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On the Axiomatization of the Satiation and Habit Formation Utility Models

We propose a preference condition called shifted difference independence to axiomatize a general habit formation and satiation model (GHS). This model allows for a general habit formation and satiation function that contain many functional forms in the 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 obtain a GHS model with a linear habit formation function and a recursively defined linear satiation function.