Logistic models of the technology life cycle as a tool for assessing the efficiency of R&D expenditures for knowledge intensive companies

The study of the life cycles of technologies, their quantifications and the definition of breakpoints is an urgent scientific task. The most well-founded theoretical construction of the technology life cycle dynamics study is the logistic curve. The basis is a comparison of the dynamic series of costs and effects. The paper deals with the calculation of logistics trends expressing the relationship between annual data of gross revenue (effects) and R&D expenditures for Yandex in 2009-2021 (costs). Based on the approximation carried out by methods of nonlinear regression analysis, the values of maximum integral efficiency and maximum differential (point) efficiency of R&D expenditures for each of the considered time intervals are calculated. The study of logistics trends and the presented tools and results allow us to reveal the periods of dominance of one or another technological (or organizational and managerial) paradigm in the life of a certain high-tech company based on a comparison of aggregate and/or instantaneous efficiency for different periods of the company's development. In addition, the proposed results are relevant for assessing the prospects of technological shifts in the development of a high-tech company, namely, determining the level of technological or cost upper limit, expressed by the upper horizontal asymptote of the corresponding logistics.