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Abstract
How does concern for consumption relative to others (”relativity”) affect the progressivity
of the optimal income tax structure? In this paper we revisit this literature and present a
more detailed analysis of the solution to the non-linear income tax problem with
consumption interdependence than is currently available, generalizing some results and
developing other results for cases with special objective functions and special distributions,
as well as numerical simulations. Of particular interest for us is the interplay between
inequality and relativity in determining the optimal tax schedule. We find support for
greater progressivity in the tax structure as relative concern increases. But our numerical
calculations show that this incremental impact is less at higher levels of inequality. We also
explore what happens when the government does not accept the relative concerns of
individuals and maximizes a non-welfarist objective function.