Graphics Discussion
Why so many graphs?
You probably have heard the expression "a picture is worth a thousand words." This statement is an excellent explanation of why you see (or will soon see!) so many graphs in economics. Once people are comfortable using graphs, they can quickly grasp ideas that are complicated when conveyed with words and would take a long time to grasp if presented verbally. A graph can convey a great deal of information very efficiently.
For example, compare the statement and graph presented below. Which more easily conveys the idea that Jay's income rose fairly quickly through the 1990's - the graph or the statement? Most would agree that the graph does, especially after they have finished a course in economics!
Statement on Jay's Income
In 1990, Jay's income was $20,000. In 1991 and 1992 it was $22,000 and $23,000, respectively. By 1993 it had risen to $24,000. Over the next three years, it rose $5,000 per year to a total of $34,000 in 1995. In 1996 it remained the same, but in 1997 and 1998 it increased by $6,000 annually. In 1999 and 2000, Jay received a $2000 raise. The percentage increase in Jay's income is found by subtracting his starting income of $20,000 in 1990 from his year 2000 income and dividing by the initial income of $20,000. The resulting value indicates how fast his income grew from 1990 to 2000.
How do you feel about graphs?
Some people are more visually oriented and some are more verbally oriented. If you are visually oriented, you will appreciate the clarity, conciseness and efficiency of a graph. However, you will be less comfortable with verbal explanations. If you are more verbally oriented, graphs can at first seem unclear and confusing. But you are probably more comfortable if you are given a verbal explanation. "Graphic Discussions" is for those who have not yet become comfortable with graphs and graphing. This overview of graphing is designed to get you started. A "Graphic Detail" section for each chapter will help guide you through the use of specific graphs found in each chapter. Remember that everything shown on a graph can be explained with words. Learning to read graphs is sort of like learning to speak a new language -- you just have to translate what the graph says into English! Once you master this new approach, you will see how useful graphs can be and will become conversant in the language of economics!
What are the basic parts of a graph?
Understanding the basic parts of any graph makes reading or drawing graphs much easier. The basic parts of a graph are described below.
Variables
Variable - something that has no fixed value; it is changeable. The purpose of a graph is to present information about one or more specific variables.
A graph is used to present information. Every graph should have a title, indicating what information is presented. Each graph presents information about some specific variable or variables. A variable is simply something that can have different values. Graphs present the different values of a variable visually, so they can be easily seen and interpreted.
For example, the graph above is showing Jay's income in the 1990's and has the title "Jay's Income." It presents information about the variable "income." Jay's income has different values in the years 1990 - 2000. Presenting this variable on a graph makes it clear that his income has gone up over the period.
An Axis (plural; Axes)
Axes - the straight lines used to measure (plot) variables on a graph.
A graph usually has two axes, called the "X" and "Y" axes. The "X" axis is the horizontal axis - it runs across the bottom of a graph. The variable measured on the "X" axis is referred to as the "X" variable. It increases as you move from left to right on the axis. The "Y" axis is the vertical axis - it runs up and down. A second variable, the "Y" variable, is measured on the "Y" axis. It increases as you move upwards on the graph. Where the "X" and "Y" axes cross is called the origin. This is the starting point for both axes, where both the "X" and "Y" variables are zero. Economics generally deals with variables that are positive. For example, prices, units produced and income can only go as low as zero, they can not be negative. This means that the graphs you will see will only have positive numbers on the axes, as shown below.
The "X" axis on this graph measures the quantity purchased. The "Y" axis measures price. This graph would show the relationship between the price of something and the quantity purchased.
It is important that a graph ALWAYS have labels on the axes. The labels show the reader what the graph is discussing. Without labels, a graph has no meaning.
A Constant
Constant - a variable that maintains the same value.
When the value of a variable stays the same, it is a constant. If the "X" variable is constant, it remains the same, regardless of the value of the "Y" variable. If the "Y" variable is constant, it remains the same regardless of the value of the "X" variable.
For example, if the quantity purchased remains the same, regardless of the price charged (i.e. consumers just HAVE to have it, no matter what the price), then quantity purchased is a constant and the graph is a vertical line (as shown below). This graph shows that consumers purchase "Q" regardless of the price charged.
In another example, sellers might receive the same price for their product, regardless of the quantity they choose to sell. This means that price is constant and the graph is a horizontal line (as shown below). The price equals "P" for every level of quantity sold.
What types of graphs do economists use most often?
There are many different types of graphs, and economists use them all. The most common types of graphs, and the types you will see in your textbook, are given below. If you see one of these types of graphs in a chapter and are unsure about how to read it, check to see if it is covered in the "Graphic Detail" for the chapter. The line graph is the type you will see most often in the text. The following sections tell you more about understanding and constructing line graphs.
How is a line graph constructed?
A line graph illustrates the relationship between two sets of numbers, one is labeled the "Y" variable and one is labeled the "X" variable. For example, if price is the "Y" variable and quantity purchased is the "X" variable, the line graph illustrates the relationship between price and quantity purchased. Each point on the line graph shows the quantity purchased at a different price. Connecting all of the points that show different combinations of price and quantity purchased that go together yields a line graph. The line shows the relationship between price and quantity purchased for the data used.
The table below shows data for price and quantity purchased. Each price/quantity combination is labeled with a letter. The corresponding graph plots each of the points and connects them to create a line graph of the data.
Point "a" shows that when price is $2, 7 will be purchased. When price increases to $4, only 6 are purchased. When price is $6, quantity is 5 and when Price is $8, quantity is 4. Connecting these points yields the line graph representing the relationship between price and quantity purchased. The graph shows a negative relationship (negative slope) that tells the viewer that when price goes up, the quantity purchased falls.
What is the slope of a line and why is it so important?
The slope of a line refers to how steep it is. That is, as you move across the horizontal axis, does the line go up or down by a little or a lot? Graph A shows a steep slope, graph B shows a flat slope. As you move from year 1 to year 2, "Y" increases from 10 to 100 in graph A, and from 10 to only 20 in graph B.
The steepest possible slope is a vertical line. The flattest possible slope is a horizontal line. These two extreme cases are discussed above under "constants."
The slope of a line can be positive (as illustrated in graphs A and B above) or negative. A positive slope represents a positive relationship between the two variables on the graph. This means that as one variable increases, the other also increases. This also means that if one variable were to decrease, the other would also. In other words, the two variables move in the same direction. In both graphs above, as you go from year 1 to year 2, "Y" increases (either to 20 or 100, but in both cases it is an increase). If two variables have a negative relationship, it means that as one increases, the other decreases. This also means that as one decreases, the other increases. In other words, the two variables move in opposite directions.
Positive relationship - when two variables move in the same direction. When one increases, the other increases and vice versa. Also known as a direct relationship.
Negative relationship - when two variables move in opposite directions. When one increases, the other decreases, and vice versa. Also known as an inverse relationship.
For example, you would expect that GPA and study time have a positive relationship. As your study time increases, so will your GPA and as your study time decreases, your GPA will decrease. You might also expect that as the price of a product increases, the quantity people buy will decrease and as price falls, people will purchase higher quantities. There is a negative relationship between price and quantity purchased.
For example, there is a negative relationship between the price of soft drinks and the quantity I will purchase. My soft drink purchase data is presented in the graph below. At a price of $.50, I buy 4 soft drinks. When price goes up to $.75, I decrease the number of soft drinks I purchase to 3. As price continues to increase to $1.00 and $1.25, I further decreases the number of soft drinks to 2 and 1. As price rises, the quantity purchased decreases, a negative relationship.
To be more precise about how much the "Y" variable increases or decreases as the "X" variable decrease, it is useful to calculate a value for slope. The slope is calculated by comparing the change in the "Y" variable (the "rise" of the line) to the change in the "X" variable (the "run" of the line).
Slope - the steepness of a line. Calculated as the change in the "Y" variable between two points on a line divided by the change in the "X" variable between two points on a line. That is, the rise divided by the run (or rise over run; rise/run).
For example, in the graph below, between point a and point b, "Y" increases by 10 (from 90 to 100) and "X" decreases by 20 (from 50 to 30). Therefore "Y" and "X" have a negative or inverse relationship. The rise is 10 and the run is -20.
Slope = rise/run = 10/(-20) = -1/2 or -5
If the change in "X" from 50 to 30 had increased "Y" by more than 10, the graph would have a steeper slope and the value for slope would be a larger number (though still negative). For example, if "Y" changed to 110 instead of 100 (point c), the rise would be 20 instead of 10 and the slope would be 20/(-20) or -1.
The slope gives information about the relationship between the two variables (through its sign - positive or negative). It also give information about the steepness of the curve (through the size of the number).
Why do some graphs have no numbers?
Economists sometimes use "abstract" graphs - graphs with no numbers. These graphs express general relationships or principles. In these cases, exact numbers are not known or are not necessary. An abstract graph clearly shows whether the relationship between two variables is positive or negative, but does not give the exact slope. An abstract graph can also show increases or decreases (shifts in the line). Or they can be used to show the relative position of two lines. Graphs with numbers are used to show specific, known information. Graphs without numbers are used to show general and/or relative information.