People who are in favor of the death penalty usually give two reasons: first, the fear of death will prevent others from committing the same terrible crime; second, the death penalty is cheaper than its alternative, life imprisonment. However, reliable research shows that life imprisonment is preferable to the death penalty from an economic point of view. People think that it is not true that the death penalty saves money. Therefore, the death penalty should be abolished.
The argument does not take into account another important reason in favor of the death penalty, so it is not a good argument is an appropriate evaluation of the argument in the main part of the question.