We study the implications of biased consumer beliefs for search market outcomes in the seminal framework due to Diamond (1971). Biased consumers base their search strategy on a belief function which specifies for any (true) distribution of utility offers in the market a possibly incorrect distribution of utility offers. If biased consumers overestimate the best offer in the market, a novel type of equilibrium may emerge in which firms make exceptionally favourable offers in order to meet biased consumers' unreasonable high expectations which then become partially self-fulfilling. Consequently, the presence of biased consumers may improve the welfare of all consumers.