All models that a person uses in various fields of his activity can be conditionally divided into two groups: material and abstract. The former are objective, they can be really touched by hands. The latter exist only in human consciousness. In the framework of this article, only mathematical methods and models in economics will be considered. They are used to analyze processes and phenomena occurring in this area. Their use allows us to pose new economic problems. Thanks to them, management makes decisions regarding the management of the organization, firm, enterprise.
Mathematical methods for studying operations in the economy are the most effective tool for studying problems in this area. In modern scientific and technical activities, they become an important form of modeling. But in the practice of planning and management, this method is the main one.
Economic and mathematical methods and models are the basis on the basis of which various programs are implemented that were originally designed to solve planning, analysis and control problems. Together with technical means, with databases, they are part of the human-machine system. It allows you to use models and knowledge to solve various kinds of problems (both unstructured and poorly structured).
Depending on the criteria that underlie the division, economic and mathematical methods and models are classified as follows.
1. For the purpose they are:
- applied, that is, with their help, specific tasks are solved;
- theoretical and analytical (they are used when it is necessary to study the general laws and signs of the development of processes occurring in the economy).
2. According to what causal relationships they reflect:
- deterministic;
- probabilistic (take into account the factor of the resulting uncertainty).
3. According to the level of those processes in the economy that they are researching:
- production and technological;
- socio-economic.
4. By the way in which the time factor is reflected:
- dynamic, you can see the ongoing changes;
- static, all dependencies here reflect only one period of time or moment.
5. According to the level of detail:
- macromodels (aggregated);
- micromodels (detailed).
6. In the form in which mathematical dependencies are expressed:
- nonlinear;
- 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 that is used at the beginning of the simulation should not depend on those parameters of the future system that are not even known at this stage of the study.
2. The principle of completeness of the initial information. It means that the initial information used must be very accurate, since the results obtained 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 each subsequent one.
4. The principle of effective implementation. Each model should be used in practice. The latest computing tools should help in its implementation.
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 her expression in the form of functions, circuits, equations.
3) Analysis of the resulting model using mathematical techniques.
4) Preparation of initial information.
5) This is actually the development of programs, compilation of algorithms and calculations.
6) Analysis of the results, their practical application.
Each of these stages may have its own specifics depending on the field of knowledge in question.