DOI link to open access article:
On optimal taxes and subsidies: A discrete saddle-point theorem with application to job matching under constraints
Journal of Mechanism and Institution Design
Volume 5, issue 1, pages 37-77 (December 2020)
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.
Keywords: Job matching, taxation, discrete convex analysis.
JEL Classification Numbers: C61, C78, D47, H21.