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



3 The equilibrium rate of compliance

If each individual chooses the alternative with the highest expected utility, then compliance
is optimal for a type-(
0, c) individual if and only if:

(1 - μp)U(R(A) - c) + μpU(V - f - c) pU(V - F) + (1 - p)U(R(A)) - 0≠(λ),

or equivalently

■>-•» -+"

where

∆ll'(c, A) = pU(V - F) + (1 - p)U(R(A)) - (1 - μp)U(R(X) - c) - μpU(V - f - c)

is the expected utility gain from being non compliant as compared with compliance.

The following lemma indicates the basic properties of the minimal adherence to the norm
(c, A), needed for compliance to be optimal.

Lemma 1 The minimal adherence to the norm (c, A) is continuous, decreasing in the com-
pliance rate
A and increasing in the compliance cost c.

Proof: Indeed, we get

~

. O^

sign— = sign
OA


(° ∆∣∙ -ɪ(


Recall that rψ is increasing in A while ∆l is decreasing in A as shown below:

δ1 = [(1 - p)U'(R) - (1 - μp)U'(R - c)] 0r0

OA                                OA

because 1 - μp 1 - p and U'(R - c) > U'(R) as U is concave.

Moreover, we have sign∣∣ = sign {d^ } = sign {(1 - μp)U'(R(A) - c) + μpU'(V - f - c)} =
+ . This concludes the proof. ■

Intuitively, the minimal adherence to the norm for compliance to be chosen must be higher
when the compliance cost
c increases. Furthermore, this threshold level decreases with the



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