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

R that any non convicted individual gets is given by

R = (r — δ) Pr(not compliant ∣ not convicted) + r Pr(compliant ∣ not convicted)

⁽1 ^— Л⁾⁽1 ^{— p) + μ}Λ(Γ ^— p⁾      (_r _   ₊

^{(1 — p)(1 —} ʌ) ⁺ A^{(1 —} μ^{) +} λμ(l ^{— p)}

(1 — ʌ + μ^λ)(1 — p) c / с ∖

r — ʌ--------P----δr∈ ∈ (r — δ.r).

1 — p + λp(1 — μ)

Note that R is increasing in λ (with limʌ^ R = r — μ(1 — p)∕(1 — μp)), is decreasing in μ
(with lim_μ→ι R = r — δ) and is increasing in p (with lim_p→ι R = r).

Besides market sanctions, the non compliant individual also suffers from a psychic cost
or social sanction due to illegal behavior equal to 0^(A) where θ ≥ 0 denotes the individual
adherence to the norm and where ^(.) is increasing in the rate of compliance. An extreme
case is where θ = 0 so that such an individual does not suffer at all from social sanctions
in case of compliance. The higher θ is, the more reluctant to non compliance the agent is.
This phenomenon is reinforced by the presence of a positive externality of A through the
function ^ on the social sanction. The social sanction is higher when the compliance rate is
large in the population. We assume that this social sanction appears only in cases where non
compliance is voluntary.

We are now in a position to derive the expected payoffs relative to a compliance or non
compliance decision. A type-(0, c) individual who chooses compliance gets an expected payoff
equal to

^{(1 — μp})^{u (R(}A^{) — c) + μpu (V — f — c)}

where U(.) is an increasing utility fonction of net monetary revenue.¹ Similarly, a type-(0, c)
who chooses non compliance gets

pU (V — F ) + (1 — p)U (R(λ)) — 0≠(λ).

¹If one were unable to distinguish voluntary from unvoluntary non compliance, then the expected payoff
of a compliant agent would write

(1 - μp)U(R(X) - c) + μpU(V - F - c) - μθψ(X).

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