A Model of Consumer Demand with Anchoring and Price Effects on Purchase Behavior

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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.

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