Graphing in Economics - Study Notes

Graphing in Economics: Overview

Visual representations between two variables.
In Mathematics: Independent variable on the horizontal axis; Dependent variable on the vertical axis. This is true for income–consumption relationships.
In Economics: price/cost data are often plotted on the vertical axis. Price is the independent variable, so this contradicts the standard math model. Economists can be somewhat arbitrary when graphing independent and dependent variables.

Independent variable: the cause or source; the variable that changes first.
Dependent variable: the effect or outcome; changes because of the independent variable.
Ceteris paribus (other things equal) assumption: all factors other than the two being examined are considered constant.
In reality, these other variables do change, which can cause a change in the graph.

Mathematics typically uses X for the independent variable (horizontal axis) and Y for the dependent variable (vertical axis).
Economics sometimes places price data on the vertical axis and may treat price as the independent variable, which can flip conventional axis roles.

Slope = ratio of vertical change to horizontal change between any two points on the line. \text{slope} = \frac{\Delta Y}{\Delta X}
Rise / Run (two ways to express the same idea).
Positive slope indicates a direct relationship; Negative slope indicates an inverse relationship.
Slope is important because it reflects marginal changes (one more or one less unit).

Slope = infinite when the change in X is zero: a ratio with 0 as the denominator.
\text{slope} = \frac{\Delta Y}{0} = \infty
Occurs when two variables are unrelated.
Example given: price of bananas and wristwatches.
Indicates that the same amount of variable X is purchased no matter what the price of Y.

A line can be located on a graph without plotting points if we know the slope and the vertical intercept.
Vertical intercept: the point where the line meets the vertical axis.
Equation of a straight line: Y = a + bX
- Y = dependent variable
- b = slope
- a = vertical intercept
- x = independent variable
Note: For consumption/income graphs this form is used with the economics convention.

Economists flip the typical math setup: independent variable on the Y axis and dependent variable on the X axis.
The Y = independent variable in this orientation.

Slope of a straight line is the same at all points.
Slope of a non-linear line changes from point to point (curves).
To measure the slope at a point on a curve, draw a tangent line to that point (touching but not intersecting).
The slope of the tangent line at that point equals the slope of the curve at that point.

Direct relationship: positive slope; both variables move in the same direction.
Inverse relationship: negative slope; variables move in opposite directions.
Ceteris paribus: all else equal; other factors held constant.
Vertical intercept: where the line crosses the Y axis.
Slope: the rate of change; the amount by which Y changes when X changes by one unit.
Tangent line: a line that touches a curve at a point and has the same slope as the curve at that point.
Equilibrium in a graph: the intersection of Demand and Supply curves; coordinates provide (P, Q).