MODIFICATIONS OF EVANS PRICE EQUILIBRIUM MODEL - Zabolotnii, Serhii; Mogilei, Sergii (Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska, 2023)
The paper regards the classical Evans price equilibrium model in the free product market in the aspect of regarding the opportunities for expanding (modifying) the model given that is aimed at perfecting the accuracy of its mathematical formulating. As an accuracy criterion, we have chosen a summary quadratic deviation of the calculated indices from the given ones. One of the approaches of modifying the basic Evans model is suggesting there is a linear dependence between price function and time as well as its first and second derivatives. In this case, the model will be described through differential equation of second order with constant coefficients, revealing some oscillatory process. Besides, it is worth regarding a non-linear (polynomial) dependence between demand, supply and price. The paper proposes mathematical formulating for the modified Evans models that have been approbated for real indices of exchange rates fluctuations. It also proves that increase of the differential and/or polynomial order of the given model allows its essential accuracy perfection. Besides, the influence of arbitrary restricting circumstances of the model on its accuracy is regarded. Each expanded Evans model is accompanied by mathematically formulated price and time dependence.