Traditional law and economics analyses of product liability assume that expected harm is proportional to usage. This paper builds on Daughety and Reinganum (2013a, 2014) by assuming that harm increases and is convex in usage. In contrast to previous contributions, we analyze liability rules when not only consumers but also third parties incur harm. We show that the social ranking of liability rules previously established for the case in which only consumers suffer harm (strict liability dominates no liability and negligence)may be reversed if third party harm is sufficiently important.