Friday, April 16, 2010

Mathematical Economics Courses Review

Economics of Science and business that are exact sciences, to study and understand it required an analysis of quantitative and qualitative. Economic subjects are math courses that will provide the foundation to the students to be able to analyze quantitative problems in the economic field. Mathematical economics courses will provide the basis for students to be able to easily learn the subjects-subjects in the economic field. The discussion in this course is always preceded by pure mathematics, followed by the application of economics and business.


In an economy, relations between the variable-economic variables that one
others are very complex.
To facilitate the relationship between these variables, then the way
The best is to choose the many economic variables with problems
economy, then connecting it in such a way that shapes the relationship between
economic variables into a simple and relevant to the existing economic situation.
Penyederhanakan relationship between variables is called the economic model.
This economic model
can form a mathematical model. Economic models shaped mathematical model consists
from a number of variables, constants, coefficients, and / or parameters.


A variable is something whose value can change in a specific problem.
Variables are denoted by letters. Variable in the economic model consists of two types:
endogenous and exogenous variables. Endogenous variable is a variable value
the solution obtained from the model, while the exogenous variables is a
variable whose values obtained from outside the model, or has been determined based on data
existing. To distinguish the writing of the endogenous variables are not given the symbol subscript 0,
but for the exogenous variables given the symbol subscript 0.
Constant is a real number whose value does not change in a model
Constant coefficient multiplier is the number of variables.
Parameter is defined as a specific value in a specific problem and
probably will be another value at some other issues.


Mathematical models often include a statement or group of statements
(Statement) that includes various symbols of the variables and constants.
Statements in the form of mathematics is considered as the symbol (expresions).
a symbol has separated the parts that a positive sign and / or negative,
then these sections individually called tribes (terms). These factors are often presented
within each tribe. One factor is a multiplier of the multiplier-separated in a
The equation is a statement that the two symbols are the same, whereas
inequality is a statement which stated that the two symbols are not
same. The equation is symbolized by the sign = (equal to), while inequality
symbolized by the sign <(smaller than) or> (greater than).


Logarithm of a number is the rank that must be imposed on (meet) numbers
principal logarithm to obtain these numbers.
xa = ma = x log m where x is a base and a is a promotion.
Logarithm base is the most commonly used because of practical considerations in the calculation
is the number 10.
The rules of logarithms
1. xlog x = 1
2. xlog 1 = 0
3. xlog xa = a
4. ma = a xlog xlog m
5. x xlog m = m

6. mn = xlog xlog xlog m + n

7. xlogm/n - xlog m - xlog n

8. xlog m. mlog x = 1
9. xlog m


Implementation of the economy and business functions in one part of
very important to study, because economic models shaped
usually expressed by mathematical functions. Function in mathematics
declare a formal relationship between the two sets of data. If the set of data
is variable, then the function can be considered as relations between the two


Function is a form of mathematical relationships which express the relationship
dependence (functional relationship) between the one variable with another variable.
A function is formed by several elements, namely: variable, coefficient, and constants.
Variable and the coefficient is always present in every function.
Variables are building blocks for functions which reflect or represent the factors
(Data), specific, denoted by Latin letters. Based on the position or
nature, in every function, there are two kinds of variables: independent variables
(Independent variable) and dependent variable (dependent variable). Independent variable
is a variable whose value does not depend on other variables, whereas variables
bound is a variable whose value depends on other variables.
The coefficient is a number or numbers related to and located in front of a
variable in a function.
Constants are numbers or number (sometimes) helped shape
a function but it stands alone as a number (not related to a variable

y = 5 + 0.8 x
y: dependent variable
x: independent variable
0.8: the coefficient of variable x
5: constant
While the notation of a general function is: y = f (x)

B. Cartesian Coordinate Systems

Each function can be presented graphically on a pair of field axis
cross (coordinate system). Images of a function can be generated by
calculate the coordinates of the points that satisfy the equation, and then
couples moving point to cross-axis system. In
describe a function of independent variables placed on the horizontal axis
(Abscissa) and the dependent variable on the vertical axis (ordinate).

The types of algebraic functions, among others:
1. Linear Function: y = a + bx
2. Quadratic function: y = ax2 + bx + c
3. Cubic function: y = ax3 + cx + d + bx2

C. System of linear equations

Completion of a system of linear equations is a set of values
that meet simultaneously (simultaneously) all the equations of the system
these. Or simply the settlement system of linear equations is
determine the intersection of two linear equations. There are three ways you can
used for the completion of a system of linear equations, namely: (1). Method
Substitution (2). Elimination Methods, and (3). The determinant method.
Substitution Method

Example: Find the value of variables x and y of the following two equations:

2x +3 y = 21 and x +4 y = 23!

One of the first transformed into the equation y = ... , or x = ....

For example equation
x +4 y = 23 is converted to x = 23-4y.

Then substituted into the equation one.

x = 23-yr 4y = 21 2x + 3 Y
2 (23-4y) + 3 Y = 21
46 - 8y + 3 Y = 21
46 - 5Y = 21
25 = 5Y
y = 5

To get the value of x, substitute y = 5 into one equation.

y = 5 Þ 2x + 3y = 21

2x + 3(5) = 21

2x + 15 = 21

2x = 21 – 15

x = 6/2

x = 3

So the set of solutions that satisfy both these equations is
set of pairs (3.5)
Elimination Method
Example: Find the value of variables x and y of the following two equations:

3x-2y = 7 and 2x +4 y = 10!


Suppose the variable to be eliminated is y
3x - 2y = 7 x 2 6x - 4y = 14
2x + 4y = 10 x 1 2x + 4y = 10 +
8x + 0 = 24
x = 3

To get the value of y, substitute x = 3 into one equation.

x = 3 Þ 3(3) - 2y = 7

-2y = 7 – 9

2y = 2

y = 1

So the set of solutions that satisfy both these equations is
set of pairs

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