Demand equations for qualitatively different foods under fixed-ratio schedules: a comparison of three data conversions.
Turn all foods into units of the learner’s top item before plotting demand and your curves will behave.
01Research in Context
What this study did
Foster et al. (2009) tested three ways to turn food consumption into demand numbers. They used fixed-ratio schedules with qualitatively different foods. The goal was to see which math trick gave the cleanest demand curves.
They compared raw counts, percentage of free-feeding, and a new method that converts everything into units of a single preferred food. This last trick uses data from a short concurrent-schedule test.
What they found
The three conversions gave different demand parameters for the same foods. The preferred-food unit method produced the most orderly curves. It also made the curves line up better across different foods.
How this fits with other research
Harrington et al. (2006) already showed that Pmax and Omax indices from demand curves match old breakpoint and peak-rate measures. Mary et al. now add that the curve itself gets cleaner if you first normalize reinforcers to a common unit.
Hatton et al. (1999) warned that how you raise price changes curve shape. Mary et al. answer by fixing the price side and instead fixing the value side—turning all foods into one currency before plotting.
Emmelkamp et al. (1986) proved you need concurrent schedules plus instructions to get clean matching with humans. Mary et al. borrow that same concurrent step, but only as a quick bias test to set the exchange rate between foods.
Why it matters
If you run reinforcer assessments with different edibles, you can now convert them to a single scale before graphing demand. Run a two-minute concurrent test between the new food and the learner’s favorite, then divide all consumption by that bias factor. Your demand curves will stack neatly and decisions about ‘best reinforcer’ become clearer.
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Join Free →Pick the learner’s favorite food, run a quick concurrent test, then divide every other food’s consumption by that ratio before graphing demand.
02At a glance
03Original 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.
Journal of the experimental analysis of behavior, 2009 · doi:10.1901/jeab.2009.92-305