1. Introduction In the economics, the presence of hysteresis phenomena has been observed since the 1950s. However, in the economy papers with the formal description within the framework of hysteresis phenomena systems theory have emerged only in the recent decades. The work considers a significant difference of the properties of systems with hysteresis from systems with functional non-linearities. This can be explained by the complexity and non-linear structure of the states of hysteresis quantizer space. Appearance of the hysteretic effects is observed in the economy at different levels. In the middle of the last century, economists identified hysteresis at the micro level with the sustainability of consumer habits. Concerning the macro level, it is possible to observe the hysteretic effect at increasing unemployment when affected by the certain motivating factors. Disappearance of these factors does not lead to unemployment slowdown, and it stays at a sufficiently high level for a long time. One of the main problems of mathematical modelling in the economy is the problem of studying of the process for establishing equilibrium price. In the classic sense, cobweb model and its analogues are used when speaking about the functions of supply and demand in the context of the pricing question. In the course of modern researches it is shown that the status of the economic system at some point in time depends on the parameters values both in the current and the previous point of time. From this follows the need to develop a mathematical model of the demand function, taking into account this feature. The hysteresis quantizers are the best way to deal with the problem. 2. Literature Review Formal description of the hysteresis quantizers is based on the operator representation of converters developed by Krasnosel'skii (Krasnosel'skii and Pokrovskii, 1989) and his followers (Semenov and Meleshenko et al, 2014; Semenov, Solovyov et al., 2015; Thalassinos et al., 2009; 2012a; 2012b; 2015, Hanias et al., 2007). They are represented as operators defined in rich functional spaces. Converters depend on their initial state as on the parameter. The dynamics can be described by two comparators: Input-status and status-output (Semenov, Kabulova et al., 2015). The properties of systems with hysteresis are significantly different from those with functional non-linearities (Semenov, Meleshenko et al., 2015). This can be explained by the complexity and non-linear structure of the hysteresis quantizer state space (Semenov, Grachikov et al., 2014). Beyond that point, mathematical models of hysteresis quantizers are generally not smooth, and this increases the difficulty of applying classical methods to analyse the corresponding systems. Economic systems are especially noteworthy among systems with hysteretic properties (Cook, 2003). In the economy, hysteresis phenomena have been observed since the 1950s (Samarskii, 1986). But the data obtained within systems theory was formalized only in the last decade (Cross et al., 2000; 2008a; 2008b;). There are a lot of reasons for that; one of them is the lack of opportunity to conduct an experiment in contrast to technical areas. Recently, the description of hysteresis in the economics is more and more often found in various sources (Macki et al., 1993; Visintin, 1994). Let us cancel some of the results. The article (Cross, 2014) investigates the influence of the hysteretic component on the natural growth of unemployment. The growth of unemployment is simulated by the Preisach model. It is known from economic theory that market mechanisms admit equilibrium (Caporale et al., 2016) in case when demand and supply are equal, thus making it possible to allocate resources efficiently. However, it is possible to give examples of crises (Kindleberger and Aliber, 2011), when equilibrium prices turned out to be unstable. This fact can be explained by non-compliance of market mechanisms in technological structure of the economics. …