My brother asks a question from one of his classes:

The goal of prisons is to reduce crime. Michigan spends much more on
prisons than neighboring states but has similar crime rates. Is Michigan
achieving the optimum amount of crime reduction? Use MC and MB to explain
why or why not.

I would say that the leading premise (the goal of prisons is to reduce crime) is incorrect. The goal of prisons is either punishment/retribution, or reformation – depending on who you ask. Another problem with the question is the cost of keeping inmates is borne by society as a whole, while the damages are almost never spread among more than 2 or 3 people. So the benefits don’t accrue to “society as a whole,” they accrue to those 2 or 3 people who otherwise would be victims. Also, the benefits of retribution are worth practically nothing to anyone but the victim of a crime. Do you benefit if OJ goes to jail? Of course not. Do the parents of Ron Goldman benefit? Sure. But that’s another story.

The question is asking about marginal costs vs. marginal benefits, so think of it that way:

The cost of housing inmates is borne by “society”, through taxes.
The benefit of keeping inmates locked up is (allegedly) reaped by “society” in the form of fewer criminals on the streets. So, does the cost of keeping additional inmates behind bars exceed the value of not having them on the streets? Let’s say it costs $80,000/year to keep a prisoner. Is it at all likely that keeping this particular prisoner off the streets (the marginal case) is worth at least $80,000?

It’s hard to talk about these things in terms of dollars-and-cents, but we might be able to come up with some sort of actuarial table of crime, that lays out the expected damages any particular criminal would commit during a given time period. For instance, the average kid who sells pot on the street corner isn’t robbing, murdering, or stealing from people. In all fairness, the amount of “damages” he inflicts on society is probably zero. Does it make sense to spend $80,000 to keep him in jail for a year? Of course not.

Now, what about the car thief? We might look at him and see that he’s likely to boost 5 or 6 cars in a year, with a mean value of $5,000. He’s causing $25,000 worth of damages to society. Does it make sense to spend $80,000 to keep him in jail? Of course not. We’d be better off spending $30,000 to pay him *not* to steal cars, saving $50,000 in the process, and keeping our cars.

So, even if we concede that releasing some prisoners will increase crime, the important question is this: If we do release some prisoners, (the marginal prisoners), which is greater – the money we don’t have to spend on their upkeep, or the money we’ll have to spend to replace whatever they destroy/steal/kill?

I’m not sure I answered the question.