society (while a continuum of abilities); in such a society individuals gain social
status if they credibly signal that their ability (the only source of heterogeneity in the
economy) exceeds a certain threshold, denoted byw.5 We emphasize that this
threshold is exogenously given. Denoting by w the perceived ability of an individual
in equilibrium, we denote by p(z) the probability that the individual's perceived ability
exceeds the threshold w, conditional on the fact that the individual has contributed z.
Formally,
(2) p(z) = Pr[w ≥ w∣z].
The parameter b captures the gain from social status. The product p(z) ∙ b thus
measures the expected gains from status.6 Note crucially that the status-signaling
activity per se (that is, apart from its direct contribution to public good provision and
to the joy of giving) is wasteful, because it does not add anything to total social
welfare; for an elaborate discussion see section 4.2.
The parameter β measures the relative importance of each contribution
motive. Whenβ= 0, contribution is purely altruistic, whereas whenβ= 1,
contribution is driven only by status seeking.
Several remarks are in order regarding the utility specification we have
chosen. First, note that contributions finance a general pure public good. This is a
simplifying assumption, as in reality many contributions finance local public
(possibly congestible) goods; dropping out this assumption will not change the
qualitative nature of the analysis. Note also that we make a 'large economy
assumption' by letting the amount of public good provision, g, be a fixed parameter
from the point of view of the individual (not depending on each individual's z). For
5 Note that while there are only two status classes, there is nevertheless a continuum of abilities. Thus,
our model is not restrictive for redistribution purposes.
6 It is assumed that consumption and leisure choices of an individual are not observed (or cannot be
verified) by other individuals. Thus, charitable contribution is the only signal observed.