Open AccessOn optimal taxes and subsidies: A discrete saddle-point theorem with application to job matching under constraints
Author(s) -
Koji Yokote
Publication year - 2020
Publication title -
journal of mechanism and institution design
Language(s) - English
Resource type - Journals
eISSN - 2399-8458
pISSN - 2399-844X
DOI - 10.22574/jmid.2020.12.002
Subject(s) - subsidy , convexity , saddle point , economics , mathematical economics , comparative statics , matching (statistics) , social welfare function , function (biology) , optimal tax , welfare , mathematics , microeconomics , mathematical optimization , finance , statistics , geometry , evolutionary biology , market economy , biology
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. For the model of job market interventions by Kojima et al. (2019), we establish the existence of optimal taxes/subsidies as well as their characterization. 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 others imply that an optimal tax/subsidy level exists and can be calculated via a computationally efficient algorithm.