Eq gives for each wealth level

Eq. (2) gives, for each wealth level, the minimal spending on private protection required to prevent crime by deterring criminals. Therefore, citizens must decide whether they will spend h on their own protection or will not invest on protecting themselves at all. They will spend h only if the prospective losses of being victimized are not exceeded. That is, if
Wealthier persons would need, ceteris paribus, to spend more on private protection to avoid being victimized. This is the conclusion reached based on the first derivative of Eq. (2) with respect to ,
But are wealthier persons willing to spend more on protection to avoid being victimized? Or will they instead prefer to bear some risk? The answer depends on the second derivative of h with respect to ,
Eq. (5) will be negative, unless the second derivative of p is both negative and large in absolute value. So the wealthy will routinely invest in private security to avoid being victimized unless p exhibits sharp diminishing returns to scale. In summary, according to the approach adopted by Gaviria and Pagés (2002), the wealth of individuals determines both their economic attractiveness to becoming victims and their capacity to protect themselves from criminals by paying for their protection. Justus and Kassouf (2013) argue that according to the findings of Becker (1968), Ehrlich (1973), Cohen et al. (1981) and Gaviria and Pagés (2002) it things is to be expected that, given the opportunity cost of crime, the likelihood of failure determined by government spending on public safety, the penalties provided for in the law, and the costs involved in planning and committing a crime, criminals will pick their victims based on their evaluation of those who are more economically attractive for the criminal act. In this subjective evaluation, criminals take into account both the wealth of potential victims and the likelihood of failure as determined by how much they spend on their own protection. By doing this, criminals optimize the expected return on crime. Therefore, the behavior of potential victims has a direct bearing on the optimization process that is implicit in the rational choice of a criminal. Thus, if the principle of economic rationality on the part of criminals holds, the risk of victimization increases with wealth. However, as pointed out by Gaviria and Pagés (2002), wealthier individuals have stronger reasons and more money to spend on their own security to protect themselves from criminals. On the other hand, poorer individuals lack the financial means to pay for their protection in order to avoid being victimized, but they are less economically attractive potential victims to criminals than wealthier individuals. Table 1 shows some selected studies that analyzed the effect of income on single victimization and repeat victimization. In sum, the effect observed in this previous literature is positive for property crimes and negative for crimes against a person.
Methodology
Results and discussion In this context, before discussing our results, alveoli is interesting to summarize some postulates in the literature (Cohen et al., 1981, and others) regarding theoretical relationships between victimization and the main variables included in the empirical model. Before showing the empirical results for repeat victimization models, we analyze how the same variables affect simple victimization. Table 5 shows the results of the simple victimization model, in which the same regressors were used. Regarding physical assault (crime against a person), it is interesting to note that most variables maintain their significance and sign, but in some cases the sign appears inverted: studying and years of schooling increase the likelihood of property victimization, but for physical assault the effect is the opposite, i.e. it protects potential victims. This demonstrates the need to distinguish the different types of crimes in the analysis, as suggested in Cohen et al. (1981).