A Model of Zero Price Effect with Prospect Theory

According to standard expected utility theory, people will choose the option with the highest cost–benefit difference when they faced with a choice of selecting one of available products (or buying nothing). Recently, by psychological experiments, Shampanier, Mazar, and Ariely (2007) showed that people do not simply subtract costs from benefits but instead they perceive the benefits associated with free products as higher. Decisions about zero price products are empirically different from the forecast of standard rational choice theory. Their experiments showed that people, who choose expensive option in non-zero condition, choose the cheaper option in the zero-price condition. However, they do not specify the mathematical condition of utility function that can generates such an inversion of preference or zero-price anomaly (Heyman and Ariely 2004; Ariely, Gneezy, and, Haruvy 2006). We give a general proof of existence of the condition of zero-price anomaly based on the prospect theory (Kahneman and Tversky 1979; Tversky and Kahneman 1981, 1992; Myagkov and Plott 1997). More specifically, we prove that the concavity at negative domain of value function is essential for the zero-price anomaly and explains the results of empirical experiments well. Additionally we test our proposal by psychological experiment which contrasts zero-price and non zero-price conditions. As a result, we succeed in showing that the prospect theory can explain the zero-price anomaly.