If you glance quickly through this text, you will find many graphs. Some seem simple, while others seem more complicated. They are included to help you visualize and understand economic relationships. Physicists and chemists sometimes illustrate their theories by building arrangements of multicolored wooden balls, representing protons, neutrons, and electrons, which are held in proper relation to one another by wires or sticks. Economists most often use graphs to illustrate their models. By understanding these “pictures,” you can more readily comprehend economic relationships. Most of our principles or models explain relationships between just two sets of economic facts, which can be conveniently represented with two-dimensional graphs.

**Construction of a Graph**

A graph is a visual representation of the relationship between two variables. In economics we represent the **independent variable** on the ** horizontal axis** and the

**dependent variable**on the

**. If the graph is a straight line we say the relationship is**

*vertical axis*

*linear**.*

**Direct and Inverse Relationships**

By a **direct relationship **(or positive relationship) we mean that two variables—in this case, consumption and income—change in the *same** *direction. An increase in consumption is associated with an increase in income; a decrease in consumption accompanies a decrease in income. When two sets of data are positively or directly related, they always graph as an *upsloping** *line.

In contrast, two sets of data may be inversely related. Consider the relationship between the price of basketball tickets and game attendance at ST. University (SU). Here we have an **inverse relationship **(or negative relationship) because the two variables change in *opposite** *directions. When ticket prices decrease, attendance increases. When ticket prices increase, attendance decreases.Observe that an inverse relationship always graphs as a *downsloping** *line.** **

**Dependent and Independent Variables**

Although it is not always easy, economists seek to determine which variable is the “cause” and which is the “effect.” Or, more formally, they seek the independent variable and the dependent variable. The **independent variable **is the cause or source; it is the variable that changes first. The **dependent variable **is the effect or outcome; it is the variable that changes because of the change in the independent variable. As noted in our income-consumption example, income generally is the independent variable and consumption the dependent variable. Income causes consumption to be what it is rather than the other way around. Similarly, ticket prices (set in advance of the season) determine attendance at SU basketball games; attendance at games does not determine the ticket prices for those games. Ticket price is the independent variable, and the quantity of tickets purchased is the dependent variable.

You may recall from your high school courses that mathematicians always put the **independent variable** (cause) on the horizontal axis and the **dependent variable** (effect) on the vertical axis. Economists are less tidy; their graphing of independent and dependent variables is more arbitrary. Their conventional graphing of the income-consumption relationship is consistent with mathematical presentation, but economists put price and cost data on the vertical axis. Hence, economists graphing of SU’s ticket price-attendance data conflicts with normal mathematical procedure.

** **

**Other Things Equal**

Our simple two-variable graphs purposely ignore many other factors that might affect the amount of consumption occurring at each income level or the number of people who attend SU basketball games at each possible ticket price. When economists plot the relationship between any two variables, they employ the *ceteris paribus** *(other things equal) assumption. In reality, “other things” are not equal; they often change. Specifically, the lines we have plotted would shift to new locations.

Consider a stock market “crash.” The dramatic drop in the value of stocks might cause people to feel less wealthy and therefore less willing to consume at each level of income. The result might be a downward shift of the consumption line.

Similarly, factors other than ticket prices might affect SU game attendance. If SU loses most of its games, attendance at SU games might be less at each ticket price.

**Slope of a Line**

Lines can be described in terms of their slopes and their intercepts. The **slope of a straight line **is the ratio of the **vertical change** (the rise or drop) to the **horizontal change** (the run) between any two points of the line, or “rise” over “run.”

** SLOPES AND MARGINAL ANALYSIS**

Recall that economics is largely concerned with changes from the status quo. The concept of slope is important in economics because it reflects marginal changes— those involving one more (or one less) unit.

**INFINITE AND ZERO SLOPES**

** **Many variables are unrelated or independent of one another. For example, the quantity of wristwatches purchased is not related to the price of bananas. The graph of their relationship is the line parallel to the vertical axis, indicating that the same quantity of watches is purchased no matter what the price of bananas. The slope of such a line is *infinite.*

Similarly, aggregate consumption is completely unrelated to the nation’s divorce rate. We put consumption on the vertical axis and the divorce rate on the horizontal axis. The line parallel to the horizontal axis represents this lack of relatedness. This line has a slope of *zero**.*

** Equation of a Linear Relationship**

If we know the vertical intercept and slope, we can describe a line succinctly in equation form. In its general form, the equation of a straight line is

*y ***= a + bx**

**where**

*y *= dependent variable

*a *= vertical intercept

*b *= slope of line

*x *= independent variable

**Slope of a Nonlinear Curve**

** **We now move from the simple world of linear relationships (straight lines) to the more complex world of nonlinear relationships. The slope of a straight line is the same at all its points. The slope of a line representing a nonlinear relationship changes from one point to another. Such lines are referred to as *curves**.* Consider the downsloping curve. Its slope is negative throughout, but the curve flattens as we move down along it. Thus, its slope constantly changes; the curve has a different slope at each point.

To measure the slope at a specific point, we draw a straight line tangent to the curve at that point. A line is *tangent *at a point if it touches, but does not intersect, the curve at that point. The slope of the curve at a point is equal to the slope of the tangent line.