On the Desirability of Taxing Charitable Contributions

Employing the first-order conditions for the optimal tax problem (see
appendix C for details), we can re-write equation (15) as follows:

w

μ₁ ∙ Z ∙ [1 - F(w)] - z ∙ ʃ[^' [VS (w)] ∙ λ^s (w'^F(w)

w

144444444424444444443

Redistributive Term

w

z ∙ ʃ[^'[VS (w)] ∙ λ^s (w)]^F(w)
w

1444442444443

Signaling Correction Term

Equation (16) decomposes the effect of a small tax on contributions into three
terms. The first term on the right-hand side of equation (16) captures the redistributive
effect of a unit increase in the tax on charitable contributions. To see this, note that the
term Z ∙ [1 - F(w)] is the additional amount of revenues raised by a unit increase in
the tax on contributions (at s=0). Multiplying it by μ₁, the marginal social benefit of a
unit increase in the transfer (T), yields the effect of the extra revenues on social
welfare. As the burden of this unit increase on each status-signaling individual (that
is, each individual with innate ability exceedingιw) is z, then, indeed, the first term
on the right-hand side of equation (16) captures the redistributive effect of a tax on
contributions. This effect is positive and works in the direction of taxing "charitable"
contributions, when the social welfare function exhibits a sufficiently large degree of
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inequality aversion.

The second term, which also works in the direction of levying a tax on
contributions, measures the corrective effect which offsets the wasteful status-
signaling costs. To see this, fully differentiate the signaling constraint in (5) with
¹¹ For instance, when the social planner is Rawlsian the second expression in the first set of brackets
disappears and, clearly the re-distributive term is positive. Notably, in such a case, also the signaling
correction term vanishes, as the contributors obtain zero weight in the social welfare measure.

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