The distribution of regional property crime and police deployment—The price of equality

Abstract

This study allows the probability of being apprehended to be a function of the number of police per capita, and assumes that the total supply of police is fixed. A country consists of two communities, which are characterized by their population densities. Minimizing national property crime creates distinct crime rates in both communities. The less-densely-populated community has more police per capita and tolerates a lower level of criminal activity but surprisingly also suffers from a higher crime rate. To balance the crime rate between the two communities, some of the police must be moved from the more-densely-populated community to the less-densely-populated one. The shift must be associated with an increment of national overall crime, the price of achieving outcome equality. This study defines the same crime rate in both communities as the outcome equality. An easily achieved and supervised equality is having the same number of police per capita in both communities, defined as the initial equality. Its price is also the increment of overall national crime. The formulas used to measure both prices are proposed and compared.