A closed dynamic model to describe and calculate the Kondratiev long wave of economic development

A full closed mathematical model to describe and calculate Kondratiev’s long wave (LW) of economic development is presented for the first time. The innovative process that generates a new long wave in the economy is described as a stochastic Poisson process. The key role in constructing production functions during both the upward and downward trends of the LW is played by the self-similarity property of the innovative process, which is determined by its fractal structure. The role of the switch from an upward wave to a downward one is played by entrepreneurial profit; this article places primary emphasis on calculation of it. The practical effect of the model developed is illustrated through predictive calculations of GDP movement paths and the number of employees in the economy and the dynamics of fixed physical capital formation and growth of labor productivity by the example of the development of the US economy during the coming sixth Kondratiev LW (2018–2050).