: Quantity restrictions with imperfect enforcement in an over-used commons: Permissive regulation to reduce over-use?

This paper presents a model of quantity regulation aimed at mitigating externalities from over-use of a commons: for example, restrictions on use of automobiles, fisheries, computer networks and electronic stock quotation systems with high-frequency traders. The model provides a counter-intuitive answer to the question of what happens when quantity restrictions are legislated but enforcement is imperfect. If the probability of enforcement depends on both violation rates and enforcement expenditures, then equilibrium congestion can become worse as the quantity restriction becomes more severe. Stricter regulation causes more agents to violate the regulation which consequently reduces the probability of detection. Aggregate payoffs respond nonmonotonically to stricter regulatory rules. We find an interior near-optimal solution which is neither too permissive nor too strict. We show, however, that this near-optimal quantity regulation falls short of achieving socially optimal levels of use. Moreover, socially optimal levels of use can never be achieved in the sense that there exist some agents who rationally choose to violate the regulation if the regulator sets the restricted activity level at the socially optimal level. We also discuss optimal enforcement.