Value equilibrium analysis based on the New Theory of Value. I

Abstract

The (traditional) labor theory of value, founded by Smith with the basic axiom that labor determines value, and supplemented and improved by Marx with the axiom that labor creates surplus-value. Neoclassical economics newly studied the utility theory of value, but it abandoned the traditional labor theory of value and theory of surplus-value. Under the basic axiomatic system analogous to theoretical mechanics, the above three theories of value has been included and developed by the new theory of value, which established the value complex variable function including three basic quantities of quantity, quality and time, as well as labor value, use-value and surplus-value. Starting from the value complex variable function, with the mathematical methods of Euler equation and Euler formula, this paper conduct a thorough and comprehensive analysis on the theory of value, under satisfactions of Marx’s first and second laws, focusing on value equilibrium by giving the mathematical explicit expressions of both value equilibrium function and price equilibrium function in various forms applicable to the general commodity economic movement process, so as to prove the existence and stability of the extremum solutions to the corresponding functions.