What economic arguments can be made in favor of mandatory seat-belt usage laws in automobiles?
The main economic argument with regard to this issue has to do with negative externalities. These are costs that are borne by people who are not involved in an economic transaction or other decision. In this case, the negative externalities are costs that are borne by others when the person decides not to wear a seat belt and gets in a wreck.
The biggest external cost will be to whoever has to pay the person's medical bills. If the person is insured, other people who pay premiums to that insurance company will pay for his or her bad judgement. If the person is not insured, it is likely that society as a whole will have to pay. If the person is killed, their family will be economically burdened. In the end, society may have to help with that as well if the person's family comes to need governmental assistance.
In these ways, the person's decision not to wear a seat belt would (if they are injured in a crash) impose costs on other people in society. Therefore it is legitimate to require seat belt use.