The death penalty in western society doesn't work as a deterrent. Taking the US as an example, non-death penalty states experience lower murder rates than states that use the death penalty. Also the transition from the non-death penalty period to the legalisation of the death penalty period has not seen a drastic change in murder rates in the US. So the deterrent argument is incorrect, as it obviously doesn't. If you wanted to argue that point more and use statistics, it could be said that the death penalty encourages murder. But that's just silly. People who tend to commit crime don't think of the consequences as its an emotionally charged action. I believe most murder victims know their murderer personally (but don't quote me on that xD).
As for costs, we don't have a system in place so I'll use the USA as an example again. Since 1995, it has cost 23 million US dollars per death sentence in New York alone with no executions in the near future. Hardly a fraction of 500,000.
Economically, it's cheaper to put murderers to sentences of life without parole.
• The average cost of keeping someone in prison is around $150 per day; the yearly cost is around $60,000. (p.34)
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http://www.spinneypress.com.au/142_book_desc.html
Sorry, couldn't get a better source. I know that's average and doesn't take into account the actual cost to imprison murderers specifically, but its good enough.