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

Recalling that both V and R decrease in S, we still have that ^dg^ < 0 while ⁹g-^ is

ambiguous in general. In the special case where μ = 0, then ^dg^ > 0 and the sign of
risk-neutrality assumption (as in Rasmussen 1996). Indeed, under risk neutrality, we have

— = ^lp - ^μp⅛ ^{+ [(1} - ^p) -⁽¹ - ^μp>^l âs

.    . _dV   ∂R∖

= ^{p(1 -μ} (₄aS^^-^dS√

= ^{p(1 - μ}> (^{—1 —} _T ) <⁰

as ∂y = —1 ≤ ∂∂f ≤ 0. This proves (iii).

Finally, with regards to p, we get

_Δ _               dΔW _R

___ = _u (V — F ) — U (R) + _     + μ lU (R — c) — U (V — f — c)|

dp                     _R dp

The two first terms are non positive because R > V and '∂^- > 0 together with ^dg^ < 0.

In the last term, the expression between the brackets is positive as R > V. This proves the
ambiguity of the sign of ^dl∂j^ and thereby part (iv). ■

Parts (i) and (ii) of Lemma 2 yield to expected results. If the probability and the penalty
for unvoluntary non compliance increase then non compliance appears to be increasingly a
better strategy than compliance. On the contrary, an increase in the penalty for voluntary
non compliance reduces the utility gain of non compliance. More surprising are the last two
results (parts (iii) and (iv)). Part (iii) suggests that the market loss S has an ambiguous
effect on Δ_ and hence on θ. Indeed, it is easy to construct examples where ^d∂^ > 0 that
is where the gain to be non compliant increases with the market loss. In turn, the threshold
θ increases too. As shown by Lemma 2 this result comes from the non linearity of the utility
function under the assumption of risk aversion. Last, part (iv) indicates that an increase in
the inspection probability p may yield to an increase in the utility gain of non compliance
and hence a similar pattern for the threshold θ(c, λ). As shown in the proof of Lemma 2, this
phenomenon is purely due to the fact that μ > 0 and expresses the fact that when compliance

<<   6   7   8   9   10   11   12   >>

More intriguing information