This paper considers the technological core model of an economic system and mathematical methods of its analysis. As a formalized criterion for the effectiveness of structural innovations, an indicator of productivity is proposed. The problem of finding an equilibrium state that optimizes the productivity of the technological core of the economy is formally stated. The method of equivalent transformation of the model considering the achieved value of indicators is developed. Several propositions on the properties of the equilibrium state are proved. A multi-stage process for calculating the trajectory that brings the economic system closer to the equilibrium state is constructed. The developed model uses the intersectoral balance of national accounts of the economy. The model is analyzed by determining the preferred structure of outputs at the development stages of the economic system’s technological core. The phased process of changing the structure of outputs that asymptotically brings the technological core to the productivity maximum is calculated on an example of Russia’s data. The results allow assessing the potential growth of economic productivity within the existing technological order by eliminating structural disproportions.