The character of the change in national incom in the harmonic osillator model with a linear dependence of external investment on time

The nature of the dependence of national income on time within the framework of the harmonic oscillator model is investigated, assuming that external investment increases depending on time according to linear law (investment growth rate is constant). At the same time the solutions of the ordinary inhomogeneous differential equation with constant coefficients (the differential equation of the harmonic oscillator), which satisfies the national income, are found where there are no transaction costs (there is no attenuation) and when they are present (there is attenuation). The economic meaning of other terms of the differential equation (the rate of change of national income. market power) is also given. To find the solution of the corresponding homogeneous differential equation, the Euler method is used, and to find one particular solution of the inhomogeneous differential equation, the method of variation of arbitrary constants is used. According to the analytical solutions obtained in the article graphs of the dependence of national income on time are plotted for various values of parameters that characterize the dynamics of changes in national income. Analytical and graphical analysis of the results obtained in the work show that with an increase in external investment, depending on time, the national income also increases. At this the nature of the increase depends on the parameters included in the differential equation of the harmonic oscillator.