Interjurisdictional competition in law enforcement

Because the return of the two occupations depends on capital, and because investment in capital in a jurisdiction depends on the crime rate in that jurisdiction, there is a bi-directional relationship between capital investment and crime which ma lead to capital concentration. [...] In standard models without occupational choice and in which capital must be allocated between competing jurisdictions (or uses), the unit return of capital in a given jurisdiction is a decreasing function of the stock of capital located in it. [...] It follows that if an extra unit of capital sufficiently increases the number of workers (and decreases the number of criminals), then the unit return of capital may be an increasing function of the stock of capital located in a jurisdiction. [...] Alternatively, if he chooses to become a criminal, he appropriates for himself some of the return on capital and some of the return on the fix factor.8 Denote by α(di) the proportion of the total return on capital, and of the return on the fixed factor located in his jurisdiction a criminal is able to steal. [...] A non-resident capitalist endowed with K̄ units of capital chooses to allocate his capital between the two jurisdictions.10 Ka denotes the amount of capital invested in jurisdiction a, and Kb = K̄ − Ka that invested in jurisdiction b. In jurisdiction i, the government chooses the level of law enforcement, di, which it can buy at a cost of one per unit.