ECONOMIC MODEL

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. VARIABLES, constants, COEFFICIENTS, AND 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

particular.

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.

B. EQUATIONS AND INEQUALITIES

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). If

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

product.

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

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. ^{x}log x = 1

2. ^{x}log 1 = 0

3. ^{x}log ^{x}a = a

4. ma = a ^{x}log ^{x}log m

5. x ^{x}log m = m

6. mn = ^{x}log ^{x}log ^{x}log m + n

7. ^{x}log^{m}/_{n} - ^{x}log m - ^{x}log n

8. ^{x}log m. mlog x = 1

9. ^{x}log m

FUNCTION

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

variables.

A. FUNCTION

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

certain).

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 = ax^{2} + bx + c

3. Cubic function: y = ax^{3} + cx + d + bx^{2}

^{ }

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!

Answer:

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!

Answer:

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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