No.
Firstly, the assumption that the death penalty is less costly to taxpayers is not backed up by evidence. According to a study by the Kansas Judicial Council, defending a death penalty case costs about four times as much as defending a case where the death penalty is not considered. In Kansas, housing prisoners on death row costs more than twice as much per year compared to those housed in general population. Some prisoners spend years on death row, going through appeal after appeal, making the system inefficient.
Secondly, the possibility of putting an innocent life is too great a risk. This often disproportionately affects the poorest who cannot afford access to quality legal representation making them more likely to be a victim of a miscarriage of justice.
Finally, there's no convincing evidence capital punishment is a deterrent. Compare the murder rates in Hong Kong, where capital punishment was abolished in 1993, and Singapore where a death sentence is mandatory for murder and you see little difference. The best deterrent for any criminal is to address socio-economic factors such as reducing rates of alcoholism, drug abuse, urban decay, investment in education and preventing breakdown in families.