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A comment on ``Pareto improving taxes''

Leventides, John and Michelacakis, Nickolas (2016): A comment on ``Pareto improving taxes''.

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In an article appeared in the Journal of Mathematical Economics, J. Geanakoplos and H. Polemarchakis, [Geanakoplos J. and Polemarchakis H.M.: "Pareto improving taxes", Journal of Mathematical Economics 44 (2008), 682-696], prove on page 685 the following theorem: "Theorem. For almost all economies with separable externalities and L>I, every competitive equilibrium is constrained Pareto suboptimal, that is, for each competitive equilibrium, there exists an anonymous tax package t and a competitive t-equilibrium allocation which Pareto dominates it." It is the purpose of this comment to show that restrictions must be applied on the limiting cases for the theorem to hold. Proposition 1.3, below, gives a counter-positive result and the ensuing Corollary shows that the Theorem in [Geanakoplos & Polemarchakis 2008][p. 685] does not hold for I=2 and subsequently the example given in Section 6, page 693, of Geanakoplos & Polemarchakis (2008)} appears to be incorrect.

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