A Theoretical Investigation of Handguns, Cops and Robbers

Abstract

We study a theoretical general equilibrium environment in which the only activity of interest is armed robbery. Agents choose whether to be citizens or robbers, and whether to purchase handguns. Armed citizens can protect themselves from robbery but any armed agent runs the risk of accidentally shooting himself or another agent. The government chooses a gun tax, and the intensity of police efforts to arrest would-be robbers and citizens who arm for self-defense. Properties of an equilibrium are characterized and the model is calibrated and solved. In all cases unique equilibria are obtained. We find that guns are an inefficient way of redistributing wealth, in the sense that social costs are very large relative to actual wealth redistribution. In this model society would be vastly better off if handguns could be eliminated. We do find, however, that handguns substantially deter crime when crime is defined as taking another's wealth by force. Yet handguns cause accidental deaths and resultantly in this model policymakers confront a fundamental trade-off between property rights and gun deaths.