The aim of this note is to investigate the effects on π of the introduction of a "quality" variable, k, a dimension of the non-life insurance demand usually neglected in the literature. k is taken to reflect not only the quality of the services offered by the insurer if the damage occurs but, more generally, is associated with the fact of being insured, i.e, with the subjective valuation of the (perhaps real) advantages associated with this situation (devices given, prevention, saving and so on). Of course (and more especially if a is α great), this subjective valuation is indirectly influenced by the quality of the services offered by the insurer if the damage occurs (his reliability, rapidity and fairness of settlement and so on).