IntroductionCapital punishment was an ancient punishment. This has caused much controversy since the 18th century. The central points are the “value of life” and ethical concerns. Additionally, economic analysis is also important because it focuses on the effects and effectiveness of capital punishment. In the article, the front part indicates the reasons which justify the death penalty, the rear part indicates the reasons which justify the death penalty. the death penalty is the harshest punishment and potential criminals are normal individuals. Because individuals are rational, so are potential criminals. They commit crimes to maximize their utility. The opportunity cost of committing a crime is the net utility of legitimate activity. Therefore, criminals desist from crime when the expected net utility of crime is less than the expected net utility of legitimate activity. We focus on the expected net utility of crime “E(U)” and the equation below: E(U)=PU(YF)+(1-P)U(Y)P is the subjective probability that the individual is arrested and convicted. ; U(_) is the utility function of individuals, which depends on Y and F; Y represents the benefits associated with committing a crime; F is the cost of committing a crime if caught, such as punishment. Therefore, potential criminals will be deterred by the harsh punishment. Almost people are afraid of death, so capital punishment is an extremely severe punishment, which effectively wipes out the benefits of the crime. . Capital punishment should be powerful in deterring crimes.Dynamic AnalysisIn the dynamic model, past crime would lead to the expansion of future crimes as the middle of paper ......e decrease in crime by crime type. Community, Social Economy Review, Vol. 43, pp. 245-259 McManus, WS (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 Static, 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/