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The Problem of Optimum Income Taxation: A Remark on Its Monotonicity Constraint
Author(s) -
RUIZ del PORTAL X.
Publication year - 2007
Publication title -
journal of public economic theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.809
H-Index - 32
eISSN - 1467-9779
pISSN - 1097-3923
DOI - 10.1111/j.1467-9779.2007.00307.x
Subject(s) - monotonic function , differentiable function , constraint (computer aided design) , economics , mathematical economics , consumption (sociology) , mathematics , mathematical optimization , mathematical analysis , geometry , social science , sociology
We apply a generalized version of Brito and Oakland's (1977) approach to deal with monotonicity constraints in the nonlinear taxation problem of Mirrlees (1971). This allows removing some analytical weaknesses in the derivation of the necessary conditions that characterize the optimal income tax, impossible to handle with the type of variation used for the proof in Mirrlees (1969). The qualitative properties of the tax are thus restored provided the candidate consumption functions are restricted to be twice differentiable, except on countably many points, with no corners near the intervals where they show a strictly concave shape.