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Econ 201/202 Review of Essential Math 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 Demand Curve: Graphs of Two Variables (price and quantity) FIGURE 1A-3 Plotting Price and Quantity Points in a Graph Appendix Graphs of Two Variables Slopes of Lines Slope Change in value on the vertical axis Δy Change in value on the horizontal axis Δx ($12 $14) 2 Rise Run FIGURE 1A-4 Calculating the Slope of a Line Slope Δ Price of pizza Δ Quantity of pizza (65 55) 10 0.2 Appendix Graphs of Two Variables Taking into Account More Than Two Variables on a Graph FIGURE 1A-5 Showing Three Variables on a Graph Appendix Graphs of Two Variables Positive and Negative Relationships FIGURE 1A-6 Graphing the Positive Relationship between Income and Consumption Appendix Graphs 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. Appendix Graphs of Two Variables Slopes of Nonlinear Curves FIGURE 1A-8 The Slope of a Nonlinear Curve Appendix Formulas Formulas for the Areas of a Rectangle and a Triangle Area of a rectangle base x height FIGURE 1A-9 Showing a Firm’s Total Revenue on a Graph Appendix Formulas Formulas for the Areas of a Rectangle and a Triangle Area of a triangle 1/2 x base x height FIGURE 1A-10 The Area of a Triangle Appendix Formulas Formula for a Percentage Change 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. GDP2004 GDP2003 x 100 GDP2003 Percentage change ( Value in the second period - Value in the first period ) x 100 Value in the first period Appendix Formulas Summary of Using Formulas Whenever you must use a formula, you should follow these steps: 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.