TOOLS USED TO EXPRESS RELATIONSHIPS Schedules Graphs Equations

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

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

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

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

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

Constructing a Graph Step 1: Number line Do this… 5 10 20 15 25 5 10 20 15 25 NOT this… 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 . Demand Quantity

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

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

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

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 Y = f(X) intercept X

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 Y = f(X) 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: Increasing at an increasing rate Increasing at a decreasing rate Decreasing at a decreasing rate Decreasing at an increasing rate

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

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

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

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