The main assumption in the economic analysis of criminal behavior is that the individual is a rational decision maker who considers the costs and benefits of participation in illegal activities. In the present context, people are assumed to subjectively weigh the potential gains and losses of committing a regulatory infraction. A fisherman’s decision of whether to comply with regulations or not is modeled as a function of: 1) the probability of getting caught violating fishery regulations, 2) severity of the penalty, 3) illegal gains, 4) a set of demographic and individual characteristics, 5) involvement with co-management activities, and 6) a set of normative (non-economic) factors such as moral, social control and legitimacy factors. By incorporating the details of the fishery laws with the regulatory, economic and normative (non-economic) factors, a more complete assessment of the decision of the people to violate the law can be developed.
An individual’s utility from illegal activity (rule violation) can be written as a function of the anticipated monetary return under violation YV, the subjective probability of detection p, and of incurring an expected monetary penalty F, if caught and penalized, with the standard form
U(V) = (1-p)U(Y) + pU(Y V – F) 
In many cases it may be assumed that in addition to the imposition of a fine , the value of the illegal income YV will be forfeited if an individual is caught. Note that YV is the income under violation and YNV is the income under no violation. Then:
U(NV)= U(YNV). 
Violation will occur if U(V) > U(NV) and that YV >YNV.
Time spent on non-compliance activity is assumed to contribute directly toward fisherman’s utility in term of generating higher income (YV). Income generated from illegal activity is used to consume goods that contribute to utility. However, subjective probability of detection p, and an expected monetary penalty F, if caught and penalized will also affect utility from non-compliance activity.
Within the standard economic framework of crime and punishment, the optimal remedy for non-compliance is
F* = (monetary return under violation)/(probability of detection)
where the optimal fine (F*) is (at least) equal to the financial gain of non-compliance (YV) divided by the probability of being detected and punished for the particular violation (p(r)). Whereas p(r) shows that the level of resources r determines the probability of detection. For some fixed expected financial gain (YV), the optimal fine will be declining when the probability of detection (p(r)) increasing.
Equation  shows that, to increase probability of detection, level of resources such as number of enforcement officers and equipments such as number of boats must be increase. At the same time optimal fine must be higher than illegal gain. However, as I mentioned earlier in my article’s “Compliance Model”, that in practice, the costs of enforcing fisheries regulations result in relatively low probabilities of detection, but penalties were not usually sufficiently high to produce a deterrent effect. Despite this, a high proportion of people complied with regulations. Other factors that can be included in explaining individual compliance behavior were variables such as “moral obligation” and “social influence”.
The individual’s expected utility from violation depends upon the expected monetary gain (Yi), the perceived probability of detection (pi), and the expected size of the penalty if caught (Fi). The violation decision by individual’s fisherman (Vi) related to the first three of these variables as mentioned in deterrence theory can be written as
Vi = f (Yi, pi, Fi, Xi) 
where Xi represents a vector of other variables including personal characteristics such as the individual’s experience, size of the boat, fishing areas and involvement with co-management activities.
We can now re-write the supply of violations  to include index variables for moral obligation , perceptions of legitimacy , and social influences . With this in mind we can write the individual’s supply of violations function as
Vi = f (Yi, pi, Fi, CO-Mi, Mi, Li, Si, Xi) 
for the initial form for estimation.
I will use this model in explaining why government intervention in a market economy has many challenges in my next articles.