Global economic development trends

Global economic development trends


Saipnazarov Shaylavbek Aktamovich Candidate of Pedagogical Sciences, Tashkent State Economic University, Department of Applied Mathematics
E-mail: [e-mail], tel: [phone].
Usarov Jurabek Abdunazirovich TMC (technology, marketing and communication) institute, head of the department "Applied mathematics",
E-mail: [e-mail], tel: [phone].


1. Critical analysis of the main economic theories. Economics is very important in our life. Therefore, it is classified as a social science. But economics studies not just social phenomena, but also their quantitative economic proportions. From this side, it is closer to the exact sciences that study the universal laws of the world around us and the Universe.
Now is economics different from the exact sciences? There is no end to such questions. After all, even mathematics owes its main achievements to the efforts of the Eastern scientists, who set themselves practical economic problems related, for example, to trade and solved them. In this regard, the scientific and philosophical works of Omar Khayyam, Al-Khwarizmi, A.R. Beruni and many other great scientists of the East. In this regard, the scientific works of the Central Asian scientist Al-Khwarizmi from Khorezm are especially valuable, who, solving economic problems, laid the foundations of algebra, after whom the basis os cybernetics – algorithm is named. And we, and especially Western scientists, almost daily, using his algebraic methods of compiling equations, do not even bother to remember him.
As you know, the functional dependence in mathematics establishes the regularity of the change in the function depending on the change in the argument and is represented in the formula: . And the numerical sequence has the form:
;
and is denoted:
.
And when the variable x sequentially takes on the values ; then the variable x is said to run through the sequence . In this case, the numerical sequence can be considered as a function, only its serial number n.
From this it is not difficult to under-stand that the behavior of macroeconomic quantities must also be considered, exclusively as numerical sequences, where the corresponding years serve as ordinal numbers.
If we accept such a rule, then the consumption schedule will take on a completely different from, shown in Fig.1a, where the numerical sequence for clarity, is conditionally depicted in the form of rectangles, the bases of which correspond to income, and the height corresponds to consumption expenditure. And the essence of the distortions in the Keynesian model of aggregate consumption and income can be Cleary illustrated by the dashed lines depicted in the same figure.

1. 
   b)
   

Fig. 1.

As can be seen from Fig. 1 b), the graph of aggregate consumption and income in the interpretation of the Keynesians is built only be folding our rectangles shown in Fig. 1a, as if one above the other. And their construction in the form of a numerical sequence (Fig. 1a) that the “smooth curve” from the Keynesian model turns info broken lines. These dashed lines, which means that the Keynesian consumption curve itself does not establish any functional relationship between total consumption spending and income, but only creates a “statistical illusion” of their functional mutual distortion of abstract images of economic quantities in the Keynesian model can be called an “accordion illusion”.
B
Fig.2
ut the failure of existing models of aggregate supple and demand lies not only in the “bellows illusion”. If you listen to the dispute between Keynesians and monetarists about the aggregate supple model, then it lies in the fact that if Keynesians see this curve on the graph as a straight line parallel to the x-axis, characterizing the growth of national production to its values at full employment, then monetarists consider this curve vertical with respect to the specified axis. As a result of disputes, a compromise was found, in the form of an intermediate curve connecting the horizontal Keynesian and vertical classical lines on the chart (Fig.2).

And this complex curve has become the basis of macroeconomic analysis of aggregate supple and this form it is used and it has entered into all popular textbooks.

Of course, macroeconomic theory does not stand still. There were new classics, and neo-Keynesians and other schools, as well as a new macroeconomics, using stochastic ones in their calculations, just like they themselves for economic science. In our opinion, in macroeconomic science, it is also connected with the fact that the existing models of economic equilibrium are built on the basis of analysis, in many ways derivatives, and indicators that do not directly follow or are not observed in macroeconomics, and they are considered as flat problems of two-dimensional measurement that establish patterns of interaction between two variables and their derivatives, which are generally written as: . And taking into account of statement of the problem, although it changes, does not go beyond the limits of two – dimensional measurement in the new plane
_{Whereas the whole problem lies in solving a four-dimensional problem, with the help of which it is possible to establish the regularities of the relationship between such variable vector quantities as, for example, gross national product, aggregate consumption, income after taxes and time.
The consideration and solution of economic problems in the plane of two dimensions, in the simplest case, can be likened to the ratio of the geometric problems of planimetry and stereometry, of course, economics in this state could not exist if separate theorists from (Jevons, Menger, Walras, etc) since the end of the last century, no other dimensions of the economic space have been sought.
The only consequence of the existence of different approaches in describing the behavior of economic entities in individual markets is the presence in modern macroeconomic theory of alternative views and models of the functioning of the market economy, which include macroeconomic models of general economic equilibrium, economic conjuncture and growth.
Studying the existing macroeconomic theories and models, at first glance it seems that they quite gully describe the behavior of economic entities. At the same time, they are based on balance methods that converge quite well with statistical data.}


2. Solving economic problems using mathematics
1) (Depreciation of equipment). The rate of depreciation due to its wear and tear is proportional to its actual cost. Find the law of change in the cost of equipment if its initial cost is equal to .