The observation that the demand for a commodity decreases as its unit price increases is called demand elasticity. Applied to food, and to rodents in an operant behavior situation, we call this cost-based anorexia. We review evidence that rats and mice show cost-based anorexia when food is available in either 23-h (continuous access) protocols or as discrete food opportunities. The decrease in food intake of rats at higher unit food price is associated with sustained high operant response rates that, in the food opportunity protocol, occupy the entire time available. In contrast, mice do not show sustained high response rates and, in the food opportunity protocol, show rapid decline of food intake within a meal even when intake is very low and weight loss rapid. Differential price experiments, either for the same food at different times or for different foods, show that mice do not maximize their response efforts. The behavior of mice under imposed cost conditions has some similarity to the behavior of human anorexia nervosa, and potential mechanisms are discussed briefly. Keywords Anorexia nervosa • Activity-based anorexia • Cost-based anorexia • Elasticity of demand • Food intake • Operant behavior • Rats • Mice • Animal model • Homeostasis • Body weight • Differential food cost • Zeitgeber • Palatability