Separability,functional structure and aggregation for a class of models in environmental economics

The purpose of this paper is to provide a theoretical bridge between the many-commodity general equilibrium models and the simpler one good-one pollutant models used in environmental economics. The interest is in determining the conditions that will permit a vector of pollutants (or goods) to be treated as if it were only one quantity, the amount of environmental pollution (or consumption). A general equilibrium model is constructed and the concepts of separability and functional structure are applied to examine the requirements for consistent aggregation. It is shown that this aggregation process may in general produce two entirely different sets of aggregate measures of pollution and consumption. This result is of theoretical and empirical significance. Alternative criteria for aggregation suggest that the aggregation depends upon very stringent features of the economy concerned.