Any economic quantity, value or rate that varies on its own or due to change in its determinants is an economic variable. All economic variables are interdependent and interrelated. This implies that a change in one variable cause a change in the value of other related variables.
There are different categories of economic variables:
• Dependent and independent variables.
• Endogenous and exogenous variables.
The relationship between variables can be analysed through three methods:
• Tabular method,
• Functional method
• Graphical method.
It is always good to use the functional form to represent the relationship between economic variables. A function is a mathematical tool to express the cause and effect relationship between economic variables. Functions can be categorized as bi-variable functions and multivariable functions.
Three types of function are used in economic analyses:
• linear functions,
• non-linear functions
• polynomial function.
Another function-related concept is the slope. The slope is the rate of change in the dependent variable as a result of change in the independent variable. The slope of the line or the curve shows how strongly or weakly two variables are related. The steeper is the curve or the steeper is the line, the weaker is the relationship.
Because of the limitation to measure a slope at a point in a curve, the technique of differential calculation generally comes into picture. Differential calculation is generally used to find an optimum solution to the problem.
The optimization technique is a specific technique of managerial decision-making which consists of either:
• Maximizing the revenue,
• Minimizing the costs, or
• Maximizing the profit
Using economic functions, the optimization technique consists of finding the value of the independent variable of the function that maximizes or minimizes the value of the dependent variable.
Taking into account the constraints, optimization may be achieved through two specific methods:
• The substitution technique
• The Lagrangian multiplier method.
In the case of substitution, the value that is obtained by substitution will be again substituted back in the objective function, which is maximized and solved to obtain the value of the other variable.
In the case of Lagrangian multiplier method, a Lagrangian function is formed on the basis of a constraint, that is the objective function. That objective function is solved through the partial derivative method in order to know the value of the unknowns.
Another economic analysis tool is Regression. It is a statistical technique used to qualify the relationship between the interrelated economic variable. It consists of estimating the coefficients of the independent variables and measuring the reliability of the estimated coefficient.
The Regression technique minimizes the error term with the view of finding the regression equation that best fits the observed data. The Least Square Method uses the sum of the square of the error term, that regression technique seeks to minimize, and finds the value of the coefficient and the constant that produce the best fit line.
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