The cheapest solution to violent crime is prevention. Oddly enough, there are a ton of sociological studies out that that show the best way to prevent crime is to provide people with access to abortion* (fun study, that one), basic living essentials, access to health care, a safe living environment (meaning early intervention in domestic abuse/violence), a safe learning environment (safe schools / bullying consequences), and most of all, access and encouragement to pursue education. It is actually cheaper to do all of that than build more prisons, hire more police, and execute more criminals.
Indeed. Now try to get politicians to efficiently implement that. The best way of dealing with crime would be to ensure people aren't inclined to go into crime in first place. A person who always could buy everything necessary, was raised with respect to law and order, was educated in a good, safe school and was a wanted child of loving parents (you mentioned access to abortion, it's a logical correlation if you think about it. There's a chance that a mother forced to give birth and raise a child will hate it, or that it'll be treated as "unwanted" in some other way. It doesn't always happen, but has disastrous consequences when it does. Orphanages have their own problems.) has very little chance of getting in conflict with the law. The few cases that do usually could be prevented with psychiatric treatment. On the other hand, ensuring everybody has such upbringing is a titanic task. Also, it can't really be accomplished by government alone, many of those require a good income, which means one or both parents are employed in a decent job.
it's nice to know that your time playing tropico 4 gave you such insight into the broader social effects of the death penalty
Oh and by the way, the reason the death penalty is so expensive in the US is primarily because there are a lot of expensive legal measures to prevent miscarriages of justice. I guess you'd prefer to execute a few innocents if it cut down on prison costs, though.
Note, this line about Tropico was meant as a joke, as was the entire game, for that matter. It is, of course, a good thing death penalty isn't used recklessly. One thing though. Shouldn't similar measures be applied to ensure a person isn't wrongfully imprisoned? It's a stigma for the entire life, and being stuck with criminals could lead to becoming like them. While child molesters and rapists get what they deserve in there, putting an innocent person in there could destroy their life for good. It might be worth the expense to ensure this doesn't happen. (well, I guess I strayed from the topic a bit)
Also, I'd say death penalty costs could be greatly reduced in case a criminal had been caught red-handed. There are situations where there's no discussing what happened and who's guilty, because the criminal had been caught in the act. I think that in such case, some procedures could be greatly simplified.