The Influence Of Mathematics On Economics Essay Sample

Introduction

XXI century can be called the century of rapid penetration of mathematical methods in a variety of science, including the economy, computer science, management theory and management. Mathematics gives people the powerful methods of learning and understanding of the world, methods of research, both theoretical and purely practical problems.
At all times, mathematics was the undisputed cultural and practical significance, played an important role in the scientific, technological and economic development. Owning mathematics has always been a strategic resource of the nation. Currently, due to the increased role of mathematics, an unusually large number of future, economists, programmers, organizers of modern production needs serious mathematical training that would enable mathematical methods to investigate a wide range of new challenges to apply modern computing, use theoretical advances in practice.
Translating economic, transport, management or any other problem in the language of mathematics, modern specialist is able to use to solve the diversity and richness of means of mathematics. The results obtained using mathematical methods of economic-mathematical analysis allows confirming or refuting our hypothesis, building a forecast, to make optimal functioning of practical action plan for the object.
At present, the usefulness and necessity of mathematization of economics and management theory is obvious. The role of mathematics in economic research often is not always clearly visible, while it is of aid transformed into an active method of investigation of economic reality. At certain stages of economic research mathematics becomes the only way of knowing. Language and mathematics methods proved to be very productive for the development of economic theory.
The contribution of mathematics in the development of the economy is very high. Therefore, it is impossible to fit in one essay all types of economic problems that can be solved with the help of mathematics. We consider only the major ones.

Body

In the management of business processes, the most important are primarily economic and mathematical models, often referred to as system models. Economic-mathematical model is a mathematical description of the entity or process to their research and management. This is mathematical notation of solving economic problems.

The main types of models:

extrapolation model
factor econometric models
optimization models
balance models
expert evaluation
game theory
network models
models of queuing systems
Currently, the analysis of economic activities of organizations is finding increasing application of mathematical methods of research. This contributes to the improvement of the economic analysis, it deepen and enhance its effectiveness.
The use of mathematical methods to achieve a fuller study of the influence of individual factors on economic indicators summarizing the activities of organizations, reducing the timing of the analysis, increases the accuracy of the implementation of economic calculations are solved multidimensional analytical tasks that cannot be met by traditional methods.

There are four main types of economic and mathematical models used in the analysis of the influence of individual factors:

additive model;
multiplicative model;
multiple model;
mixed models.
Additive models can be defined as the algebraic sum of the individual indicators. Such models can be characterized by the following formula:
yi=xi

An example of an additive model is the balance of marketable products.

Multiplicative model can be defined as the product of the individual factors.
One example of such a model can be a two-factor model, which expresses the relationship between the volume of output, the number of units of the equipment and production reports based on one piece of equipment:
V=N*Y
where Vis the volume of production, N is the number of pieces of equipment, Y is the yield per unit of equipment.

Multiple models are the ratio of individual factors. They are characterized by a formula:

I=xy
Here I is a synthesis economic indicator, which is under the influence of individual factors x and y. An example of a multiple model can serve as a formula expressing the relationship between the duration of the current assets turnover in days, the average value of these assets for the period and one-day sales:
D=AI
where D is duration of turnover, A is the average value of current assets and I is one-day sales.
Finally, the mixed model is a combination of the species we have examined models. For example, such a model can be described as return on assets, the level of which is influenced by three factors: the net profit, the value of non-current assets, current assets:
Ra=Net ProfitNon-current assets+current assets

In summary, the mixed model can be represented by a formula:

Z=ixiiyi
So, should first build economic-mathematical model that describes the effect of individual factors on the generalized economic performance of the organization. Very common in the analysis of economic activity received multivariate multiplicative model, as they allow us to study the effect of a significant number of factors on the summary measure and thus achieve greater depth and accuracy of the analysis.
Then you need to choose a way to solve this model. Traditional methods: a method of chain substitutions, the methods of absolute and relative differences balance method, the index method, as well as methods of correlation and regression, cluster, analysis of variance, and others. In addition to these methods and techniques used in the economic analysis and specific mathematical methods and techniques.

One of the most interesting methods of solving economic and mathematical modeling is game theory.

As well as queuing theory, game theory is one of the branches of applied mathematics. Game theory studies the optimal solution, the possible situations of the game character. This includes situations that are associated with the choice of optimal management decisions, with the choice of the most appropriate options for relationships with other organizations, etc.
One of the economic and mathematical methods used in the analysis of business organizations is the so-called sensitivity analysis. This method is often used in the analysis of investment projects, as well as to predict the amount of profit remaining at the disposal of the organization.
In order to optimize the planning and forecasting activities of the organization must provide in advance the changes that may occur in the future with the economic indicators analyzed.
For example, it should be to predict the change in the values of the factors that affect the amount of profit: the level of purchase prices for acquired material resources, the level of sales prices for the products of the organization, changes in customer demand for these products.
The sensitivity analysis is to determine the future value of generalizing economic indicator, provided that the values of one or more factors that influence the rate change.
For example, the set on which the amount of profit will change in the future, subject to change in the number of products sold per unit. In this way, we analyze the sensitivity of net income to changes in one of the factors affecting it, that is, in this case a factor in sales. The rest of the factors that influence the amount of profit are unchanged in this case. You can determine the amount of income and also with a simultaneous change in the future of several factors. Thus the sensitivity analysis allows us to establish the power of generalizing economic indicator of response to changes in the individual factors that influence this indicator.

References

Alpha C. Chiang and Kevin Wainwright, [1967] 2005. Fundamental Methods of Mathematical Economics, McGraw-Hill Irwin. Contents.
Michael Carter, 2001. Foundations of Mathematical Economics, MIT Press. Contents.