On Social and Market Sanctions in Deterring non Compliance in Pollution Standards

In the particular situation where there is absence of social norms (θ = 0), then there
exists a unique value c(A) such that if с ≤ c(A) then a type-с firm chooses to be compliant.
The threshold value c(λ) is increasing in A and is defined implicitly by

(1 - μp)U(R(A) - c(A)) + μpU(V - f - c(A)) = _PU(V - F) + (1 - p)U(R(λ))

and consequently the equilibrium compliance rate is defined by

_fc(λ)

I    dG(0,c).

Note that in the absence of social norms, then compliance is possible only if f < F.
Otherwise, no individual would find an interest in being compliant. Hence, it is necessary for
the regulator to observe whether с has been spent in order to distinguish between voluntary
and unvoluntary non compliance.

Let us look at how C(λ) varies with δ. Differentiating, we get

^- [(^{1 - μp}>^u'^{(R(A) -} c^{(a)) +} /Φ^u'^{(V - f -} c^(a))] "jʌ ^{+ (1 - μp}>^u'^{(R(A) -} ^^(A))“ô+
^{l                                                      j} dδ                                Oδ

+ μpU'(V - f - c(A)) ɪʌ - pU'(V - F) ∣^v
Oδ               oδ

Thus the sign of f is given by the sign of (1 - μp)U'(R(A) - C(A))∣f + μpU'(V - f -

C(A))ɪ - pU'(V - F)ɪ - (1 - p)U'(R(λ))∣y, which is ambiguous as shown above, because
of risk aversion.

4.1 The impact of self-reporting

If one allows self-reporting as part of the mechanism, then an individual has always the
option to declare his status (compliant∕non compliant) before being inspected at random. If
he declares to be non compliant, we assume that the individual will pay a sanction s ≤ f
with probability one if с has been spent and S ≤ F if с has not been spent. Hence, if an
individual is non compliant because he has not spent с, he declares his status if and only if

U (V - S ) > pU (V - F ) + (1 - p)U (R(A)).

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