Before revision:  Our habit-formation model allows for both addictive ( \alpha=1 ) and non-addictive ( 0<\alpha<1 ) habits.
After revision:  Our habit-formation model allows for both addictive ( \alpha=1 ) and non-addictive ( 0<\alpha<1 leads to partially addictive models, with the level of addictiveness increasing with \alpha. In contrast to the existing habit-formation literature, our constraint cannot be incorporated in the objective function through infinite marginal utility.