Multiple interactive pollutants in water quality trading

Efficient environmental management calls for the consideration of multiple pollutants, for which two main types of transferable discharge permit (TDP) program have been described: separate permits that manage each pollutant individually in separate markets, with each permit based on the quantity of the pollutant or its environmental effects, and weighted-sum permits that aggregate several pollutants as a single commodity to be traded in a single market. In this paper, we perform a mathematical analysis of TDP programs for multiple pollutants that jointly affect the environment (i.e., interactive pollutants) and demonstrate the practicality of this approach for cost-efficient maintenance of river water quality. For interactive pollutants, the relative weighting factors are functions of the water quality impacts, marginal damage function, and marginal treatment costs at optimality. We derive the optimal set of weighting factors required by this approach for important scenarios for multiple interactive pollutants and propose using an analytical elasticity of substitution function to estimate damage functions for these scenarios. We evaluate the applicability of this approach using a hypothetical example that considers two interactive pollutants. We compare the weighted-sum permit approach for interactive pollutants with individual permit systems and TDP programs for multiple additive pollutants. We conclude by discussing practical considerations and implementation issues that result from the application of weighted-sum permit programs.