Modeling of Piecewise Linear Ecological and Economic Public Utility Functions

Environmentally dangerous phenomena and processes occurring in the modern world are largely related to human activity, i.e., irrational use of nature, uncontrolled and harmful behavior of consumers and producers, unjustified economic goals, environmental policies harmful to human life, etc. All this indicates the urgent need and relevance of research and deep scientific substantiation of the processes of ecological and economic interaction in all spheres of human life. Expanding and improving the toolkit for evaluating the effectiveness of ecological and economic systems using ecological and economic functions of social utility. Development of a model of such a function in the class of piecewise linear functions. The research used the methodology of constructing functions of economic and ecological-economic behavior as functions with predetermined properties. The concept of the function of ecological and economic utility, which depends on the economic and ecological components of the state of the socio-economic system, is revealed. Its properties are analyzed, reflecting the general regularities of the impact of ecological and economic processes on the environment and the quality of human life. Basic properties for smooth functions of ecological and economic utility and their piecewise linear analogues are formalized. The geometric interpretation of piecewise linear functions of ecological and economic utility with two variables is substantiated. One of the approaches to the construction of continuous piecewise linear functions of ecological and economic utility based on its statistical or expert values is specified. The necessary and sufficient conditions for the concavity (convexity upwards) of the piecewise linear function given on the rectangular region and the conditions for its monotonicity with respect to the relevant variables have been established. A model of the ecological and economic function of public utility with nodal (vertical) values, which are solutions for optimization problems or conditional approximation problems, is proposed. The model of such a function allows you to determine the ecological and economic utility at any point of the admissible set of its arguments. The approach to constructing a piecewise linear function of public utility has a fairly wide application when modeling behavioral functions in economic and ecological-economic systems. It is easily implemented in practice and is convenient for both theoretical and practical needs. The adequacy of the model of the proposed utility function is significantly related to the adequacy of its information support. The subject of further research in this direction is the issue of constructing smooth functions of ecological and economic utility and their application in models of economic and ecological and economic systems of a more complex specification.