The effects of differing response types and price manipulations on demand measures.
The way you raise the price—more responses or more effort—changes the shape of the demand curve.
01Research in Context
What this study did
Hatton et al. (1999) asked a simple question: does it matter how we make a reinforcer cost more? They ran pigeons on fixed-ratio schedules. In one condition the bird had to peck many times. In another the bird had to peck hard. Both bumps raised the price, but in different ways.
The team drew demand curves for each price type. They also tried a unit-price rule that blends ratio and force into one number.
What they found
More pecks gave smooth, straight demand curves. More force gave bent, wobbly curves. The birds quit sooner when effort rose than when number rose.
Unit price helped the two curves slide closer, yet they never fully overlapped. How you charge the price still shaped the final picture.
How this fits with other research
Harrington et al. (2006) later showed the same curve metrics work with people who use drugs. They found Pmax and Omax lined up with old breakpoint scores. C et al. opened the toolbox; W et al. proved it travels well.
Foster et al. (2009) tinkered with the math after C et al. They compared three ways to convert food amounts. All tweaks target the same goal: cleaner demand curves.
Reynolds et al. (1968) set the stage. Their ratio equation predicted response rate from reinforcement rate. C et al. built on that by asking what happens when price itself comes in two flavors.
Why it matters
When you graph how hard a client will work for a reinforcer, pick your price axis with care. Adding five more tokens is not the same as asking for a firmer squeeze or louder vocal response. If you switch price types mid-program, the curve may bend and mislead you. Try both forms, then plot unit price to see if the data merge. This guards you against false conclusions about reinforcer strength.
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02At a glance
03Original abstract
Animals' behavioral needs have become an important component of animal welfare legislation. Behavioral economics provides a framework for the study of such needs. A function, analogous to a demand function relating consumption rate to price, can be obtained by increasing the price (or work) required for access to a commodity. This experiment investigated the effects of different response types and price manipulations on these functions. Six hens pushed a door or pecked a key for food under open economic conditions (short experimental sessions and supplementary food). In Part 1, the number of door pushes required (fixed‐ratio schedule) was increased each session, and the force needed to push the door was increased across conditions. In Part 2, the force needed to push the door was increased session to session, and the fixed‐ratio schedule was increased across conditions. In Part 3, the number of key pecks required was increased each session. Both response types produced similarly shaped (approximately linear in logarithmic coordinates and downward sloping) demand functions when price was increased by increasing the number of responses required. These imply an elastic demand for food under these conditions. In contrast, increasing the force required to push the door resulted in highly curvilinear functions. These functions indicated little change in consumption across lower door forces and abrupt drops in consumption at higher force requirements, implying mixed elasticity in the animals' demand for food. The differences between the shapes of the two functions seem to arise from the different ways that the two price manipulations alter the time taken to complete the work required. Increasing the fixed‐ratio requirement necessarily increases the time needed to complete each response unit, whereas increasing the force requirement does not. The different shapes of the functions were robust when either force or number was varied across sessions and the value of the other was varied over conditions. They were also robust when the price increases were taken from different conditions, showing that the shapes of the functions were independent of the place in the experiment in which the price was examined. Unit price (which combines number and force into a single price measure) unified the data from the two price manipulations to a large degree, producing moderately curved functions. However, there was some variance around the unit price functions, and this was attributable to the different shapes of the underlying functions. The data suggest that different price manipulations may give different measures of animal demand but that unit price might provide some unification.
Journal of the experimental analysis of behavior, 1999 · doi:10.1901/jeab.1999.71-329