On the Desirability of Taxing Charitable Contributions



To see why the equality in (6) holds, note that, by employing the envelope theorem,
the inequality in (6) implies:

(7)     λs(w)(1 -1) [1 -ls(w)]-λN(w)(1 -1)[1 -Γ'(w)] 0,

where λS and λNS are, correspondingly, the Lagrange multipliers in the individual
maximization for the 'signaling' and 'non-signaling' cases. By virtue of the strict
concavity of the functions
u, h and v, both consumption, c, and leisure, l, are normal
goods. Thus,
lSlNS and λSλNS (as cScNS), which implies that the inequality in
(7) is satisfied. This concludes the proof and the characterization of the equilibrium.
To summarize:

(8a)


c *( w ) = <


cs (w)   if z1Ns (w) z and w w

cNS (w)   otherwise


(8b)


(8d)


l*(w)=<


ls (w)   if zNS (w) z and w w

lNS (w)   otherwise


(8c)


z*(w) = <


zs (w)   if z(w) z and w w

zNS (w) otherwise


V * (w) = max{V NS (w),V S (w)}

Note also that z itself is determined in equilibrium, so as to make all individuals (and
only these individuals) with innate ability above the threshold
w contribute an
amount (weakly) exceeding
z. Formally z is defined implicitly by equation (5).

4.The Tax-Treatment of Contributions

The government is seeking to maximize some egalitarian social welfare function by
choosing the fiscal instruments
t,T,s and g, subject to a revenue constraint, taking

11



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