Economic-mathematical methods and models

All models that a person uses in various spheres of their activity can be conditionally divided into two groups: material and abstract. The first are objective, they can be really touched. The latter exist only in the human mind. Within the framework of this article, only mathematical methods and models in the economy will be considered. They are used to analyze the processes and phenomena occurring in this area. Their use makes it possible to set new economic tasks. Thanks to them, management takes decisions related to the management of the organization, firm, enterprise.

Mathematical methods of studying operations in the economy are the most effective tool for studying problems in this field. In modern scientific and technical activities they become an important form of modeling. And in the practice of planning and management this method is the main one.

Economic-mathematical methods and models are the basis on which various programs, originally intended for solving planning, analysis and control problems, are implemented. Together with technical means, with databases they are part of the human-machine system. It allows the use of models and knowledge to solve various kinds of problems (both unconstructed and weakly structured).

Depending on the criteria that underlie the division, economic-mathematical methods and models are classified as follows.

1. On purpose they are:

- Applied, that is, they solve specific problems with their help;

- theoretical-analytical (they are used when it is necessary to investigate general patterns and signs of development of processes occurring in the economy).

2. By what causality they reflect:

- deterministic;

- probabilistic (take into account the factor of arising uncertainty).

3. By the level of those processes in the economy that they are exploring:

- production and technological;

- socio-economic.

4. By the way in which the time factor is reflected:

- dynamic, they show the changes taking place;

- static, all the dependencies here reflect only one period of time or time.

5. By level of detail:

- macromodels (aggregated);

- Micromodels (detailed).

6. In the form in which mathematical dependencies are expressed:

- non-linear;

- linear - they are very convenient to use for calculation and analysis, which led to their wider distribution.

Economic and mathematical methods and models have their own principles of construction. These include:

1. The principle of uniqueness of data. According to him, the information used at the beginning of modeling should not depend on those parameters of the future system, which are not even known at this stage of the study.

2. Principle of completeness of initial information. It means that the initial information used must be very accurate, since the results depend on it.

3. The principle of continuity. He says that those features of the object that were reflected or installed in the first models should be preserved in every subsequent one.

4. The principle of effective implementation. Each model should be used in practice. In its implementation, the newest computing facilities should help.

Economic and mathematical methods and models are always built in several stages:

1) Definition of the problem, its analysis.

2) Construction of a mathematical model. This is its expression in the form of functions, schemes, equations.

3) Analysis of the obtained model using mathematical techniques.

4) Preparation of initial information.

5) This is actually the development of programs, the compilation of algorithms and calculations.

6) Analysis of the results obtained, their practical application.

Each of these stages can have its own specificity depending on the field of knowledge in question.