Is there a case for public provision of private goods if preferences are heterogeneous? : an example with day care

A strong case for public provision of certain private goods has been established for an economy in which individuals have homogeneous preferences but differ in skill levels. There has been a critique of this model/mechanism arguing that heterogeneous preferences at a given skill level would invalidate the mechanism, implying that public provision of private goods is merely of theoretical, not of practical interest. The argument is that if the public provision level is set so as to fit the low skill person with a high preference for the publicly provided good, the low skill person with a low preference for the good comes out worse than in a system without public provision. In this paper we take this critique seriously and investigate if a public provision scheme can be constructed so that we obtain a strict Pareto improvement when going from a pure tax/transfer system to the public provision scheme even if preferences are heterogeneous. We find that heterogeneous preferences do not invalidate the benefits of publicly provided private goods. We also characterise the optimum tax and public provision policy.