Demand equations for qualitatively different foods under fixed-ratio schedules: a comparison of three data conversions.

Concurrent schedules were used to establish 6 hens' preferences for three foods. The resulting biases suggested wheat was preferred over honey-puffed and puffed wheat, and puffed wheat was the least preferred food. The hens then responded under fixed-ratio schedules for each food in 40-min (excluding reinforcer time) sessions, with the response requirement doubling each session until no reinforcers were received. At the smaller ratios, the less preferred the food, the faster the hens' overall response rates (mainly as a result of shorter postreinforcement pauses) and the more reinforcers they received. The relations between the logarithms of the number of reinforcers obtained (consumption) and the response ratio (price) were well fitted by curvilinear demand functions. Wheat produced the smallest initial consumption (ln L), followed by honey-puffed and puffed wheat, respectively. The response requirement at which the demand functions predicted maximal responding (P(max)) were larger for wheat than for the other foods. Normalizing consumption and price, as suggested by Hursh and Winger (1995), moved the data for the three foods towards a single demand function; however, the P(max) values were generally largest for puffed wheat. The results of normalization, as suggested by Hursh and Silberberg (2008), depended on the k value used. The parameter k is related to the range of the data, and the same k value needs to be used for all data sets that are compared. A k value of 8.0 gave significantly higher essential values (smaller alpha values) for puffed wheat as compared to honey-puffed wheat and wheat, and the P(max) values, in normalized standard price units, were largest for puffed wheat. Normalizing demand by converting the puffed and honey-puffed wheat reinforcers to wheat equivalents (by applying the bias parameter from the concurrent-schedules procedure) maintained separate demand functions for the foods. Those for wheat had the smallest rates of change in elasticity (a) and, in contrast to the other analyses, the largest P(max) values. Normalizing demand in terms of concurrent-schedule preference appears to have some advantages and to merit further investigation.