### Wealth-dependent Fines

Tyler Cowen alerts us to an intriguing story:

My first thought is no. We fine activities that have negative externalities, such as putting others at risk. If X is the size of the externality, and p is the probability of being caught, then the optimal fine is X/p. That will give people the right incentive to produce the optimal quantity of the externality. Under this policy, the rich may choose to speed more, but that is optimal. If we have an optimal carbon tax, the rich will produce more carbon too. Optimal pigovian taxes do not eliminate income effects.

On further reflection, however, I think a case can be made, at least theoretically, to support the judges' ruling. First, assume that the negative externalities are very great, so the optimal quantity of the externality is about zero. By itself, that argues for a large fine, not a wealth-dependent one. But then add another assumption: Suppose there is some small probability that an innocent person will be found guilty because of a rogue, or simply a mistaken, policeman. This possibility, together with risk aversion, would induce us to temper how large the fine is. And this tempering of the large fine would seem to be less for richer taxpayers: Because the mistaken ticket is a proportionately smaller fraction of their wealth, we need to worry less about the uncertainty large fines impose. The result is larger fines for richer offenders.

A Swiss court has slapped a wealthy speeder with a chalet-sized fine — a full $290,000.

Judges at the cantonal court in St. Gallen, in eastern Switzerland, based the record-breaking fine on the speeder's estimated wealth of over $20 million.

A statement on the court's Web site says the driver — a repeat offender — drove up to 35 miles an hour (57 kilometers an hour) faster than the 50-mile-an-hour (80-kilometer-an-hour) limit.Is it optimal to base fines on wealth?

My first thought is no. We fine activities that have negative externalities, such as putting others at risk. If X is the size of the externality, and p is the probability of being caught, then the optimal fine is X/p. That will give people the right incentive to produce the optimal quantity of the externality. Under this policy, the rich may choose to speed more, but that is optimal. If we have an optimal carbon tax, the rich will produce more carbon too. Optimal pigovian taxes do not eliminate income effects.

On further reflection, however, I think a case can be made, at least theoretically, to support the judges' ruling. First, assume that the negative externalities are very great, so the optimal quantity of the externality is about zero. By itself, that argues for a large fine, not a wealth-dependent one. But then add another assumption: Suppose there is some small probability that an innocent person will be found guilty because of a rogue, or simply a mistaken, policeman. This possibility, together with risk aversion, would induce us to temper how large the fine is. And this tempering of the large fine would seem to be less for richer taxpayers: Because the mistaken ticket is a proportionately smaller fraction of their wealth, we need to worry less about the uncertainty large fines impose. The result is larger fines for richer offenders.

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