Mode of sustainable economic development

TL;DR

This paper characterizes the conditions and solutions for sustainable economic development within input-output models, including optimal consumption, equilibrium states, and taxation strategies, using linear and quadratic programming frameworks.

Contribution

It provides a comprehensive mathematical description of sustainable development modes, including solution characterization, equilibrium analysis, and taxation restrictions in input-output economic models.

Findings

Complete description of non-negative solutions for sustainable development

Conditions for the economy to operate sustainably under input-output models

Existence of taxation vectors enabling sustainable economic functioning

Abstract

To implement the previously formulated principles of sustainable economic development, all non-negative solutions of the linear system of equations and inequalities, which are satisfied by the vector of real consumption, are completely described. It is established that the vector of real consumption with the minimum level of excess supply is determined by the solution of some quadratic programming problem. The necessary and sufficient conditions are established under which the economic system, described by the "input-output" production model, functions in the mode of sustainable development. A complete description of the equilibrium states for which markets are partially cleared in the economy model of production "input-output" is given, on the basis that all solutions of system of linear equations and inequalities are completely described. The existence of a family of taxation vectors in the "input-output" model of production, under which the economic system is able to function in the mode of sustainable development, is proved. Restrictions were found for the vector of taxation in the economic system, under which the economic system is able to function in the mode of sustainable development. The axioms of the aggregated description of the economy is proposed.