TOOLS USED TO EXPRESS RELATIONSHIPS

SchedulesGraphs

Equations

Schedule ( or Table)

Definition: a list of different

values of a variable and the value of a related variable

Price Quantity$2 204 156 108 5

Equation

Definition: a mathematical statement usually

involving dependent and independent variables.

Example: Qd = f(P)

Dependent 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

Graph

Definition: a visual

representation of functional relationships or the movements of a variable over time.

Purpose to visualize the

relationship

P

D

Q

Constructing a Graph

Step 1: Number lineY

X00

Positive YNegative X

Positive YPositive X

Negative YNegative X

Negative YPositive X

Constructing a Graph

Step 1: Number line

0 5 10 15 20 25

NOT this…

Do this…

0 5 20 30 52 55 70 72

Constructing a Graph

Step 2: Label axis

Price

Quantity

Constructing a Graph

Step 2: Plot Points on graph

Price

Quantity

. . .

Constructing a Graph

Step 3: Connect Points on graph

Price

Quantity

. . .

Constructing a Graph

Step 4: Label Lines

Price

Quantity

. . . Demand

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

X

Y = f(X)

Linear Relationships between Variables

Positive Relationshipalso called:Direct Relationship

as values of X change, values of Y change in the same direction

Y

X

Y = f(X)

Measuring Linear Relationships

Slope measures how

strongly the dependent variable is influenced by the independent variable

FormulaSlope = Rise / Run

= Change in Y

Change in X

Measuring Linear Relationships

Negative lines have negative slopes

Positive lines have positive slopes

Straight lines have only one slope along the line.

Intercept:

the value of the dependent variable (Y) when the value of the independent variable (X) is zero

Y = f(X)

Y

X

intercept

Graphical Assumptions

Homogeneous Units each unit of the independent variable

(X) is identical

Divisibility each unit of the independent variable

can be divided infinitesimally

Nonlinear Relationships

Exhibit changing relationship between variables

Have more than one slope along the line

Y

X

Y = f(X)

Nonlinear relationships

At the minimum point the slope is equal to zero

At the maximum point the slope is equal to zero

Nonlinear Relationships

Four types:

1. Increasing at an increasing rate

2. Increasing at a decreasing rate

3. Decreasing at a decreasing rate

4. Decreasing at an increasing rate

Nonlinear relationship

Increasing at an Increasing Rate: increases in the X

variable lead to larger increases in the Y Variable

Y

X

Y = f(X)

Nonlinear relationship

Increasing at a Decreasing Rate: increases in the X

variable lead to smaller increases in the Y Variable

Y

X

Y = f(X)

Nonlinear relationship

Decreasing at a Decreasing Rate: increases in the X

variable lead to smaller decreases in the Y Variable

Y

X

Y = f(X)

Nonlinear relationship

Decreasing at an Increasing Rate: increases in the X

variable lead to larger decreases in the Y Variable

Y

X

Y = f(X)