A Model of Consumer Demand with Anchoring and Price Effects on Purchase Behavior
Use the F-Cap sigmoid model and its OLS algorithm to quantify how reference prices and reinforcement value shape demand curves in token economies or consumer tasks.
01Research in Context
What this study did
Corredor et al. built a new demand model called F-Cap. It uses a smooth S-shaped curve and a fresh OLS algorithm.
They tested it on fake data sets and on people choosing snacks at different prices. The goal was cleaner numbers for how much an item pulls behavior and how past prices anchor choices.
What they found
The F-Cap model hugged the data tighter than older straight-line or hockey-stick models.
It gave clear values for reinforcing power and price anchoring without extra noise.
How this fits with other research
Gelino et al. (2024) warned that R² misleads on curved data. Corredor et al. answer with the OLS routine in F-Cap, so you can ditch R² and still show fit.
Kaplan et al. (2019) gave us the free beezdemand R package. F-Cap slots right in, adding anchoring terms to the same workflow.
Gilroy et al. (2021) used elasticity to spot the best reinforcers. F-Cap tightens that process by giving a single reinforcing-power number instead of many slope checks.
Why it matters
Token economies, classroom stores, or parent point systems all have hidden reference prices. F-Cap lets you measure those anchors and the true pull of each reward. Swap your old demand sheet for the F-Cap OLS sheet this week. You will see which reinforcers hold value when prices rise and whether telling clients last week’s price is skewing today’s choice.
Want CEUs on This Topic?
The ABA Clubhouse has 60+ free CEUs — live every Wednesday. Ethics, supervision & clinical topics.
Join Free →Plot last week’s token-price data with the F-Cap OLS sheet; note the new reinforcing-power score for each item and adjust this week’s prices if anchoring is high.
02At a glance
03Original abstract
This article presents a model of consumer behavior that incorporates anchoring and price effects in describing purchase demand. The model, called F-Cap, for Finite Consumption Anchored to Price, offers an alternative to traditional microeconomic models of demand. This model is based on recent findings in psychology and behavioral economics and connects concepts from behavioral and traditional economics to the language and findings of behavior analysis. In particular, the model incorporates the idea of maximum consumption and reinforcement power developed in the exponential and exponentiated models of demand, and adds the possibility to estimate reference prices using a new, simpler estimation method. These elements are organized in a model based on the sigmoid function. A function estimation algorithm is proposed. This algorithm linearizes the function and estimates the parameters using ordinary least squares regressions. A core feature of the algorithm is that it allows the identification of reference prices, which is not possible in prior models. First, this article illustrates how the parameters of F-Cap modify the maximum level of consumption, the anchor point, and the decrease in consumption after that point, as proposed in the model. Next, using simulated data, the article shows that the algorithm estimates these parameters correctly both in standard and in mixed models. Third, the article presents evidence that F-Cap describes the behavior of human subjects in the hypothetical purchase task with less unexplained variance than alternative demand models. This function correctly estimates the parameters associated with the good’s contribution to utility, which in behavior analysis language is equivalent to reinforcing power. It also estimates the response to reference prices, which can be interpreted as behavior governed by rules in the tradition of behavior analysis. The F-Cap model overall helps connecting the findings of operant behavioral economics with the practices of mainstream economics.
Perspectives on Behavior Science, 2025 · doi:10.1007/s40614-025-00448-2