This paper investigates the history of kinked demand curves. Different criteria of appraisal provided by the three most influential schools of economic methodology-instrumentalism, a priori methodology, and falsificationism-are used to explain the success and decline of kinked demand curves in economics. We find that in the history of kinked demand curves economists put much emphasis on the reality of assumptions and adopt criteria of appraisal quite different from instrumentalism. We also find that although the predictions of kinked demand curves are repeatedly rejected by empirical tests, most economic textbooks still accept this theory as the standard explanation of price rigidity. This historical fact is obviously inconsistent with falsificationism. We believe that the puzzling phenomena found in the history of kinked demand curves reflect the profound influence of a priori methodology on economics.