A little game theory: does crime pay?

I think I'll jump ahead of Joel and write a little about the conclusions of our conversation today on game theory.
The question, arising from a class at UCR, is: does crime pay? Here's our analysis.

In the simple model introduced in that class, the criminal has a choice between committing or not committing a certain crime (for a benefit S). He has a probability p of being caught, for a penalty F. The payoff matrix is

payoff	crime	no crime
caught (p)	S-F	0
not caught (1-p)	S	0
expected payoff	S-pF	0

Conclusion
It pays off to commit the crime as long as the probability p of getting caught is less than S/F. In particular, unless the penalty is larger than the benefit obtained from the crime, no amount of law enforcement can make it disadvantageous (on average) to commit the crime. This is certainly not the conclusion that the UCR professor wanted to reach, which involved some argument about decreasing profit leading to less crime but no discussion of threshold values of the probability of getting caught.

Possible extensions include:

• Make the utility of the crime or the penalty depend on the current utility of the criminal. For instance: if the benefits and penalties are monetary, what happens if the utility of money is nonlinear? How does risk-prone versus risk-averse utility affect the analysis? Are poor people more likely than wealthy people to commit the crime? What if the criminal is so poor that they can't pay the fine?
  
• Consider replacing the one-shot crime with a probability of committing the crime per unit time (say, the number of "jobs" per year).