The welfare costs of informationally efficient prices

Consider a market with two substitute products and a sequence of consumers. The consumers are uncertain about the quality of each product but obtain some private information about it. Additionally, each consumer observes the purchase decisions of her predecessors but not their private information. Absent prices, the standard logic of herding is that all but finitely many consumers may, with positive probability, select the lower quality product. One perspective in the literature is that informationally efficient market prices can resolve the herding inefficiency and induce asymptotic learning where the beliefs of consumers about product qualities converge to the truth. This paper shows that, while informationally efficient prices induce asymptotic learning, they also inflict a welfare cost. That is, we show that the expected welfare is decreasing in the frequency with which prices are set to be informationally efficient.