Demand Equations for Qualitatively Different Foods Under Fixed‐ratio Schedules: A Comparison of Three Data Conversions

Abstract

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.

The effects of reinforcer magnitude in the preceding and upcoming ratios on between‐ratio pausing in multiple, mixed, and single fixed‐ratio schedules

“…In summary, running response rates decreased with FR increases for all three schedule types as has been found in other studies. Running response rates were not consistently affected by magnitude of the reinforcer, a result similar to the effects of delay to the reinforcer (Harris et al, ) and reinforcer quality (Foster et al, ). The present findings show that the main effects of the discriminative stimuli, the reinforcer magnitude and the context of the experiment were on PRP and not on running response rates.…”

Effects of a Signaled Delay to Reinforcement in the Previous and Upcoming Ratios on Between‐ratio Pausing in Fixed‐ratio Schedules

“…These findings, together with those from the present experiment, suggest that the between-ratio pause duration might be a useful measure for assessing the effects of varying the parameters of the reinforcer (e.g., quality, magnitude, or delay) on FR schedule performance. This might be more consistent than the overall response rate which is presently the most frequently used measure (e.g., Foster et al, 2009;Hursh & Silberberg, 2008).…”

“…Such a suggestion could be examined further using other parameters known to affect the value of reinforcement. For example, varying the quality of the reinforcer has been found to influence behavior under single FR schedules (e.g., Foster, Sumpter, Temple, Flevill & Poling, 2009). Thus, the present research could be extended by using reinforcers of differing quality rather than delay.…”

The Effects of Session Length on Demand Functions Generated Using Fr Schedules

“…Mixed elasticity is a frequent finding (e.g., Foltin, 1992; 1994; Foster, Sumpter, Temple, Flevill, & Poling, 2009; Hursh, 1984; Hursh, Raslear, Shurtleff, Bauman, & Simmons, 1988) and Hursh et al (1988) proposed the following equation to describe such functions, in natural logarithms:…”

“…The changes in the parameters of the demand function seen with the total session data may be interpretable in the light of within‐session data. Given these considerations, the present study assessed the effects of different‐length sessions on both the within‐session response patterns and the total‐session responding of domestic hens responding under FR schedules that were increased each session using a similar procedure to Foster et al (2009). The session lengths used in this study (10, 40, 60, and 120 min) covered the range found in most open and closed economy experiments.…”