Interpretation(s) of elasticity in operant demand
Use η only for slope-based elasticity; keep Essential Value and PMAX as separate labels.
01Research in Context
What this study did
Gilroy et al. (2020) wrote a map of the word "elasticity." They looked at how BCBAs use three numbers: plain elasticity, Essential Value, and PMAX. The paper shows each number measures a different curve feature. It tells us to stop swapping the words like they mean the same thing.
The authors used math, not new data. They drew demand curves and labeled the exact spots each index captures.
What they found
Elasticity (η) is only the slope of the demand curve at one price. Essential Value is the whole area under the curve. PMAX is the single price where spending peaks.
Calling all three "elasticity" mixes apples, oranges, and bananas.
How this fits with other research
Axe et al. (2021) did the same clean-up job for the term "discriminative stimulus." Both papers yell, "Stop sloppy labels!" They share the same mission but fix different words.
Burgio et al. (1991) warned us first. That older paper said we fight over what "reinforcer" and "discriminative stimulus" even mean. Gilroy et al. (2020) picks up the torch and adds elasticity to the list of messy terms.
Simó-Pinatella et al. (2013) reviewed 31 studies that use demand curves. Their review sits in the same assessment world but never fixed the math labels. Gilroy fills that gap.
Why it matters
Next time you graph a reinforcer assessment, write η for slope, not "elasticity" for everything. Clear labels help teams read your graph the same way. One word, one meaning, fewer fights over data.
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02At a glance
03Original abstract
This brief report provides an account of varying interpretations of elasticity (η) in the operant demand framework. General references to "demand elasticity" have existed since the Exponential model of operant demand was proposed by Hursh and Silberberg (2008). This term has been used interchangeably with Essential Value (EV), PMAX , and the rate of change constant α. This report provides an in-depth account of η and the various ways in which this metric has been used to interpret fitted demand functions. A review of relevant mathematic terms, operations associated with differentiating parameters, and worked solutions for η are provided for linear and nonlinear demand functions. The relations between η and EV, PMAX , and α are described and explained in terms of their mathematical bases and recommendations are provided regarding their individual interpretation. This report concludes with recommendations for providing additional mathematical detail in published works and emphasizing a consistent use of terms when describing aspects of operant demand.
Journal of the Experimental Analysis of Behavior, 2020 · doi:10.1002/jeab.610