IDEAS home Printed from https://ideas.repec.org/a/jmi/articl/jmi-v5i1a2.html
   My bibliography  Save this article

On optimal taxes and subsidies: A discrete saddle-point theorem with application to job matching under constraints

Author

Listed:
  • Koji Yokote

    (Waseda Institute for Advanced Study, Waseda University, Japan)

Abstract

When a government intervenes in markets by setting a target amount of goods/services traded, its tax/subsidy policy is optimal if it entices the market participants to obey the policy target while achieving the highest possible social welfare. In the model of job market interventions by Kojima et al. (2019), we establish the existence of optimal taxes/subsidies as well as their characterization and efficient computation. Our methodological contribution is to introduce a discrete version of Karush-Kuhn-Tucker's saddle-point theorem based on the techniques in discrete convex analysis. We have two main results: we (i) characterize the optimal taxes/subsidies and the corresponding equilibrium salaries as the minimizers of a Lagrange function, and (ii) prove that the function satisfies a notion of discrete convexity (called L#-convexity). These results together with Kojima et al.'s (2019) result imply that an optimal tax/subsidy level exists and is calculated via a computationally efficient algorithm.

Suggested Citation

  • Koji Yokote, 2020. "On optimal taxes and subsidies: A discrete saddle-point theorem with application to job matching under constraints," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 5(1), pages 37-77, December.
    • Handle: RePEc:jmi:articl:jmi-v5i1a2
    DOI: 10.22574/jmid.2020.12.002
    as

    Download full text from publisher

    File URL: http://www.mechanism-design.org/arch/v005-1/p_02.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.22574/jmid.2020.12.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. John William Hatfield & Scott Duke Kominers & Alexandru Nichifor & Michael Ostrovsky & Alexander Westkamp, 2013. "Stability and Competitive Equilibrium in Trading Networks," Journal of Political Economy, University of Chicago Press, vol. 121(5), pages 966-1005.
    2. Yuichiro Kamada & Fuhito Kojima, 2020. "Accommodating various policy goals in matching with constraints," The Japanese Economic Review, Springer, vol. 71(1), pages 101-133, January.
    3. Arnaud Dupuy & Alfred Galichon & Sonia Jaffe & Scott Duke Kominers, 2020. "Taxation In Matching Markets," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 61(4), pages 1591-1634, November.
    4. William J. Baumol & Wallace E. Oates, 1971. "The Use of Standards and Prices for Protection of the Environment," Palgrave Macmillan Books, in: Peter Bohm & Allen V. Kneese (ed.), The Economics of Environment, pages 53-65, Palgrave Macmillan.
    5. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
    6. Ning Sun & Zaifu Yang, 2009. "A Double-Track Adjustment Process for Discrete Markets With Substitutes and Complements," Econometrica, Econometric Society, vol. 77(3), pages 933-952, May.
    7. Kojima, Fuhito & Tamura, Akihisa & Yokoo, Makoto, 2018. "Designing matching mechanisms under constraints: An approach from discrete convex analysis," Journal of Economic Theory, Elsevier, vol. 176(C), pages 803-833.
    8. Candogan, Ozan & Epitropou, Markos & Vohra, Rakesh V., 2016. "Competitive Equilibrium and Trading Networks: A Network Flow Approach," Economics Series 323, Institute for Advanced Studies.
    9. Satoru Fujishige & Akihisa Tamura, 2007. "A Two-Sided Discrete-Concave Market with Possibly Bounded Side Payments: An Approach by Discrete Convex Analysis," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 136-155, February.
    10. Kazuo Murota, 2016. "Discrete convex analysis: A tool for economics and game theory," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 151-273, December.
    11. Lawrence M. Ausubel, 2006. "An Efficient Dynamic Auction for Heterogeneous Commodities," American Economic Review, American Economic Association, vol. 96(3), pages 602-629, June.
    12. Ian W. H. Parry & Margaret Walls & Winston Harrington, 2007. "Automobile Externalities and Policies," Journal of Economic Literature, American Economic Association, vol. 45(2), pages 373-399, June.
    13. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    14. Hatfield, John William & Kominers, Scott Duke & Nichifor, Alexandru & Ostrovsky, Michael & Westkamp, Alexander, 2019. "Full substitutability," Theoretical Economics, Econometric Society, vol. 14(4), November.
    15. Satoru Fujishige & Zaifu Yang, 2003. "A Note on Kelso and Crawford's Gross Substitutes Condition," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 463-469, August.
    16. Yuichiro Kamada & Fuhito Kojima, 2017. "Recent Developments in Matching with Constraints," American Economic Review, American Economic Association, vol. 107(5), pages 200-204, May.
    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. Kazuo Murota, 2016. "Discrete convex analysis: A tool for economics and game theory," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 151-273, December.
    2. Yokote, Koji, 2021. "Consistency of the doctor-optimal equilibrium price vector in job-matching markets," Journal of Economic Theory, Elsevier, vol. 197(C).
    3. Ozan Candogan & Markos Epitropou & Rakesh V. Vohra, 2021. "Competitive Equilibrium and Trading Networks: A Network Flow Approach," Operations Research, INFORMS, vol. 69(1), pages 114-147, January.
    4. Kojima, Fuhito & Tamura, Akihisa & Yokoo, Makoto, 2018. "Designing matching mechanisms under constraints: An approach from discrete convex analysis," Journal of Economic Theory, Elsevier, vol. 176(C), pages 803-833.
    5. Eric Balkanski & Renato Paes Leme, 2020. "On the Construction of Substitutes," Mathematics of Operations Research, INFORMS, vol. 45(1), pages 272-291, February.
    6. Jagadeesan, Ravi & Kominers, Scott Duke & Rheingans-Yoo, Ross, 2018. "Strategy-proofness of worker-optimal matching with continuously transferable utility," Games and Economic Behavior, Elsevier, vol. 108(C), pages 287-294.
    7. Yokote, Koji, 2018. "The discrete Kuhn-Tucker theorem and its application to auctions," MPRA Paper 83811, University Library of Munich, Germany.
    8. Kazuo Murota, 2018. "Multiple Exchange Property for M ♮ -Concave Functions and Valuated Matroids," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 781-788, August.
    9. Satoru Fujishige & Zaifu Yang, 2017. "On a spontaneous decentralized market process," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 2(1), pages 1-37, December.
    10. Huang, Chao, 2018. "Independence systems in gross-substitute valuations," Economics Letters, Elsevier, vol. 173(C), pages 135-137.
    11. Chao Huang, 2024. "A dynamic auction for multilateral collaboration," Papers 2411.06545, arXiv.org.
    12. Satoru Fujishige & Zaifu Yang, 2020. "A Universal Dynamic Auction for Unimodular Demand Types: An Efficient Auction Design for Various Kinds of Indivisible Commodities," Discussion Papers 20/08, Department of Economics, University of York.
    13. Talman, Dolf & Yang, Zaifu, 2011. "A model of partnership formation," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 206-212, March.
    14. Kumar, Ujjwal & Roy, Souvik, 2024. "Local incentive compatibility on gross substitutes and other non-convex type-spaces," Journal of Mathematical Economics, Elsevier, vol. 112(C).
    15. Elizabeth Baldwin & Paul Klemperer, 2019. "Understanding Preferences: “Demand Types”, and the Existence of Equilibrium With Indivisibilities," Econometrica, Econometric Society, vol. 87(3), pages 867-932, May.
    16. Ingebretsen Carlson, Jim, 2016. "An Auction with Approximated Bidder Preferences - When an Auction has to be Quick," Working Papers 2016:12, Lund University, Department of Economics.
    17. Jinpeng Ma & Qiongling Li, 2016. "Convergence of price processes under two dynamic double auctions," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 1-44, December.
    18. Marzena Rostek & Nathan Yoder, 2020. "Matching With Complementary Contracts," Econometrica, Econometric Society, vol. 88(5), pages 1793-1827, September.
    19. Sun, Ning & Yang, Zaifu, 2016. "An Efficient and Strategy-Proof Double-Track Auction for Substitutes and Complements," Center for Mathematical Economics Working Papers 523, Center for Mathematical Economics, Bielefeld University.
    20. Roy, Souvik & Kumar, Ujjwal, 2021. "Local incentive compatibility in non-convex type-spaces," MPRA Paper 110872, University Library of Munich, Germany.

    More about this item

    Keywords

    Job matching; taxation; discrete convex analysis.;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • H21 - Public Economics - - Taxation, Subsidies, and Revenue - - - Efficiency; Optimal Taxation

    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:jmi:articl:jmi-v5i1a2. 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: Paul Schweinzer (email available below). General contact details of provider: https://edirc.repec.org/data/deyoruk.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.