In this discussion I explain there is more to the death penalty than the emotional aspects and the end result. Numerous studies have been conducted that indicate the death penalty has no deterrent effect. In other words, the fact that you can be executed does not stop people from committing first-degree murder.
So, why does Arizona have it? It could be because it makes us feel better to know that a person "got what they deserved." That they took someone from this world so they should not be able to live in it either, the old adage "an eye for an eye." Some suggest it is for the basic human desire of revenge.
Regardless of the purpose, implementation and execution of the death penalty takes a large amount of time and resources from the initial investigation of the crime to the final insertion of the needle.
Think of the State v. Jodi Arias trial alone -- the defense has already racked up a tab of over $2 million (of taxpayer money). That amount does not include jail costs, court costs, prosecution costs, post-trial appeal costs and actual execution costs; and the trial itself isn't even over. This one example puts a dollar amount on just a small part of a death penalty case.
Take the time and the amount of resources involved and weigh those aspects against the purposes above. Once that is done, you might find that your answer to the question "is the death penalty worth it" is different than at the beginning of the conversation.