Ecological pricing and transformity: A solution method for systems rarely at general equilibrium

This paper outlines a new method for determining ecological prices/transformities in complicated ecological-economic systems where non-equilibrium prices are likely to be prevalent. That is, an eigenvalue-eigenvector mathematical solution method for solving an overdetermined, homogeneous system of simultaneous linear equations is proposed and tested. Previous mathematical approaches to the problem of ecological pricing are reviewed before proceeding with an explanation of the new solution method for the determination of ecological prices. The proposed method seeks to avoid the need to make a number of untenable assumptions used in previous methods-e.g., the assumption that there necessarily needs to be an equal number of processes and quantities in the ecological-economic system. The paper also provides practical advice and an algorithm for solving the ecological pricing problem. For example, advice on how to overcome the problem of ill-conditioned matrices which are sometimes encountered.