consumer's preference set is non-convex, then (for some prices) the consumer's demand is not connected. A disconnected demand implies some discontinuous behavior by the consumer as discussed by Hotelling: If indifference curves for purchases be thought of as possessing a wavy character, convex to the origin in some regions and concave in others, we are forced to the conclusion that it is only the portions convex to the origin that can be regarded as possessing any importance, since the others are essentially unobservable. They can be detected only by the discontinuities that may occur in demand with variation in price-ratios, leading to an abrupt jumping of a point of tangency across a chasm when the straight line is rotated. But, while such discontinuities may reveal the existence of chasms, they can never measure their depth. The concave portions of the indifference curves and their many-dimensional generalizations, if they exist, must forever remain in unmeasurable obscurity.: Following Hotelling's pioneering research on non-convexities in economics, research in economics has recognized non-convexity in new areas of economics. In these areas, non-convexity is associated with market failures, where any equilibrium need not be efficient or where no equilibrium exists because supply and demand differ. Non-convex sets arise also with environmental goods and other externalities, and with market failures, and public economics. Non-convexities occur also with information economics, and with stock markets (and other incomplete markets). Such applications continued to motivate economists to study non-convex sets. Works Harold Hotelling's review of Fishers' Statistical methods for research workers. Papers See also Cournot competition References I. Olkina and A. R. Sampsonb (2001). "Hotelling, Harold (1895–1973)," International Encyclopedia of the Social & Behavioral Sciences, pp. 6921–6925. Abstract. External links New School: Harold Hotelling American Statistical Association: Harold Hotelling Harold Hotelling The following have photographs: Harold Hotelling on the Portraits of Statisticians page. National Academy of Sciences Biographical Memoir Presidents of the Institute of Mathematical Statistics Fellows of the American Statistical Association American statisticians American social scientists Psychometricians Statistics educators 20th-century American economists American social democrats 1895 births 1973 deaths University of Washington alumni Fellows of the Econometric Society Presidents of the Econometric Society Mathematical economists American operations researchers Econometricians Environmental economists Regional economists Stanford University Department of Mathematics faculty Columbia University faculty University of North Carolina at Chapel Hill faculty American United Methodists People from Fulda, Minnesota Distinguished Fellows of the American Economic Association Economists from Minnesota 20th-century