On the Desirability of Taxing Charitable Contributions

(ii) Given the probability function p(z), all individual whose innate ability is
exceeding w choose to contribute an amount z ≥ z, whereas all other individuals
optimally set their contribution at a level z < z. We emphasize that z is endogenously
determined (in equilibrium). Each individual who donates an amount exceeding z
credibly signals that her innate ability is above the exogenously givenw, and hence
derives a status gain.

Each individual has to decide on the levels of consumption, leisure and
charitable contribution, given the function p(z), so as to maximize the utility subject to
the budget constraint:

(3)     (1 -1) ∙ w ∙ (1 -1) + T ≥ c + (1 + 5) ∙ z .

We turn next to study the solution for the consumer optimization problem. Denote it
by c^*(w), l^*(w) and z^*(w), where the tax parameters are henceforth omitted to
abbreviate the notation. Similarly, we denote by V ^* (w) the maximized level of utility.

We can describe the individual decision as a two-stage process. First, she
ignores the signaling motive and respective status benefit [that is, ignoring the term
β∙ p(z) ∙b in the utility function (1)], and chooses c, l and z so as to maximize the
utility function (1) subject to the budget constraint (3). This is a standard utility
maximization problem. We denote by c^NS(w), l^NS(w) and z^NS(w) , the optimal choices
of consumption, leisure and charitable contribution, respectively, for an individual of
ability w in this case, where the superscript NS stands for 'no-signaling'. Similarly,
denote the corresponding value of the maximized utility by V^NS(w) . Now, in the
second stage, we reinstate the signaling benefit term, β∙ p(z) ∙b , and ask whether and
how her choices in the first stage will be altered. There are two cases to consider.

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