The article is dedicated to forming and developing a mathematical model of an economic ECO-system of the engineering business. The relevance of the goals and objectives of this research is in the necessity of creating a mathematical model that ensures an integrated management including: 1 – creative design management in manufacturing-technological systems, 2 – management accounting within technological stages that are zones of financial responsibilities and 3 – continuous innovation management of an equilibrium operational cycle for converting the manufacturing capital into monetary capital in the form of sold products. The methods of research are based on rethinking Kondratyev’s publications presenting the economic systems of developed countries such as Germany, France, England and the USA for the period of 150 years [1–4]. These studies allowed us to conclude that mathematically the vector fields of monetary flows in an economic system are similar to the vector fields of heat flows in thermodynamic systems. Therefore, the mathematical models of the first and second thermodynamic laws describing equilibrium and reversible thermodynamic processes and cycles could be used for describing the equilibrium operation cycle converting manufacturing capital in a manufacturing-technological system into monetary capital in the form of manufactured and sold products on external and domestic markets. The criterial equation and the system of criteria are created based on an equilibrium approach to the mathematical model. This innovative equilibrium approach allowed us to create a graphical interpretation system used for designing, management accounting and innovative improvement of the conversion operation cycle. Further research will focus on the development of a digital model of equilibrium cycles for converting manufacturing capital into monetary capital in the form of sold products..