Within a framework of optimal taxation a la Mirrlees, we add a new heterogeneity between the individuals who differ not only on their marginal productivity, but also on their initial endowment in a good which is interpreted as an aggregate consumption. We consider other goods in the economy whose characteristics (impossibility of resale, impossibility of increasing on the private market a public supply) are those of the hospital care or education for example. We show that one can justify the public supply of this good on an economic criterion of efficiency, in spite of an assumption of separability of work and consumption in the utility function of the individuals.