On the Axiomatization of the Satiation and Habit Formation Utility Models

We propose a preference condition called shifted difference independence to model the reference point dependent measurable time preference. Based on this condition, we axiomatize a general habit formation and satiation model (GHS) to capture both effects of habit formation and satiation. This model allows for a general habit formation function and satiation function that contain the functional forms in the existing literature as special cases. Since the GHS model can be reduced to either a general satiation model (GSa) or a general habit formation model (GHa), our theory also provides approaches to axiomatize both the GSa model and the GHa model. Furthermore, by adding extra preference conditions into our axiomatization framework, we axiomatize a GHS model with a linear habit formation function and a recursively defined linear satiation function. Finally, we show that the idea developed in this paper also applies to the axiomatization of these models for risky time preference.