When do more police induce more crime?

Abstract

We provide a necessary and sufficient condition on the equilibrium of a Walrasian economy for an increase in police expenditure to induce an increase in crime. It turns out that this is essentially the condition for the Laffer curve to be downward sloping at a given ad valorem tax rate. Notably, such a perverse effect of police on crime is consistent with any appropriation technology and could arise even if the level of police protection is the socially optimal one.