Deceptive advertising, regulation and naive consumers

In markets where buyers have incomplete information about product quality, consumer sophistication strengthens the case for stronger regulation of deceptive advertising by firms. In a model where a fraction of buyers are naive (i.e., cannot update beliefs based on market signals and believe all advertising claims) and they stand to gain from receiving reliable information about product quality, I show that the socially optimal level of penalty is (a) substantially higher than the penalty required to merely avoid deception by firms and (b) increasing in the proportion of sophisticated buyers. The optimal penalty for false advertising not only discourages deception but also reduces prices by eliminating signaling distortion. Moreover, a low level of penalty is worse than no penalty from a social welfare standpoint.