Stability of a crime level equilibrium

We consider crime level in an economic market with a supply of potential criminals. These criminals differ in their opportunity cost for committing crime, reflecting differences in the value of foregone opportunities such as performing productive labor. The realized demand is influenced by the expected value for crime, which depends on several socio-economic variables including wealth, police enforcement, and police arrest ability. After determining the equilibria level suggested by our approach, we propose a dynamic setup and study the stability of this system. Two critical enforcement levels are determined. Exceeding the lower enforcement threshold will push crime to stabilize (converge) to an equilibrium level. Correspondingly, exceeding the higher enforcement threshold will collapse the crime market to zero.