CHAPTER 2 THINKING LIKE AN ECONOMIST Table 2A-1 NOVELS PURCHASED BY EMMA s20,000 s40,000 This table shows the number of s10 8 novels novels Emma buys at various incomes and prices For any given level of income, the data on 8 260482 13 16 17 ice and quantity demanded can graphed to produce Emma's demand curve for novels, as in 28 Figure 2A-3 Demand Demand curve, D3 curve, D, curve, D2 Figure 2A-3 Novels DEMAND CURVE. The line D, shows how Emma's purchases of novels depend on th of novels when her income is held 9 (9,$9) constant. Because the price and the quantity demanded are negatively related, the demand (17,多7 curve slopes downward 10+15+2021+20 of Novels Purchased put the information from Table 2A-1 in graphical form, we need to hold one of the three variables constant and trace out the relationship between the other two Be- cause the demand curve represents the relationship between price and quantity demanded, we hold Emma's income constant and show how the number of nov- els she buys varies with the price of novels Suppose that Emma's income is $30,000 per year. If we place the number of novels Emma purchases on the x-axis and the price of novels on the y-axis, we can
CHAPTER 2 THINKING LIKE AN ECONOMIST 39 put the information from Table 2A-1 in graphical form, we need to hold one of the three variables constant and trace out the relationship between the other two. Because the demand curve represents the relationship between price and quantity demanded, we hold Emma’s income constant and show how the number of novels she buys varies with the price of novels. Suppose that Emma’s income is $30,000 per year. If we place the number of novels Emma purchases on the x-axis and the price of novels on the y-axis, we can Table 2A-1 NOVELS PURCHASED BY EMMA. This table shows the number of novels Emma buys at various incomes and prices. For any given level of income, the data on price and quantity demanded can be graphed to produce Emma’s demand curve for novels, as in Figure 2A-3. INCOME PRICE $20,000 $30,000 $40,000 $10 2 novels 5 novels 8 novels 9 6 9 12 8 10 13 16 7 14 17 20 6 18 21 24 5 22 25 28 Demand Demand Demand curve, D3 curve, D1 curve, D2 Price of Novels 5 4 3 2 1 30 Quantity of Novels Purchased 6 7 8 9 10 $11 0 5 10 15 20 25 Demand, D1 (5, $10) (9, $9) (13, $8) (17, $7) (21, $6) (25, $5) Figure 2A-3 DEMAND CURVE. The line D1 shows how Emma’s purchases of novels depend on the price of novels when her income is held constant. Because the price and the quantity demanded are negatively related, the demand curve slopes downward
40 PART ONE INTRODUCTION graphically represent the middle column of Table 2A-1. When the points that rep- resent these entries from the table--(5 novels $10),(9 novels, $9), and so on-are connected, they form a line. This line, pictured in Figure 2A-3, is known as Emmas demand curve for novels; it tells us how many novels Emma purchases at any given price. The demand curve is downward sloping, indicating that a higher price reduces the quantity of novels demanded. Because the quantity of novels demanded and the price move in opposite directions, we say that the two vari- ables are negatively related.( Conversely, when two variables move in the same di- rection, the curve relating them is upward sloping, and we say the variables are positively related. Now suppose that Emmas income rises to $40,000 per year. At any given price, Emma will purchase more novels than she did at her previous level of in- come Just as earlier we drew Emma's demand curve for novels using the entries from the middle column of Table 2A-1, we now draw a new demand curve using the entries from the right-hand column of the table. This new demand curve (curve D2)is pictured alongside the old one(curve D1)in Figure 2A-4; the new curve is a similar line drawn farther to the right. We therefore say that Emmas de- mand curve for novels shifts to the right when her income increases. Likewise, if Emmas income were to fall to $20,000 per year, she would buy fewer novels at any given price and her demand curve would shift to the left(to curve D3) In economics, it is important to distinguish between movements along a cure nd shifts of a curve. As we can see from Figure 2A-3, if Emma earns $30,000 per year and novels cost $8 apiece, she will purchase 13 novels per year. If the price of lovels falls to $7, Emma will increase her purchases of novels to 17 per year. The demand curve, however, stays fixed in the same place. Emma still buys the same Figure 2A-4 SHIFTING DEMAND CURVES he location of Emmas demand urve for novels depends on how much income she earns. The nore she earns, the more novels she will purchase at any given price, and the farther to the right her demand curve will lie 9876 21(10.$8 the demand curve shifts to the right Curve D, represents Emmas original demand curve when her income is $30,000 per year. If her ncome rises to $40,000 p demand curve 40:060 her demand curve shifts to D2. If 432 shifts to the left $20,000)(income her income falls to $20,000 per year, her demand curve shifts to 101315162025 Purchased
40 PART ONE INTRODUCTION graphically represent the middle column of Table 2A-1. When the points that represent these entries from the table—(5 novels, $10), (9 novels, $9), and so on—are connected, they form a line. This line, pictured in Figure 2A-3, is known as Emma’s demand curve for novels; it tells us how many novels Emma purchases at any given price. The demand curve is downward sloping, indicating that a higher price reduces the quantity of novels demanded. Because the quantity of novels demanded and the price move in opposite directions, we say that the two variables are negatively related. (Conversely, when two variables move in the same direction, the curve relating them is upward sloping, and we say the variables are positively related.) Now suppose that Emma’s income rises to $40,000 per year. At any given price, Emma will purchase more novels than she did at her previous level of income. Just as earlier we drew Emma’s demand curve for novels using the entries from the middle column of Table 2A-1, we now draw a new demand curve using the entries from the right-hand column of the table. This new demand curve (curve D2) is pictured alongside the old one (curve D1) in Figure 2A-4; the new curve is a similar line drawn farther to the right. We therefore say that Emma’s demand curve for novels shifts to the right when her income increases. Likewise, if Emma’s income were to fall to $20,000 per year, she would buy fewer novels at any given price and her demand curve would shift to the left (to curve D3). In economics, it is important to distinguish between movements along a curve and shifts of a curve. As we can see from Figure 2A-3, if Emma earns $30,000 per year and novels cost $8 apiece, she will purchase 13 novels per year. If the price of novels falls to $7, Emma will increase her purchases of novels to 17 per year. The demand curve, however, stays fixed in the same place. Emma still buys the same Price of Novels 5 4 3 2 1 30 Quantity of Novels Purchased 6 7 8 9 10 $11 0 5 13 16 10 15 20 25 (13, $8) (16, $8) D3 (income = $20,000) D1 (income = $30,000) D2 (income = $40,000) (10, $8) When income increases, the demand curve shifts to the right. When income decreases, the demand curve shifts to the left. Figure 2A-4 SHIFTING DEMAND CURVES. The location of Emma’s demand curve for novels depends on how much income she earns. The more she earns, the more novels she will purchase at any given price, and the farther to the right her demand curve will lie. Curve D1 represents Emma’s original demand curve when her income is $30,000 per year. If her income rises to $40,000 per year, her demand curve shifts to D2. If her income falls to $20,000 per year, her demand curve shifts to D3
CHAPTER 2 THINKING LIKE AN ECONOMIST number of novels at each price, but as the price falls she moves along her demand curve from left to right. By contrast, if the price of novels remains fixed at $8 but her income rises to $40,000, Emma increases her purchases of novels from 13 to 16 per year. Because Emma buys more novels at each price, her demand curve shifts out, as shown in Figure 2A There is a simple way to tell when it is necessary to shift a curve. When a vari- able that is not named on either axis changes, the curve shifts. Income is on neither the x-axis nor the y-axis of the graph, so when Emmas income changes, her de- mand curve must shift. Any change that affects Emmas purchasing habits besides a change in the price of novels will result in a shift in her demand curve. If, for in- stance, the public library closes and Emma must buy all the books she wants to read, she will demand more novels at each price, and her demand curve will shift to the right. Or, if the price of movies falls and Emma spends more time at the movies and less time reading, she will demand fewer novels at each price, and her demand curve will shift to the left. by contrast, when a variable on an axis of the graph changes, the curve does not shift. We read the change as a movement along the SLOPE One question we might want to ask about Emma is how much her purchasing abits respond to price. Lo ured in fis curve is very steep, Emma purchases nearly the same number of novels regardless Figure 2A-5 Novel CALCULATING THE SLOPE OF A $11 LINE. To calculate the slope of the demand curve, we can look changes in th y-coordinates as we move from int(21 novels, S6)to th 8 ) The slope of the line is the ratio of the chang in the y-coordinate(-2)to the 2113:=8 change in the x-coordinate(+8), emand, D: which equals -1/4 of Novels
CHAPTER 2 THINKING LIKE AN ECONOMIST 41 number of novels at each price, but as the price falls she moves along her demand curve from left to right. By contrast, if the price of novels remains fixed at $8 but her income rises to $40,000, Emma increases her purchases of novels from 13 to 16 per year. Because Emma buys more novels at each price, her demand curve shifts out, as shown in Figure 2A-4. There is a simple way to tell when it is necessary to shift a curve. When a variable that is not named on either axis changes, the curve shifts. Income is on neither the x-axis nor the y-axis of the graph, so when Emma’s income changes, her demand curve must shift. Any change that affects Emma’s purchasing habits besides a change in the price of novels will result in a shift in her demand curve. If, for instance, the public library closes and Emma must buy all the books she wants to read, she will demand more novels at each price, and her demand curve will shift to the right. Or, if the price of movies falls and Emma spends more time at the movies and less time reading, she will demand fewer novels at each price, and her demand curve will shift to the left. By contrast, when a variable on an axis of the graph changes, the curve does not shift. We read the change as a movement along the curve. SLOPE One question we might want to ask about Emma is how much her purchasing habits respond to price. Look at the demand curve pictured in Figure 2A-5. If this curve is very steep, Emma purchases nearly the same number of novels regardless Price of Novels 5 4 3 2 1 30 Quantity of Novels Purchased 6 7 8 9 10 $11 0 5 21 10 15 20 25 13 Demand, D1 (13, $8) (21, $6) 6 8 2 21 13 8 Figure 2A-5 CALCULATING THE SLOPE OF A LINE. To calculate the slope of the demand curve, we can look at the changes in the x- and y-coordinates as we move from the point (21 novels, $6) to the point (13 novels, $8). The slope of the line is the ratio of the change in the y-coordinate (2) to the change in the x-coordinate (8), which equals 1/4.
42 PART ONE INTRODUCTION of whether they are cheap or expensive. If this curve is much flatter, Emma pur- chases many fewer novels when the price rises. To answer questions about how much one variable responds to changes in another variable, we can use the con- cept of slope c The slope of a line is the ratio of the vertical distance covered to the horizonta istance covered as we move along the line. This definition is usually written out in mathematical symbols as follows where the Greek letter A(delta)stands for the change in a variable. In other words, the slope of a line is equal to the rise"(change in y) divided by the "run"(change in x). The slope will be a small positive number for a fairly flat upward-sloping line, a large positive number for a steep upward-sloping line, and a negative number for a downward-sloping line. A horizontal line has a slope of zero because in his case the y-variable never changes; a vertical line is defined to have an infinite slope because the y-variable can take any value without the x-variable changing at all What is the slope of Emma's demand curve for novels? First of all, because the curve slopes down, we know the slope will be negative. To calculate a numerical value for the slope, we must choose two points on the line. With Emmas income at $30,000, she will purchase 21 novels at a price of 6 or 13 novels at a price of $8 When we apply the slope formula, we are concerned with the change between these two points; in other words, we are concerned with the difference between them which lets us know that we will have to subtract one set of values from the other as follows Ay first y-coordinate-second y-coordinate 6-8 -1 slope= Ar first x-coordinate-second x-coordinate 21-13 8 4 Figure 2A-5 shows graphically how this calculation works. Try computing the lope of Emma's demand curve using two different points. You should get exactly the same result-1/4. One of the properties of a straight line is that it has the same slope everywhere. This is not true of other types of curves, which are steeper in some places than in others The slope of Emma's demand curve tells us something about how responsive her purchases are to changes in the price. A small slope (a number close to zero) means that Emma's demand curve is relatively flat; in this case, she adjusts the number of novels she buys substantially in response to a price change. A larger slope (a number farther from zero) means that Emmas demand curve is relatively steep; in this case, she adjusts the number of novels she buys only slightly in sponse to a price change CAUSE AND EFFECT Economists often use graphs to advance an argument about how the economy works. In other words, they use graphs to argue about how one set of events causes another set of events. With a graph like the demand curve, there is no doubt about cause and effect. Because we are varying price and holding all other
42 PART ONE INTRODUCTION of whether they are cheap or expensive. If this curve is much flatter, Emma purchases many fewer novels when the price rises. To answer questions about how much one variable responds to changes in another variable, we can use the concept of slope. The slope of a line is the ratio of the vertical distance covered to the horizontal distance covered as we move along the line. This definition is usually written out in mathematical symbols as follows: slope = , where the Greek letter ∆ (delta) stands for the change in a variable. In other words, the slope of a line is equal to the “rise” (change in y) divided by the “run” (change in x). The slope will be a small positive number for a fairly flat upward-sloping line, a large positive number for a steep upward-sloping line, and a negative number for a downward-sloping line. A horizontal line has a slope of zero because in this case the y-variable never changes; a vertical line is defined to have an infinite slope because the y-variable can take any value without the x-variable changing at all. What is the slope of Emma’s demand curve for novels? First of all, because the curve slopes down, we know the slope will be negative. To calculate a numerical value for the slope, we must choose two points on the line. With Emma’s income at $30,000, she will purchase 21 novels at a price of $6 or 13 novels at a price of $8. When we apply the slope formula, we are concerned with the change between these two points; in other words, we are concerned with the difference between them, which lets us know that we will have to subtract one set of values from the other, as follows: slope = = = = = . Figure 2A-5 shows graphically how this calculation works. Try computing the slope of Emma’s demand curve using two different points. You should get exactly the same result, 1/4. One of the properties of a straight line is that it has the same slope everywhere. This is not true of other types of curves, which are steeper in some places than in others. The slope of Emma’s demand curve tells us something about how responsive her purchases are to changes in the price. A small slope (a number close to zero) means that Emma’s demand curve is relatively flat; in this case, she adjusts the number of novels she buys substantially in response to a price change. A larger slope (a number farther from zero) means that Emma’s demand curve is relatively steep; in this case, she adjusts the number of novels she buys only slightly in response to a price change. CAUSE AND EFFECT Economists often use graphs to advance an argument about how the economy works. In other words, they use graphs to argue about how one set of events causes another set of events. With a graph like the demand curve, there is no doubt about cause and effect. Because we are varying price and holding all other 1 4 2 8 68 2113 first y-coordinatesecond y-coordinate first x-coordinatesecond x-coordinate y x y x
CHAPTER 2 THINKING LIKE AN ECONOMIST variables constant, we know that changes in the price of novels cause changes in the quantity Emma demands. Remember, however, that our demand curve came from a hypothetical example. When graphing data from the real world, it is often more difficult to establish how one variable affects another The first problem is that it is difficult to hold everything else constant when measuring how one variable affects another. If we are not able to hold variables constant, we might decide that one variable on our graph is causing changes in the other variable when actually those changes are caused by a third omitted variable not pictured on the graph. Even if we have identified the correct two variables to look at, we might run into a second problem-reverse causality In other words,we might decide that A causes B when in fact B causes A. The omitted-variable and reverse-causality traps require us to proceed with caution when using graphs to draw conclusions about causes and effects Omitted Variables To see how omitting a variable can lead to a decep- tive graph, let's consider an example. Imagine that the government, spurred by public concern about the large number of deaths from cancer, commissions an ex haustive study from Big Brother Statistical Services, Inc. Big Brother examines of the items found in peoples homes to see which of th em are asso the risk of cancer. Big Brother reports a strong relationship between two vari- ables: the number of cigarette lighters that a household owns and the prob- ability that someone in the household will develop cancer. Figure 2A-6 shows this relationship What should we make of this result? Big Brother advises a quick policy re- sponse. It recommends that the government discourage the ownership of cigarette lighters by taxing their sale. It also recommends that the government require herr ning labels: Big Brother has determined that this lighter is dangerous to your In judging the validity of Big Brother's analysis, one question is paramount Has Big Brother held constant every relevant variable except the one under con- sideration? If the answer is no, the results are suspect. An easy explanation for Fig ure 2A-6 is that people who own more cigarette lighters are more likely to smoke cigarettes and that cigarettes, not lighters, cause cancer. If Figure 2A-6 does not Figure 2A-6 Risk of GRAPH WITH AN OMITTED VARIABLE. The upward-sloping curve shows that members of households with more cigarette lighters are more likely to develop cancer. Yet we should not conclude that ownership of lighters causes cancer because the Number of Lighters in House graph does not take into accoun
CHAPTER 2 THINKING LIKE AN ECONOMIST 43 variables constant, we know that changes in the price of novels cause changes in the quantity Emma demands. Remember, however, that our demand curve came from a hypothetical example. When graphing data from the real world, it is often more difficult to establish how one variable affects another. The first problem is that it is difficult to hold everything else constant when measuring how one variable affects another. If we are not able to hold variables constant, we might decide that one variable on our graph is causing changes in the other variable when actually those changes are caused by a third omitted variable not pictured on the graph. Even if we have identified the correct two variables to look at, we might run into a second problem—reverse causality. In other words, we might decide that A causes B when in fact B causes A. The omitted-variable and reverse-causality traps require us to proceed with caution when using graphs to draw conclusions about causes and effects. Omitted Variables To see how omitting a variable can lead to a deceptive graph, let’s consider an example. Imagine that the government, spurred by public concern about the large number of deaths from cancer, commissions an exhaustive study from Big Brother Statistical Services, Inc. Big Brother examines many of the items found in people’s homes to see which of them are associated with the risk of cancer. Big Brother reports a strong relationship between two variables: the number of cigarette lighters that a household owns and the probability that someone in the household will develop cancer. Figure 2A-6 shows this relationship. What should we make of this result? Big Brother advises a quick policy response. It recommends that the government discourage the ownership of cigarette lighters by taxing their sale. It also recommends that the government require warning labels: “Big Brother has determined that this lighter is dangerous to your health.” In judging the validity of Big Brother’s analysis, one question is paramount: Has Big Brother held constant every relevant variable except the one under consideration? If the answer is no, the results are suspect. An easy explanation for Figure 2A-6 is that people who own more cigarette lighters are more likely to smoke cigarettes and that cigarettes, not lighters, cause cancer. If Figure 2A-6 does not Risk of Cancer Number of Lighters in House 0 Figure 2A-6 GRAPH WITH AN OMITTED VARIABLE. The upward-sloping curve shows that members of households with more cigarette lighters are more likely to develop cancer. Yet we should not conclude that ownership of lighters causes cancer because the graph does not take into account the number of cigarettes smoked