Dynamics of national income change in harmonic ocsillator model with disturbance

This work is devoted to identifying the patterns of changes in national income depending on time on the assumption that this function satisfies the inhomogeneous ordinary differential equation of a harmonic oscillator, the right side of which (external investment) represents the product of an exponent and a periodic function as a function of time. The economic meaning of the other members of this differential equation (the rate of change in national income, market power, transaction costs) has been determined. When finding its general solution (the sum of the general solution of the corresponding homogeneous differential equation and one particular solution of the inhomogeneous differential equation), Euler’s methods and the method of variation of arbitrary constants are used. The case of resonance is considered (the frequencies of natural fluctuations of national income and fluctuations of external investment coincide), when there are no transaction costs (attenuation is not taken into account) and when they are present (attenuation is taken into account). On the basis of the obtained analytical solutions in the case of resonance, graphs of changes in national income depending on time were constructed. Moreover, when constructing them, various values of the parameters were taken (damping coefficient, the frequency of natural fluctuations of the national income), which determine the nature of the dynamics of the national income. Shows the oscillating nature of national income as a function of time.