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

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  • 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
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    References listed on IDEAS

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    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

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