Research Reports from the Department of Operations
Document Type
Dissertation
Publication Date
6-11-1975
Abstract
This thesis is concerned with the following problems involved in the analysis of economic systems with antipollution activities: (i) a mathematical formulation of the problem of determining their equilibrium, (ii) a solution technique for this model, (iii) approximation of interregional transaction figures, and (iv) the formulation of a general model for water quality management of a watershed basin economy. Extending the Leontief input-output model, an economic system with pollution abatement activities is formulated as a complementarity problem with upper bounding constraints. The complementarity problems for M-matrices are studied, and it is shown that the model is always feasible and that the solution is unique. An algorithm for solving the problem is provided and illustrated with a simple example. Economic interpretations of the solution are presented, and the relationship between the complementarity problem formulation and the Leontief formulation is discussed. A counter-example is provided which shows that the Leontief formulation may be infeasible for some final bills of goods. Some theoretical results on the upper bounded complementarity problems for P-, 2-, and M-matrices are obtained. The complementarity formulation is extended for an interregional setting of an economy. In order to reduce the difficulty involved in collecting interregional transaction data, we develop an approximation method with which the necessary data can be determined from a national input-output table that is readily available. Also, the problem of aggregation of the regions is formulated as a “matching” problem. As an application, water quality management problem of a watershed basin economy is formulated as a linear programming problem in which economic activities and hydrology of the basin are explicitly considered. This model simultaneously determines regional industrial output levels, a waste treatment configuration and concentration profiles of pollutants in the basin by minimizing total treatment costs. It is shown that this model can be decomposed into two sub-problems which are easily solvable and that, under some simplifying assumptions, the model reduces to one of the existing models which has been tested. To measure the effects of waste discharge on the water quality at various points along a waste receiving water body, dispersion and degradation models are developed for polluting substances released in a river stream and a lake water.
Keywords
Operations research, Environmental economics, Pollution--Economic aspects, Input-output analysis, Complementarity (Physics), Water quality management--Mathematical models, Watersheds--Mathematical models
Publication Title
Dissertation, Department of Operations Research, Case Western Reserve University
Issue
Technical memorandum no. 356 ; Submitted in partial fulfillment of the requirements for the Degree of Doctor of Philosophy.
Rights
This work is in the public domain and may be freely downloaded for personal or academic use
Recommended Citation
Lee, Kwang-Soo, "Antipollution Activities in Input-Output Analysis: an Application to Water Quality Management" (1975). Research Reports from the Department of Operations. 39.
https://commons.case.edu/wsom-ops-reports/39