Theft in equilibrium

We incorporate theft into the standard partial equilibrium model. We focus on two scenarios, one in which the whole wealth is subject to theft, and another in which only final goods are stealable. There are major differences between the two scenarios. In the first one, a policy that increases output reduces crime, which is not necessarily so in the second one. In the first model, public police protection reduces crime, but in the second one it may very well increase it. In the first model, the competitive equilibrium allocates private police efficiently conditional on the crime rate, but does not in the second model. The differences are due to the fact that while in both models output markets affect crime, only in the second model does crime affect output markets.