Externalities do not necessarily require larger message spaces for realizing pareto-efficient allocations

Classes of economies with consumption externalities and decisive, nonwasteful, and informationally decentralized allocation mechanisms on classes including these classes of economies are constructed. The informational size of the message spaces is shown to be minimal among the message spaces used by any allocation mechanisms with the same properties on the same class of economies. The message spaces are shown to be as large as <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$n(\ell - 1)$</EquationSource> </InlineEquation>-dimensional Euclidean space, where n is the number of economic agents and <InlineEquation ID="Equ2"> <EquationSource Format="TEX">$\ell$</EquationSource> </InlineEquation> is the number of commodities. The presence of consumption externalities does not necessarily require larger message spaces for realizing Pareto-efficiency. Copyright Springer-Verlag Berlin/Heidelberg 2005