Unit price as a useful metric in analyzing effects of reinforcer magnitude.
Calculate unit price (schedule ÷ magnitude) to predict whether your client will work harder or quit earlier when you change reinforcer size or schedule.
01Research in Context
What this study did
Szempruch et al. (1993) wrote a theory paper. They asked: can one simple number predict how both reinforcer size and schedule affect behavior?
The number they picked is unit price. You get it by dividing the schedule requirement by the reinforcer size. A bigger ratio or smaller snack makes the price go up.
What they found
The authors showed that unit price neatly ties together past data. When price is equal, response rate and consumption stay the same, even if you change size or schedule separately.
That means you can forecast what will happen before you run the session. Just calculate unit price and compare to past cases.
How this fits with other research
Tyrer et al. (2009) later tested the idea with real rats. They used progressive-ratio schedules and varied sucrose volume. Larger reinforcers pushed the breakpoint higher, exactly as unit price predicts.
Schulingkamp et al. (2023) used a cousin metric, behavioral-economic demand curves. They showed that social interaction obeys the same cost-benefit rules, even though they looked at demand instead of unit price.
Together, the three studies form a ladder: J et al. gave the rule, F et al. proved it with magnitude, and Schulingkamp et al. showed the rule works for other reinforcers too.
Why it matters
When you adjust both token cost and treat size in your token board, compute unit price first. If the new price matches an old condition that worked, you can expect similar responding. This saves you from running extra pilots and keeps motivation steady across program changes.
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Join Free →Before you raise the token cost from 3 to 5, either give a slightly bigger reinforcer or check that the new unit price still falls inside the 'good' range you have seen before.
02At a glance
03Original abstract
In this paper, we applied the behavioral-economic concept of unit price to the study of reinforcer magnitude in an attempt to provide a consistent account of the effects of reinforcer magnitude on behavior. Recent research in the experimental analysis of behavior and in behavioral pharmacology suggests that reinforcer magnitude interacts with the schedule of reinforcement to determine response rate and total consumption. The utility of the unit-price concept thus stems from its ability to quantify this interaction as a cost-benefit ratio (i.e., unit price = characteristics of the schedule of reinforcement divided by magnitude of reinforcement). Research employing the unit-price concept has shown that as unit price increases, a positively decelerating function exists for consumption (i.e., a function with an increasingly negative slope, when plotted on log coordinates) and a bitonic function exists for response rate. Based on these findings, the present analysis applied the unit-price concept to those studies of reinforcer magnitude and drug self-administration that examined the effects of reinforcer magnitude on response rate using simple schedules of reinforcement (e.g., fixed-ratio schedule). This resulted in three findings: (a) Reinforcer-magnitude manipulations and schedule manipulations interact in a manner that can be quantified in terms of unit price as benefit and cost factors, respectively; (b) different reinforcer-magnitude manipulations are functionally interchangeable as benefit factors in the unit-price ratio; and (c) these conclusions appear warranted despite the differences in reinforcers (food or drug), species (dogs, monkeys, or rats), and schedules (interval or ratio), and despite the fact that these studies were not designed for a unit-price analysis. In methodological terms, these results provide further evidence that employing the unit-price concept is a parsimonious method for examining the effects of reinforcer magnitude. In theoretical terms, these results suggest that a single process may underlie the effect of combined reinforcer-magnitude and schedule manipulations.
Journal of the experimental analysis of behavior, 1993 · doi:10.1901/jeab.1993.60-641