Note that this inequality does not depend on the cost of compliance, c. This means that
all individuals voluntarily non compliant and sharing the same preferences U(.) will take the
same decision whatever their private cost of compliance. Suppose for now that μ = 0 so that
unvoluntary non compliance does not exist. Then, the situation where self-reporting appears
at the equilibrium is such that all non compliant individuals declare their status. Otherwise,
we would be back to the case in which there is no self-reporting. Consequently, a type-c
individual chooses to comply if and only if,
U (R(A) - c) > U (V - S )
where R = r and V = r—δ. Indeed, the direct consequence of truthtelling by all non compliant
individuals is that the market faces no more asymmetric information. The threshold level is
given by R(A) — c = V — S or equivalently by c = δ + S and consequently, there exists an
unique equilibrium compliance rate give by A = 77(0. δ + S). We thus obtain the following
result.
Proposition 4 Assume that non compliance can only be voluntary, i.e. μ = 0. Whenever
self-reporting appears at the equilibrium, it implies complete information for the market and
thereby selects an unique equilibrium compliance rate. Consequently, introducing the possibil-
ity of self-reporting yields ambiguous welfare results.
Indeed, introducing self-reporting is ambiguous from a welfare point of view as we may
select an equilibrium with a lower compliance rate than the one we get before. And conversely.
Now consider the situation where unvoluntary non compliance exists, i.e. μ > 0. An
individual who is unvoluntarily non compliant chooses to declare his status if and only if
U (V — s — c) > PU (V — f — c) + (1 — p)U (R(A) — c). (2)
Note first that if f = s, ie there is no rebate for truthtelling, then the inequality simply
becomes
U (V — f — c) > U (R(A) — c)
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