most people this would reflect reality, whereas for the very rich individuals this might
be violated. However, this assumption may reflect also the fact that contributors often
gain very little from the projects financed by their own donations.7 The parameter
α> 0 represents the intensity of the preference for the public good (relative to other
goods).
We assume that a linear labor income tax system is in place, where the
marginal tax rate is denoted by t, and the uniform lump-sum transfer (possibly
negative) is given by T. We further assume that a tax (s) on charitable contributions
(possibly negative, that is a subsidy) may be levied. Note that allowing individuals to
deduct their charitable contributions from their taxable incomes, or, granting them tax
credits, amounts to such a subsidy. We turn next to characterize the equilibrium for
the signaling game.
3.Equilibrium
For tractability, we follow Glazer and Konrad (1996) and Ireland (1994 and
2001) in restricting attention to the separating fully revealing equilibrium, which in
our framework implies that all individuals (and only those) with ability (weakly)
exceeding the threshold w signal their ability and enjoy the respective social status.
This equilibrium is defined by a threshold level of contributions, z > 0, and a
probability function p(z), such that:
(i)
Γ1
_ 2.
z≥z
z < z
7 Relaxing this assumption will not alter the gist of our analysis. An alternative assumption concerning
the provision of public good is that each individual has a positive (that is, non-atomistic) mass; see, for
instance, Green and Laffont (1979) and Bergstrom, Blume and Varian (1986). The latter assumption
may be particularly relevant in the context of local public goods.
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