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Abstract

Content

Introduction

Modern market economy is a class of mixed. It develops under the influence of the production of their own market effects callers often do not quite logically reasonable consumer activity of households. The state regulates this process: establishes the legal structure of the business and monitors compliance, based on the statistics of production and consumption, typically having

Macroeconomic model of an economy should be a complicated apparatus, in particular taking into account the variety and description uncertainty of market and state, the internal and external regulation. You need to implement a mathematical methodology, more fully takes into account the "behavioral" aspects in the description of the development of market economy in crisis and transition conditions.

The aim of this work is the development of the apparatus of macroeconomic modeling using fuzzy-possibilistic mathematical methods analysis of microeconomic processes.

To achieve this goal you must perform a number of tasks:

The object of this work is to study the market mechanism to establish a general equilibrium in an economy at the macro- and meso-level.

The subject of the study — a modern machine simulation of the establishment and maintenance of general economic equilibrium and the possibility of application.

1. The main problem of improving the adequacy of the models and methods of macroeconomic modeling

Outlines the basic problems of development of adequate models of market economy. A detailed analysis and methodological aspects of the analysis of macroeconomic relationships. On the basis of consideration of the features of modern methodology of macroeconomic Studies are general concepts and the classification of macroeconomic models developed to date [1].

An analysis of the models and methods of macroeconomic modeling revealed some important problems of the use of the mathematical theory choice under uncertainty in macroeconomic models. Outlines the methodological basis of current and future macroeconomic concepts.

Initially separately examines the foundations and the problems of higher concepts (macroeconomic) and lower (microeconomic) levels. Further, as a result of the composition of these concepts, focuses on the problems of general equilibrium models and theory methodology public choice. In this case, details the conceptual model of general equilibrium and the mathematical model of public choice.

In conclusion, based on an analysis of existing models revealed the problems of synthesis models of general equilibrium, synthesis macroeconomic conceptual models, as well as the problems of investigation of the laws of macroeconomic interactions with factors uncertainty [2].

2. The development of tools of macroeconomic modeling

Considered fuzzy-probabilistic methods of research and the global problem of estimation capabilities in modeling problems of macroeconomics. on Based on the analysis of economic and mathematical modeling methodology using the methods of decomposition of relations, as well as using Decomposition Methods maps the approaches to the representation of the formalized models of general equilibrium.

Substantiates the transition from the classical formalization of general equilibrium models to formalized neoclassical and Keynesian model that takes into account the various factors of uncertainty and ensure the correctness of convergence of micro- and macroeconomic models. With For this purpose, a concept of fuzzy measures and generalized fuzzy-possibilistic approach to modeling the macroeconomy.

Based on the analysis of the categories of uncertainty used in the study of complex systems, provides the relevant mathematical structure for modeling economic systems taking into account uncertainties. Analyzes the main ways and methods for solving fuzzy Optimization models of motivation of economic agents [3].

3. Investigation of the possibility of using fuzzy algebra tools for calculations

Given selected in the second section and directions set forth the requirements for macroeconomic modeling introduces the basics of creating special mathematical tools of fuzzy algebra for modeling processes in complex economic systems.

To do this, based on the concept of fuzzy numbers and operations with fuzzy numbers developed a mathematical description of the binary algebraic and logical operations with fuzzy numbers. As a generalization of these mathematical structures developed tools for fuzzy algebra predicate based mixtures [4].

In this case, the general definition of the basic algebraic operations on mixtures are specified development of fuzzy binary algebraic operations given on the basic tier sets of linear functions of the arguments. Further studies are developed mathematical toolkit. Initially investigated methods of logical and algebraic calculations in economic models with fuzzy parameters. then analyzed basic properties of fuzzy algebraic binary operations [5].

4. Development of methodological support for macrolevel problems with the use of fuzzy-possibilistic mathematical tools

On the basis of the methodology outlined in the previous sections, are considered some of the important results of application fuzzy-probabilistic approach to macroeconomic problems. In particular, the solution of problems of choice of stock capital in the presence of fuzzy information about the profitability of securities, which is in the Modigliani — Miller theorem (MM). On the basis of the classical statement of the theorem MM and factors such modern economic reality, as the impact of interest rates on personal loans for investors and the impact of differences in the interest rates on bonds give a new formulation of fuzzy MM theorem, devoid of the drawbacks of traditional deterministic and stochastic productions [6].

In conclusion, we consider the solution of linear linguistic state recognition of economic agents in a fuzzy description financial and economic parameters. Developed the general provisions of the method of linguistic recognition and proposes new interapproaches using a twodimensional and multidimensional models of uncertain parameters identification.

The problems of the developed section three instruments operating with fuzzy numbers to form linearized representation quality scale linguistic recognition [7].

Conclusion

In the process of researching the topic graduate works identified the main problem of improving the adequacy of the models and methods of macroeconomic, modeling, developed a means of macroeconomic modeling, application capabilities that are focused on widely used possibilistic fuzzy mathematical apparatus; investigated the possibility of using fuzzy algebra tools for calculations. In the future we plan to develop a methodological support to address macroeconomic challenges with the use of fuzzy-possibilistic mathematical tools.

References

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