AbstractThere is widespread evidence that some firms use false advertising to overstate the value of their products. We consider a model in which a policy maker can punish such false claims. We characterize an equilibrium where false advertising actively influences rational buyers and analyze the effects of policy under different welfare objectives. We establish precise conditions where policy optimally permits a positive level of false advertising and show how these conditions vary intuitively with demand and market parameters. We also consider the implications for product investment and industry self‐regulation and connect our results to the literature on demand curvature.