grade point average). Because study tune and grade point average typically move in the same direction, we say that these two variables have a fosit/iv correlation. By contrast, if we were to graph party lime and grades, we would likely find that higher party time is associated with lower grades; because these variables typically move in opposite directions, we call this a nrgitfw correlation. In either case, the coordinate system makes the correlation between the two variables easy to see.
Students who study more do tend to gel higher grades, but other factors also influence a student's grade. Previous preparation is an important factor, for instance, as are talent, attention from teachers, even eating a good breakfast. A scatterplot like Figure A-2 does not attempt to isolate the effect that study has on grades from the effects of other variables. Often, however, economists prefer looking at how one variable affects another, holding everything else constant.
To see how this is done, let's consider one of the most important graphs in economics: the demand curve. The demand curve traces out the effect of a good's price on tlx? quantity of the good consumers want to buy. Befoiv showing a demand curve, however, consider Table A-l, which shows how the number of novels that Emma buys depends on her income and on the price of novels. When novels are cheap, Emma buys them in large quantities. As they become more expensive, she instead borrows books from the library or c hooses to go to the movies rather than read. Similarly, at any given price, Emma buys more novels when she has a higher income. That is, when her income increases, she spends part of the additional income on novels and part on other goods.
We now have three variables—the price of novels, income, and the number of novels purchased—which arc more than we can represent in two dimensions. To put the information from Table A-l in graphical form, we need to hold one of the three variables cons Lin I 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 f 30,000 per year. If we place the number of novels Emma purchases on the.*-axis and the price of novels on the y-axis, we can graphically represent the middle column of Table A-l. When the points that represent these entries from the table <5 novels, SHI), (S* novels. $9), and so on are connected, they form a line, This line, pictured in Figure A-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 »loping, and we say the variables are fWSJf;iWy related)
Now suppose that Emma's income rises toS40,CKX) per year. At any given price, Emma will purchase more novels than she did al her previous level of income. Just a» earlier we drew Emma's demand curve for novels using the entries from the middle column of Table A-l, we now draw a new demand curve using the entries from the right column of the table. This new demand curve (curve D:) is pictured alongside the old one (curve L>,) in Figure A-l; the new curve i» a similar line drawn farther to the right. We therefore say that Emma's demand curve for novels sJ'ills to the right when her income increases. Likewise, if Emma's income were lo fall to 320,000 per year, she would buy fewer novels at any given price and her demand curve would shift to the left (to curve DJ.
In economics, it is important to distinguish between mownents ¡¡long a eunv and sfu/ts of a curxv. As we can see from Figure A-3, if Emma tarns 330,0C0 per year and novels cost 38 apiece, she will purchase 13 novels per year. If the price of
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