2 The model
We consider a continuum population of risk-averse individuals, where each individual faces
a binary choice: whether or not to engage into compliance with regards to an (exogenous)
environmental law (or standard). The cost of compliance is c but we assume that compliance
is stochastic from the individual’s point of view. Indeed, with probability μ, the individ-
ual that has spent the compliance cost c will be non compliant in the end due to external
circumstances. Also, we assume that there is no chance that an individual that has chosen
not to spend c will be found compliant. If we denote p the probability of being audited and
convicted, then the probability of being found non compliant while having spent the cost c
is μp.
In order to induce individuals to conform to the standard, the regulator imposes a penalty
upon non-compliant agents. With probability p, the individual who has not spent c has to
pay a fine F through random audits. However, we allow the regulator to distinguish between
unvoluntary non compliance from voluntary non compliance by imposing a fine f ≤ F to
the formers. Such a fine might be needed in cases where a compensation to the victims of
violation even if unvoluntary is to be paid.
We denote λ the expected (and actual) rate of compliance in the population. Besides the
incentives brought by the regulator, we introduce also the possibility that individuals may
suffer from a loss in market revenue if found non compliant. Assume that an individual who
is found non compliant and convicted gets a market revenue equal to V = r — δ where r > 0
is the potential maximal revenue and δ ≤ r is the loss of revenue due to non compliance. We
assume that the market faces incomplete information on the true status of any individual but
observes convictions. Hence, if the market anticipates a compliance rate λ, then the revenue
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