Optimal negligence rule under limited liability

We study the standard economic model of unilateral accidents, in its simplest form, assuming that the injurers have limited assets.We identify a second-best optimal rule that selects as due care the minimum of first-best care, and a level of care that takes into account the wealth of the injurer. We show that such a rule in fact maximizes the precautionary effort by a potential injurer. The idea is counterintuitive: Being softer on an injurer, in terms of the required level of care, actually improves the incentives to take care when he is potentially insolvent. We extend the basic result to an entire population of potentially insolvent injurers, and find that the optimal general standards of care do depend on wealth, and distribution of income. We also show the conditions for the result that higher income levels in a given society call for higher levels of care for accidents.