The honored science and education member of the RANS, corresponding-member of the IAS of HS, Dr.S. (eng.). Professor, Pil E.A. Russia, Saint-Petersburg, Saint-Petersburg State Marine Technical University

Classification of evolution of variables e_t and p_t

Economic growth or recession are affected by a large number of factors one of which is growth or decrease in population for objective reasons. In order to find out the interconnection between theoretical economic growth or recession e_t and theoretical growth or decrease in population p_t respectively, we developed special Table, where possible variants of interconnection of variables e_t and p_t in question are presented. In this work and for our case the word economy will be understood as GDP in the country in question.

As a result of the analysis of the whole Table the presented dependences of variables e_t and p_t can be for our purpose divided into the following 23 types:

1. e_t and p_t nonintersecting lines;

2. e_t and p_t intersecting lines;

3. e_t and p_t nonintersecting line and curve;

4. e_t and p_t nonintersecting lines;

5. e_t and p_t intersecting lines;

6. e_t and p_t nonintersecting line and curve ;

7. e_t and p_t nonintersecting lines changing into a curve and curves;

8. e_t and p_t intersecting line and curve;

9. e_t and p_t nonintersecting curves changing into lines;

10. e_t and p_t nonintersecting curves;

11. e_t and p_t nonintersecting curves symmetrical in relation to one axis parallel to axis Q_t as with same T_ptmax = T_etmax and T_ptmin = T_etmin values, so with different T_etmin, T_ptmin, T_etmax and T_ptmax values;

12. e_t and p_t nonintersecting curves symmetrical in relation to two axes parallel to axes Q_t and t;

13. e_t and p_t curves intersecting in one point;

14. e_t and p_t curves intersecting in two points;

15. e_t and p_t tangent line and curve;

16. e_t and p_t tangent curves;

17. e_t and p_t tangent curves symmetrical in relation to axis parallel to axis Q_t ;

18. e_t and p_t tangent curves symmetrical in relation to axis parallel to axis t and symmetrical in relation to axes t и Q_t ;

19. e_t and p_t joining lines;

20. e_t and p_t joining curves;

21. e_t and p_t curves changing into joining lines ;

22. e_t and p_t joining lines changing into diverging curves;

23. e_t and p_t joining and diverging curves.

Using the calculations which were made we developed a classification of dependences of variables e_t and p_t, which is shown in Figure 1. As we can see on Figure 1, variables e_t and p_t can be divided into three classes: the linear dependence class, the linear and curvilinear dependence class and the curvilinear dependence class. These classes in their turn are divided into three subclasses: increasing, decreasing, and increasing and decreasing. The subclasses are divided into the following five kinds: merging, nonmerging, diverging, etc. These kinds themselves are divided into five subkinds depending on the kind in question, such as: parallel, nonparallel, etc. On the last level variables e_t and p_t are divided into two types depending on the law or laws according to which they change.

The classification shown in Figure 1 can be represented as the graph shown in Figure 2, where the graph’s peaks are linear, curvilinear dependences or their combinations, which can go up or down, be symmetrical, etc., and the branches are their characteristics. Thus, the better we know the parameters of peak branch characteristics, the easier it is to make right conclusions while analyzing the economic state of a country and its population.

This classification allows us to quickly relate specific variables e_t and p_t in question to their class, subclass, etc.