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

rate of compliance A as an increase in the compliance rate increases both the social norm and
the market revenue effects. Indeed, the expected utility gain of non compliance ∆W (c, A)
decreases in A because of the market revenue effect. The following lemma indicates some
further comparative results for ∆W (c, A).

Lemma 2 The expected utility gain of non compliance ∆W (c, A)

(i) is increasing in the penalty f for unvoluntary non compliance and the probability μ of
unvoluntary non compliance,

(ii) is decreasing in the penalty F for voluntary non compliance,

(iii) varies ambiguously with the loss δ in market revenue if non compliant, under the as-
sumption of risk aversion

(iv) varies ambiguously with the probability p of being inspected, as long as the probability of
unvoluntary non compliance μ is strictly positive.

Proof: First , we have

-∆W

= μpU'(V - f - c) > 0

^-f

and

- ∆W  -∆W∂R

ɪ =        ⁺ p [U (R -c) - U (V - f - c)] > 0

oμ -R -μ

because ^dg^ < 0,    < 0 as shown above and R > V. This proves (i).

Next, we have

which proves (ii). Considering the impact of δ, we have

-∆W -V  -∆W -R

-V -δ⁺ -R -δ

[pU'(V - F) - μpU'(V - f - c)] ^-v + [(1 - p)U'(R) - (1 - μp)U'(R - c)] Ц
^{l                                    j} -δ                                              -δ

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