1. TOOLS USED TO EXPRESS RELATIONSHIPS
Schedules
Graphs
Equations

2. Schedule ( or Table) Definition:
a list of different values of a variable and the value of a related variable

3. Equation Definition: Example:
a mathematical statement usually involving dependent and independent variables.
Example:
Qd = f(P)

4. Independent variable:
a variable that changes as the controlled variable is changed
Independent variable:
the controlled variable
a variable that is not a function of the equation and causes change in the dependent variable

5. Graph Definition: Purpose
a visual representation of functional relationships or the movements of a variable over time.
Purpose
to visualize the relationship P D Q

6. Constructing a Graph Step 1: Number line Y X Positive Y Negative X
Positive X X
Negative Y
Negative X
Negative Y
Positive X

7. Constructing a Graph Step 1: Number line Do this… 5 10 20 15 255 10 20 15 25
NOT this… 5 20 30 52 55 70 72

8. Constructing a Graph
Step 2: Label axis
Price
Quantity

9. Constructing a Graph
Step 2: Plot Points on graph . .
Price .
Quantity

10. . . . Constructing a Graph Step 3: Connect Points on graph Price
Quantity

11. Constructing a Graph
Step 4: Label Lines . .
Price .
Demand
Quantity

12. Linear Relationships between Variables
Negative Relationship
also called:
Inverse or Indirect Relationship
as values of X change, values of Y change in the opposite direction Y
Y = f(X) X

13. Linear Relationships between Variables
Positive Relationship
also called: Direct Relationship
as values of X change, values of Y change in the same direction Y
Y = f(X) X

14. Measuring Linear Relationships
Slope
measures how strongly the dependent variable is influenced by the independent variable
Formula
Slope = Rise / Run
= Change in Y
Change in X

15. Measuring Linear Relationships
Negative lines have negative slopes
Positive lines have positive slopes
Straight lines have only one slope along the line.

16. Intercept:
the value of the dependent variable (Y) when the value of the independent variable (X) is zero Y
Y = f(X)
intercept X

17. Graphical Assumptions
Homogeneous Units
each unit of the independent variable (X) is identical
Divisibility
each unit of the independent variable can be divided infinitesimally

18. Nonlinear Relationships
Exhibit changing relationship between variables
Have more than one slope along the line Y
Y = f(X) X

19. Nonlinear relationships
At the minimum point the slope is equal to zero
At the maximum point the slope is equal to zero

20. Nonlinear Relationships
Four types:
Increasing at an increasing rate
Increasing at a decreasing rate
Decreasing at a decreasing rate
Decreasing at an increasing rate

21. Nonlinear relationshipY
Increasing at an Increasing Rate:
increases in the X variable lead to larger increases in the Y Variable
Y = f(X) X

22. Nonlinear relationshipY
Increasing at a Decreasing Rate:
increases in the X variable lead to smaller increases in the Y Variable
Y = f(X) X

23. Nonlinear relationshipY
Decreasing at a Decreasing Rate:
increases in the X variable lead to smaller decreases in the Y Variable
Y = f(X) X

24. Nonlinear relationshipY
Decreasing at an Increasing Rate:
increases in the X variable lead to larger decreases in the Y Variable
Y = f(X) X