Mathematical Modeling
In an analysis of the economic condition of both enterprises and the larger subject of the national economy applies dismemberment problem or situation into smaller questions. This allows the procedure to the study of the logic which is a simulation. In particular, this method is applicable to the social processes that, among others, form the socio- economic system. Thus, we are able to understand the factors that determine the social conscience and the state of the productive forces, the institutional framework of the society. Modeling of social processes is an important part of mathematical methods in economics that highlight the impact of social economic processes. Useful in the analysis of economic phenomena and to take into account the social component that is sometimes overlooked. The study of social processes allows us to include their effects in a specific model even at the expense of quality, if not quantitative characteristics. Thus, the economic entity may predict consider and utilize social changes in the structure of society and its welfare, the feasibility of the family, the team, their participation in employment and other aspects of social processes.
Mathematical modeling of economic phenomena and processes is, as mentioned above, an important tool for economic analysis. It allows you to get a clear idea about the object, and to characterize quantitatively describe its internal structure and external relations. Model - conditional image of the object management (research). She constructed the subject of management (research) so that display characteristics of an object - property relationships, structural and functional parameters, etc., are essential for management purposes (research). Contents modeling method make design model based on a preliminary review of the facility and the allocation of its essential characteristics, experimental or theoretical analysis model to compare the results with the data of the object, the adjustment model.
In economic analysis, mainly used mathematical models studied phenomena or processes. Distinguish mathematical models with the quantitative characteristics specified in the form of formulas, numerical models with specific numerical values ; logical recorded using logical expressions, and graphic, expressed in graphical images. Model, implemented with the help of electronic computers, called machine or electronic.
Economic and mathematical model should be adequate to reality, reflect the essential aspects of communication and the object being studied. Note the basic features that are typical for the construction of economic and mathematical model of any kind.. The modeling process can be divided into three phases: 1) analysis of the theoretical patterns inherent studied phenomenon or process, and empirical data on its structure and characteristics, based on this analysis formed the model, 2) identification of methods by which you can solve the problem, 3) analysis of the results.
When economic-mathematical modeling is often the case when studying the economic system is too complex structure has not yet developed such mathematical methods, schemes that would cover all the main features of such a system and communication, for example such as the economy of the whole enterprise, its dynamics and development. There is a need to simplify the object being studied, exclusion and analysis of some of its minor features in order to take this simplified system of a class of known structures that are amenable to mathematical description and analysis. The degree of simplification should be such that substantially all the part of the features of the entity in accordance with the purpose of the study were included in the model.
Regression Analysis
For the purposes of analysis and planning of economic activities are widely used correlation and regression analysis.
Correlation and regression analysis is the classic method of stochastic modeling business. It examines the relationship of indicators of economic activity, when the relationship between them is not strictly functional and distorted influence of outsiders, random factors. When conducting regression analysis and correlation build multiple regression models of economic activity. In these models, isolated factor and productive indicators (signs).
Correlation analysis sets the task to measure the closeness of the relationship between the varying variables and evaluate factors that have the greatest impact on symptom score.
Regression analysis is used to select forms of communication and the type of model to determine the estimated values of the dependent variable (productive attribute).
Methods of correlation and regression analysis are used in combination. Most developed in theory and widely used in practice is the pair correlation when studying relations resultant variable and one factor variable. This is a univariate correlation and regression analysis.
Regression analysis is used mainly for planning as well as for the development of the regulatory framework.
In contrast to the correlation analysis, which only responds to the question, there is a link between the analyzed features, regression analysis gives and formalized expression. Furthermore, if the correlation analysis examines any correlation factors, the regression - sided dependence, i.e. communication, showing how the change affects the factor variables attribute score.
In Module 1 we have constructed a linear regression model which helps us to predict the amount of lemonade cups sold based on the price level. This equation helps us to make approximations and forecasts.
Profit Maximization
Traditionally it is believed that the main purpose of enterprises in the market economy is to maximize profits. Although it is currently not so obtaining sufficient income is a prerequisite for development and, therefore, an important motive for the conduct of any business.
Profit is acts as the excess proceeds from the sale of goods (services) produced over costs (capital). Profit is one of generalizing estimates of enterprises (organizations, institutions).
Profit performs two major functions : 1) characterizes the final financial results of the company, the size of his cash savings, 2) is the main source of financing the costs of production and social development of the enterprise (income tax - a key element of state budget revenues).
The main principle of the enterprise (firm) is to seek to maximize profits. For this reason, the profit is the main indicator of the efficiency of production.
Maximum profit is achieved in interaction of internal and external factors of the company. The main requirement of profit maximization - the profitability of each unit of output. The firm seeks to maximize the difference between the times total revenue and total costs. Production of each additional unit of output increases the volume of the amount of marginal costs, but also increase and total revenue - the amount of marginal revenue. Until marginal revenue is greater than marginal cost, the profit increases in general, to maximize its limit has not been reached and the firm can increase production. Once the marginal costs are higher than marginal revenue, total profit growth slows and increase production becomes unprofitable. Consequently, the profit margin reaches a maximum at this output, at which marginal revenue equals marginal cost.
Thus, a firm deciding to increase production may be guided by a simple rule : it should increase production to a level at which the marginal revenue becomes equal to marginal cost.
We have used methods of extremum of functions to find maximum profit in Module 3.
Sources
Brechner, Robert. (2006). Contemporary Mathematics for Business and Consumers, Thomson South-Western. ISBN 0-324-30455-2
Wegner, Trevor. (2010). Applied Business Statistics: Methods and Excel-Based Applications, Juta Academic. ISBN 0702172863
Larson, Ron, Bruce H. Edwards (2010). Calculus, 9th ed., Brooks Cole Cengage Learning. ISBN 978-0-547-16702-2
McQuarrie, Donald A. (2003). Mathematical Methods for Scientists and Engineers, University Science Books. ISBN 978-1-891389-24-5
Salas, Saturnino L.; Hille, Einar; Etgen, Garret J. (2006). Calculus: One and Several Variables (10th ed.). Wiley. ISBN 978-0-471-69804-3.
