In this article, we study the behavior that local governments face to the choice of financing a certain quality of public goods provision. More especially, we inspect whether the local governments must tax the mobile capital or not. For this, we examine if the Samuelson rule for the optimal resources allocation between private-goods and public-goods is satisfied or not. We show that if local governments finance the public-goods in taxing the households without varying their tax rate on capital, then the optimality, as defined in Samuelson, is constrained by the funding of the quality of public-goods. Otherwise, taxing the capital modify the Samuelson rule. Thus, there is a supplementary cost supported by the households linked to a distorting tax.