Freedom in Economics by Fleurbaey Marc;Gravel Nicolas;Laslier Jean-François;Trannoy Alain;

Author:Fleurbaey, Marc;Gravel, Nicolas;Laslier, Jean-François;Trannoy, Alain;
Language: eng
Format: epub
Publisher: Taylor & Francis Group
Published: 1998-08-15T00:00:00+00:00

Evidently , so that the Pigou-Walrasian budget set reduces to when the Pigou price vector t=0.

Then the combination (,, , p, t, m) is a Pigou-Walrasian equilibrium with lump-sum transfers (or PWELT) if (,, ) is a feasible allocation satisfying, for almost all iI, both and also pxi+t ei>mi whenever with . Thus, (,, p, t, m) is effectively a Walrasian equilibrium with lump-sum transfers in the economy with complete competitive markets in both private goods and externalities, but with the mean externality vector fixed. Also, a NWELT is effectively just a PWELT for which the Pigou price vector t happens to be 0.

As in Hammond (1995a), a feasible allocation (,, ) is said to be fexternality constrained Pareto efficient if, except for a null set I0⊂I of exceptional agents, no finite coalition C⊂\I0 can find an alternative allocation to its members which satisfies the three conditions that: (i) and (iii) for all iC. Hence, only finite coalitions C that include members of the negligible set I0 are able to gain from exchanging combinations of goods and externalities. In fact, it is easy to prove, in an entirely standard way, that any PWELT allocation is f-externality constrained Pareto efficient. Pareto improvements can only result from changes made by (large) coalitions of positive measure which affect the widespread externalities in a beneficial way. Since an NWELT is a particular instance of a PWELT, the same is true for those externalities which are not controlled at all.

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