1. CHAPTER 2
GRAPHICAL ANALYSIS
2nd Semester, S.Y 2013 – 2014

2. Graphs in Economic Analysis
One way to express the relationship between variables is with a graph.
Graphs serve two purposes:
1. Graphs offer a way to visually express ideas that might be less clear if described with equations or words.
2. When analyzing economic data, graphs
provide a way of finding how variables are related in the world.
Graphs in one variable
Pie Graph
Bar Graph
Line or Time Series Graph

3. Forms of Graphs Pie graph Bar graph Line Graph
is a circular chart divided into sectors illustrating proportion. It is a convenient way to represent the different parts of something that when added together equal the whole.
Bar graph
is a chart with rectangular bars with lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally. It is used for marking clear data which has learned value.
Line Graph
is a type of graph, which displays information as a series of data points connected by straight line segments. It is an extension of a scatter graph, and is created by connecting a series of points that represent individual measurements with line segments.

4. Number of Android Tablets Sold
Pie Graph
Month
Number of Android Tablets Sold
January 88
February 76
March
100
April 67
May 55
June 60
July 40
August 45
September 56
October 68
November 78
December
125

5. Number of Android Tablets Sold
Bar Graph
Month
Number of Android Tablets Sold
January 88
February 76
March
100
April 67
May 55
June 60
July 40
August 45
September 56
October 68
November 78
December
125

6. Number of Android Tablets Sold
Line Graph
Month
Number of Android Tablets Sold
January 88
February 76
March
100
April 67
May 55
June 60
July 40
August 45
September 56
October 68
November 78
December
125

7. Graphs of Two Variables: The Coordinate System
Economists are often concerned with the relationships between variables. Thus, they need to display two variables on a single graph. The coordinate system makes this possible.
Five ordered pairs (including the origin) plotted as points on the Cartesian plane. The dashed lines are for axis location reference.

8. Variable and Constant
Variable – A quantity that assumes different values in a particular problem. It is a value that may change within the scope of a given problem or set of operations.
Constant – a quantity whose value remains unchanged throughout a particular problem.
Numerical Constant – has the same value in all problems
Parametric Constant (Parameter) – has the same value throughout the problem but may assume different values in different problems
Ex.
𝑅=10𝑥 (Revenue function)
𝑇𝐶=𝑎 + 𝑏𝑋 (Cost)
𝐶= 𝑎 +𝑏𝑌 (Consumption)
𝑄𝑑=𝑎 – 𝑏𝑌 (Quantity Demanded)

9. Dependent and Independent Variables
A Function is a relationship between two or more variables such that a unique value of one variable is determined by the values taken by the other variables in the function. These variables can be:
Independent Variable – the variable representing the value being manipulated or changed.
Dependent Variable – observed result of the independent variable being manipulated
If every value of x is associated with exactly one value of y, then y is said to be a function of x
y = f (x). Where y is the dependent variable and x is the independent variable

10. Direct vs. Inverse Relationship
Direct Relationship
a positive relationship between two variables in which change in one variable is associated with a change in the other variable in the same direction.
In a direct relationship, as one variable, say 𝑥, increases, the other variable, say 𝑦, also increases, and if one variable decreases, the other variable decreases
Inverse Relationship
a negative relationship between two variables in which change in one variable is associated with a change in the other variable in the opposite direction
In a direct relationship, as one variable, say 𝑥, increases, the other variable, say 𝑦, decreases, and if one variable decreases, the other variable increases. For example, there is an inverse relationship between education and unemployment — that is, as education increases, the rate of unemployment decreases

11. Inverse and Direct Relationship
Inverse Relationship
Direct Relationship
Inverse – negative relations
Direct – positive relationship

12. Negative Linear RelationshipX Y

13. Positive Linear RelationshipX Y

14. Slope 𝑚= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = ∆𝑌 ∆𝑋 = 𝑌 2 − 𝑌 1 𝑋 2 − 𝑋 1
The slope of the line represents the change in one variable that occurs when another variable changes.
It is an exact numerical measure of the relationship between the change in Y and the change in X.
Slope measures the rate of change.
𝑚= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = ∆𝑌 ∆𝑋 = 𝑌 2 − 𝑌 1 𝑋 2 − 𝑋 1

15. Slope of a Straight Line
Negative
Undefined Slope
Positive
Zero Slope
Slope is negative if the line slopes downward to the right
Slope is positive if the line slopes upward to the right
Slope of the x-axis or horizontal line is is zero
The slope of the y-axis or vertical line is undefined S

16. Slope of a Straight Line

17. Linear Equation to Economic Analysis
Fall '97
Linear Equation to Economic Analysis
An equation is a statement about a relationship between two or more variables
Y = f (X) says the value of Y is determined by the value of X ; Y is a “function of X.”
Y is the dependent variable
X is the independent variable
A linear relationship may be specified: 𝑦 = 𝑚𝑥 + 𝑏 [the function will graph as a straight line]
Where Y and X are variables
m is slope, b is y-intercept
fall ‘ 97

18. X and Y – Intercepts
The x-intercept is the point where a line crosses the x-axis. The general form of the x-intercept is (x, 0). The y-coordinate will always be zero.
The y-intercept is the point where a line crosses the y-axis.The general form of the y-intercept is (0, y). The x-coordinate will always be zero.

19. Let’s Check Your Understanding
Study the four accompanying diagrams. Consider the following statements and indicate which diagram matches each statement. Which variable would appear on the horizontal and which on the vertical axis? In each of these statements, is the slope positive, negative, zero, or infinity?
a. If the price of movies increases, fewer consumers go to see movies.
b. More experienced workers typically have higher incomes than less experienced workers.
c. Whatever the temperature outside, people consume the same number of hotdogs per day.
d. Consumers buy more frozen yogurt when the price of ice cream goes up.
e. Research finds no relationship between the number of diet books purchased and the number of pounds lost by the average dieter.
f. Regardless of its price, consumers in Lingayen buy the same quantity of salt.

20. Let’s Check Your Understanding!
Fall '97
Let’s Check Your Understanding!
1. Graph the equation: 𝑦= − 3𝑥 +9
What is the Y intercept? The slope?
What is the X intercept? Is this a positive (direct) relationship or negative (inverse)?
2. Graph the equation 𝑦= 2𝑥 +8
fall ‘ 97