On the Desirability of Taxing Charitable Contributions

Consider first an individual who chose in the first stage to contribute an
amount (weakly) exceeding the threshold z, that is an individual with innate ability w
for which z^NS (w) ≥ z . For this individual, the term β ■ p(z) ■ b is a constant added to
the utility function. Thus, there will be no change in behavior, that is:
c^*(w) = c^NS(w), l^*(w) = l^NS(w) and z^*(w) = z^NS(w).

Consider next an individual who chose in the first stage to make a contribution
below the threshold z. Such an individual now has the option to increase her
contribution to a level equaling or exceeding z and enjoy the status benefit of β∙ b
(recalling that p(z)=1 in this case). Imagine such an individual as maximizing her
utility in (1), with the term β∙ b, subject to the budget constraint (3), and an
additional (signaling) constraint:
(4) z ≥ z .

We denote by c^S(w), l^S(w) and z^S(w), the optimal choices in this case of
consumption, leisure and charitable contribution, respectively, for an individual of
ability w, where the superscript S stands for 'signaling'. Similarly, we denote by
V ^S (w) the corresponding maximized level of utility. An individual with innate ability
w will choose to increase her contribution to z (but not beyond z - see below) if, and
only if, V^S(w)≥V^NS(w).

In equilibrium the following condition has to be satisfied:

(5)     V^ns ( τ^) = V^s ( w).

In words, the individual with the ability level w, the threshold ability above which
individuals gain social status, has to be indifferent between signaling and not
signaling. To see this, note that in a separating equilibrium, an individual with ability
w will choose to signal. Thus, the term on the left-hand side of (5) should not exceed

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