Debapriya & Tauman, Yair, 2022. "Optimal patent licensing: from three to two part tariffs," MPRA Paper 111624, University Library of Munich, Germany.
    12. 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.
    13. 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.
    14. 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.
    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. 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.
    17. 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.

    More about this item

    Keywords

    cost function; strict convexity; strict sub-additivity;
    All these keywords.

    JEL classification:

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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:80579. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.