A general equilibrium investigation of handguns, cops and robbers

We study a general equilibrium environment in which the only activity of interest is armed robbery. Agents choose to be citizens or robbers, and to purchase handguns or not. By arming, citizens can protect themselves from robbery. The government chooses the intensity of police efforts to arrest would-be robbers and to arrest citizens who arm for self-defense. Properties of an equilibrium are characterized and comparative statics results are obtained. We then show why empirical work that examines variations in "shall issue" laws could lead to wrong conclusions. Our analysis produces counterexamples to the following propositions: raising the arrest rate of robbers reduces crime; increasing the arrest rate of armed citizens reduces the number of armed citizens (crime rate, gun death rate).