VM,
1. At the very least person who is executed will never do it again. Even if he imprisoned he might murder. These things do happen.
2. It also gives him the opportunity for a kappara if he regrets his action.
3.I did see that there is a study that claims that the death penalty costs more than life imprisonment but I have my doubts. In the latter case the convict gets food, clothing, shelter, medical care, etc. at taxpayer expense perhaps for decades.In any case, I do not think that here we should make a bottom line decision. From what I know of the subject, game theory includes placing values on what cannot be valued in accounting, such as making a statement about the heinousness of murder and possibly preventing even one. Halachic considerations would, of course, override everything.