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

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...

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Main Author: Koji Yokote
Format: Article
Language:English
Published: Society for the Promotion of Mechanism and Institution Design 2020-12-01
Series:Journal of Mechanism and Institution Design
Subjects:
Online Access: http://www.mechanism-design.org/arch/v005-1/p_02.pdf
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author Koji Yokote
author_facet Koji Yokote
author_sort Koji Yokote
collection DOAJ
description 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.
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spelling doaj.art-f9427867e54843f69410ed2c55715d662022-12-21T23:21:18ZengSociety for the Promotion of Mechanism and Institution DesignJournal of Mechanism and Institution Design2399-844X2399-84582020-12-0151377710.22574/jmid.2020.12.002jmi-v5i1a2On optimal taxes and subsidies: A discrete saddle-point theorem with application to job matching under constraintsKoji Yokote0 Waseda Institute for Advanced Study, Waseda University, Japan 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. http://www.mechanism-design.org/arch/v005-1/p_02.pdf job matchingtaxationdiscrete convex analysis
spellingShingle Koji Yokote
On optimal taxes and subsidies: A discrete saddle-point theorem with application to job matching under constraints
Journal of Mechanism and Institution Design
job matching
taxation
discrete convex analysis
title On optimal taxes and subsidies: A discrete saddle-point theorem with application to job matching under constraints
title_full On optimal taxes and subsidies: A discrete saddle-point theorem with application to job matching under constraints
title_fullStr On optimal taxes and subsidies: A discrete saddle-point theorem with application to job matching under constraints
title_full_unstemmed On optimal taxes and subsidies: A discrete saddle-point theorem with application to job matching under constraints
title_short On optimal taxes and subsidies: A discrete saddle-point theorem with application to job matching under constraints
title_sort on optimal taxes and subsidies a discrete saddle point theorem with application to job matching under constraints
topic job matching
taxation
discrete convex analysis
url http://www.mechanism-design.org/arch/v005-1/p_02.pdf
work_keys_str_mv AT kojiyokote onoptimaltaxesandsubsidiesadiscretesaddlepointtheoremwithapplicationtojobmatchingunderconstraints