Essay about Economics of Crime: Capital Punishment

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Introduction
Capital punishment was an ancient penalty. This has incurred many argues since 18th century. The focal points are ‘value of life’ and ethical concerns. Besides, the economics analysis also is important, which focuses on the effects and efficiency of capital punishment. In the article, the anterior part indicates the supporting reasons of death penalty, the posterior part indicates the cons.

Support Reason
Deterrence of punishment
Becker (1968), first of all, assumes that the crime is bad which incurs social loss, it should be deterred, death penalty is the severest punishment, and potential criminals are normal individuals. Because individuals are rational, the potential criminals also are rational. They commit crime
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Then, then higher expected net utility from crime induce the more incentive of crime. The more crimes will disperse the police forces again and again, these become a vicious circle.
Contrary, the severe punishment can deter criminals, reduce the crime rate, police investigate fewer crimes and increase the detection rate (P). Lastly, the higher detection rate reduce crime rate again and again. Therefore, the severe punishment (such as death penalty) can prevent the vicious circle and reduce the crime.

Cost of punishment
The policy forces are costly and limited, besides the punishment also costly. So the economic analysis moves towards ‘efficiency of punishment (optimal level)’ to minimize the loss from the crime, not to eradicate crime. Assume that imprisonment is the unique punishment, and the policy force (detection rate) is unchanged in the case below.
Cost = Social cost + Control cost
The equation above shows the effect of crimes (Cost) which include social cost and control cost;
Social cost = D[∑▒〖C_i (x_(i)) 〗] the social cost is the social damage from the crime ‘D[_]’, C_i is the amount of crimes of type I which has inverse relationship with the length of imprisonment (severe level of punishment) for crime of type i ‘x_i’ as the deterrence effect;
Control cost = b∑▒〖p_i C_i x_i 〗 the control cost is the cost of punishment, b is the unit cost of imprisonment, p_i is the

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