In a recent contribution, H. Naito (1999) has shown that production efficiency may be violated in the optimum with non-linear income taxation. Using a slightly simpler framework, this paper complements Naito's analysis in showing that production efficiency does not hold in the optimum with (i)...

Using the traditional model of voluntary public good provision, it is shown that an expansion of group size exacerbates free riding tendencies as long as private consumption and the public good are strictly normal and weak gross substitutes. This result generalizes a previous Cobb-Douglas...