On the Desirability of Taxing Charitable Contributions

W                          w

∫W[V^NS(w)]dF(w)+∫W[V^S(w)]dF(w)

W                          W

W                           W

∫ W[1 -l^NS(W)]dF(W) +∫ W[1 -l^S(W)]dF(W)

W                           W

μ_z [g - Z • [1 - F ( W)]]+ μ3 V^s ( W) - VN ( W)]
where μ_i, i = 1,2,3 denote the Lagrange multipliers, associated, respectively, with the
revenue constraint given in equation (10), the public good provision constraint in
equation (11) and the signaling constraint in equation (5). Clearly, in the case of pure
status-signaling, only individuals whose innate ability exceeds the threshold, W,
engage in signaling via "charitable" contributions, and all of them will set their
contributions at the level of Z . All other individuals will set their contributions at
zero. This implies that the total amount of contributions is given by the term
Z • [1 - F ( W)], which appears both in the revenue constraint and the public good
provision constraint in the Lagrangean expression in (14).¹⁰

Starting from an optimal linear tax system with zero tax on contributions
(5=0), we examine the effect of a small tax on contributions. We seek to sign the
following derivative (see appendix B for details):

+ μ₁ • z • [1 - F(W)] - μ₃ • λ^s (W) • Z,

¹⁰ In this separating equilibrium all the individuals who signal, whose number is given by1 - F(W),
obtain, each, a status level of b; all other individuals gain no status. The average level of status is given
by [1 - F( W)] b.

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