Economic of Crime by Simon W. Bowmaker. Summary

Plan:
1. Ehrlich’s model
2. Models connected to the rise of private protection
a) ‘More guns, less crimes’ written by John Lott
b) Zedlewski’s model
c) Ayres and Levitt (1998): The case of Lojack
3.Difficulties with a data
4. Literature
5. Apendix
1. Despite recent declines crime is still one of the most serious problems of the society. Thus it is important to understand the causes and consequences of criminal activity. A lot of works, researches and theories were proposed by criminologists, jurists and economists. In the last few years economists have directly impacted on government penal policies, especially in the United States.
One of such economists was Gary Becker. He did not try to determine the causes of crime, but to identify the variables that structure the costs of and return to criminal activity to predict the incident of crime in future. Ehrlich (1973) extended Becker’s model by adding a theory of occupational choice. He assumes a utility function of the form:

Us=U (Xs, C);
C – amount of time devoted to consumption or non-market activity
X – stock of a composite market good

Then he assumes that there are two states in S: arrest (a) or success (b):

Xᵃ=W¹+Wᵀ(T)+Wᴸ(L);
Xᵇ=W¹+Wᵀ(T)-F(T)+Wᴸ(L);
W¹ - initial asset
Wᵀ- earnings from illegal activities,
F – monetary equivalent of punishment
Wᴸ - earnings from legal activities  
T – time spent in illegal activities
L – time in legal earning activities

Expected utility is given by:
E[U(Xs, C)] = (1-P) U(Xᵃ, C) + PU(Xᵇ,C)
P – probability of a successful crime. The objective is to maximize expected utility over T subject to a time constraint:
Max E[U(Xs,C] subject to k=T+L+C
k-the total hours available to the individual

If C is fixes than the optimal allocation of working time between T and L is represented by:
-(Wʹᵀ-Wʹᴸ)-(Wʹᵀ-F-Wʹᴸ)=PUʹ(Xᵃ)/[(1-P)Uʹ(Xᵇ)];
Derivatives are written by the prime symbol (ʹ). The left side of this equation is the slope of a production... [continues]

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