A little game theory: does crime pay? (II)

I want to look at the effect of prison terms on the crime problem. The conclusion is that jail terms don't significantly alter criminal behaviour. Here's my model. In view of the conclusion, maybe we should look really critically at the assumptions.

Suppose that a criminal commits, on average, j crimes per unit time (or carries
out j "jobs"). Each crime results in a payoff of S. If caught (with
probability p), the criminal is fined F and spends a time T in jail. If the criminal would lose revenue from legal activities for being in jail, we can take that opportunity cost into account by adding the lost revenue to the fine. So, what is
the optimal crime rate j?


If the criminal commits j crimes per unit time and each time he can be caught
with probability p, this means that he will be caught at a crime jp times
per unit time. The criminal can expect, on average, to be "active" for a time
1/jp before he gets caught. Each time he gets caught, he spends a time T
in jail.


While the criminal is active, he obtains a payoff of jS per unit time. That means he can expect to win an average of S/p for each period that he is active. Note
that this is independent of the crime rate. When he gets caught, he has to
pay a fine F. From the time the criminal starts his activity to the time he
becomes active again after coming out of jail, a time T+1/jp passes.
This means that the expected payoff per unit time is S/p-F
divided by T+1/jp. This is


π=(S-pF)/(pT+1/j)

Conclusions


From the form of the function π it follows that:

• Whether or not crime pays still only depends on S-pF, except that
  now the "fine" includes the (legal) opportunity cost of being in jail. Hovewer, if someone is accruing debt throught their legal acivities, this just means that jail times only make crime more, not less profitable for him. Remember how in the table-top game "monopoly" you can still buy and sell property and collect rent while you're in jail?
  
• when crime pays, the optimal crime rate is "as high as physically possible",
  independently of intensity of law enforcement or legth of jail terms.
  

These conclusions are not unreasonable, but now the question becomes: can someone come up with a model of crime and punishment where the crime rate depends continuously on things like law enforcement pressure, fines or jail times, or is crime essentially a yes-no problem?