Suppose that a certain fixed subset of a society consists of identical individuals who are willing to commit crimes (crime elements) under some circumstances. Each individual i in this subset must choose a share of his time si to devote to crime. Doing so leads to benefit of B(si), but the expected cost is a penalty F times the probability of being caught p(si, ), where is the average of time devoted to crime by members of this criminal elements (=E(s)). Assume that B'>0, B'''<), > 0, 2 2 > 0, and 2 < 0