IntroductionCapital punishment was an ancient punishment. This has sparked much discussion since the 18th century. The focal points are the “value of life” and ethical concerns. Furthermore, economic analysis, which focuses on the effects and efficiency of capital punishment, is also important. In the article, the front indicates the reasons for the death penalty, the back indicates the cons. Supporting Reason Punishment Deterrence Becker (1968), first of all, assumes that the crime is serious and involves social loss, should be deterred, the death penalty is the most severe punishment, and potential criminals are normal individuals. Since individuals are rational, potential criminals are also rational. They commit crime as utility maximization. The opportunity cost of committing a crime is the net utility derived from a legitimate activity. Therefore, criminals give up crime when the expected net utility from crime is less than the expected net utility from legitimate activity. We focus on the expected net utility from the crime “E(U)” and the equation shows below: E(U)=PU(YF)+(1-P)U(Y)P is the subjective probability of being caught and convicted; U(_) is the individual's utility function, which depends on Y and F; Y are the benefits resulting from the commission of a crime; F is the cost of committing a crime if caught, such as punishment. Therefore potential criminals will be deterred by severe punishment. Almost people are afraid of death, so capital punishment is an extremely severe punishment, which efficiently erases the benefits of crime. Capital punishment should have a deterrent effect on crimes. Dynamic Analysis In the dynamic model, past crime would lead to the expansion of future crime as the decrease... of paper......and crime by crime type Community, Review of Social Economics, Vol. 43, pages 245-259McManus, W.S. (1985) Estimates of the deterrent effect of capital punishment: the importance of the researcher's prior beliefs, The Journal of Political Economy, vol. 93, No. 2, pages 417-425Dickens, W. (1986) Crime and Punishment Again: The Economic Approach With a Psychological Twist, Journal of Public Economics, Vol.30, pages 97-107Hansen, K., Machin, S. (2002) Spatial Crime Patterns and the introduction of the minimum wage in the UK, Oxford Bulletin of Economics and Statics, vol. 64, Supplement 1, pages 667-697Oppedahl, J. (2009) Montana Can't Afford the Death Penalty, Helena Independent Record - http://www.deathpenaltyinfo.org/new-voices-death-penalty-too-expensive- overloaded courts[5] Northern Ireland: The Troubles, BBC History, http://www.bbc.co.uk/history/recent/troubles/