【正文】 grows slowly. Concluding that using lawn mowers causes the grass to grow faster would be making the error of reverse causality. 33 of 34 169。 2022 Pearson Education, Inc. Publishing as Prentice Hall Are Graphs of Economic Relationships Always Straight Lines? The relationship between two variables is linear when it can be represented by a straight line. Few economic relationships are actually linear. If we carefully plot data on the price of a product and the quantity demanded at each price, holding constant other variables that affect the quantity demanded, we will usually find a curved—or nonlinear—relationship. In practice, it is often useful to approximate a nonlinear relationship with a linear relationship. If the relationship is reasonably close to being linear, the analysis is not significantly affected. 34 of 34 169。 2022 Pearson Education, Inc. Publishing as Prentice Hall Figure The Slope of a Nonlinear Curve The relationship between the quantity of iPhones produced and the total cost of production is curved rather than linear. In moving from point A to point B, the quantity produced increases by 1 million iPhones, while the total cost of production increases by $50 million. Farther up the curve, as we move from point C to point D, the change in quantity is the same—1 million iPhones—but the change in the total cost of production is now much larger: $250 million. Because the change in the y variable has increased, while the change in the x variable has remained the same, we know that the slope has increased. 35 of 34 169。 2022 Pearson Education, Inc. Publishing as Prentice Hall Here we measure the slope of the curve at a particular point by the slope of the tangent line. The slope of the tangent line at point B is 75, and the slope of the tangent line at point C is 150. 75175Q ua nt i t yCo s t ??? ?1501150Q ua nt i t yCos t ??? ?Figure The Slope of a Nonlinear Curve 36 of 34 169。 2022 Pearson Education, Inc. Publishing as Prentice Hall Formulas Formula for a Percentage Change 100 pe ri odfi rs t i n t he V a l ue pe ri odfi rs t i n t he V a l uepe ri od s e c on d i n t he V a l uec ha ng e P e rc e nt a g e ???One important formula is the percentage change, which is the change in some economic variable, usually from one period to the next, expressed as a percentage. 37 of 34 169。 2022 Pearson Education, Inc. Publishing as Prentice Hall Formulas for the Areas of a Rectangle and a Triangle Figure Showing a Firm’s Total Revenue on a Graph The area of a rectangle is equal to its base multiplied by its height. Total revenue is equal to quantity multiplied by price. Here, total revenue is equal to the quantity of 125,000 bottles times the price of $ per bottle, or $250,000. The area of the greenshaded rectangle shows the firm’s total revenue. H e i g h tB a s er e c t a n g l e a of A r e a ??38 of 34 169。 2022 Pearson Education, Inc. Publishing as Prentice Hall Figure The Area of a Triangle H e i g htBa s e21 t ri a ng l ea of A re a ???The area of a triangle is equal to 1?2 multiplied by its base multiplied by its height. The area of the blueshaded triangle has a base equal to 150,000 – 125,000, or 25,000, and a height equal to $ – $, or $. Therefore, its area equals 1/2 25,000 $, or $6,250. 39 of 34 169。 2022 Pearson Education, Inc. Publishing as Prentice Hall Summary of Using Formulas 1. Make sure you understand the economic concept the formula represents. 2. Make sure you are using the correct formula for the problem you are solving. 3. Make sure 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: