Econ 201/202

Review of EssentialMath and Graphing Skills

What do you need to know?

• Calculating and interpreting slopes of graphs– Linear and non-linear functions

• Calculating and interpreting areas under a graph– Geometric areas: triangles, rectangles– More sophisticated – integrals (or summing

up)• Systems of equations

– Interpreting the results– Simultaneous equations and equilibrium

Slope of linear function

FIGURE 1A-3Plotting Price and Quantity Points in a Graph

Demand Curve: Graphs of Two Variables (price and quantity)

Appendix

FIGURE 1A-4Calculating the Slope of a Line

Graphs of Two VariablesSlopes of Lines

Δ

Δ

Change in value on the vertical axis y RiseSlope

Change in value on the horizontal axis x Run

($12 $14) 20.2

(65 55) 10

Δ

Δ

Price of pizzaSlope

Quantity of pizza

Appendix

FIGURE 1A-5Showing Three Variables on a Graph

Graphs of Two VariablesTaking into Account More Than Two Variables on a Graph

Appendix

FIGURE 1A-6Graphing the Positive Relationship between Income and Consumption

Graphs of Two VariablesPositive and Negative Relationships

AppendixGraphs of Two Variables

Are Graphs of Economic Relationships Always Straight Lines?

The graphs of relationships between two economic variables that we have drawn so far have been straight lines. The relationship between two variables is linear when it can be represented by a straight line.

Few economic relationships are actually linear.

AppendixGraphs of Two Variables

Slopes of Nonlinear Curves FIGURE 1A-8The Slope of a Nonlinear Curve

AppendixFormulas

Formulas for the Areas of a Rectangle and a Triangle

FIGURE 1A-9Showing a Firm’s Total Revenue on a Graph

height x baserectangle a of Area

AppendixFormulas

Formulas for the Areas of a Rectangle and a Triangle

FIGURE 1A-10The Area of a Triangle

height x base x trianglea of Area 1/2

AppendixFormulas

Formula for a Percentage Change

100x GDP

GDPGDP

2003

20032004

100x )periodfirst thein Value

periodfirst thein Value - period second thein Value( change Percentage

One important formula is the percentage change.

The percentage change is the change in some economic variable, usually from one period to the next, expressed as a percentage.

AppendixFormulas

Summary of Using Formulas

1 Make sure you understand the economic concept that the formula represents.

2 Make sure you are using the correct formula for the problem you are solving.

3 Make sure that the number you calculate using the formula is economically reasonable. For example, if you are using a formula to calculate a firm’s revenue and your answer is a negative number, you know you made a mistake somewhere.

Whenever you must use a formula, you should follow these steps: