Graphs and Relationships in Microeconomics: Appendix Study Notes

Graphs in Economics

Introduction to Economic Graphs

Graphs are essential tools in microeconomics for visualizing relationships between variables such as price, quantity, income, and expenditure. Understanding how to interpret and construct these graphs is fundamental for analyzing economic data and models.

• Graph: A visual representation of the relationship between two or more variables.

• Axes: The vertical axis is called the y-axis, and the horizontal axis is the x-axis. The point where both axes meet is the origin.

• Variables: Common economic variables include quantities produced, prices, income, and expenditure.

Plotting Points and Reading Graphs

To plot a point on a graph, you need the values for both variables. For example, plotting a point at 5,959 meters above sea level at 10°C requires locating the x-value (temperature) and the y-value (height).

• Example: Point A (x = 10°C), Point B (y = 5,959 m), Point C (combines both values).

• Graphs can represent economic data, such as the quantity of movie tickets sold at a given price.

Scatter Diagrams

A scatter diagram plots the value of one variable against another for multiple observations. This helps reveal whether a relationship exists between the variables.

• Definition: A scatter diagram is a graph of paired data points for two variables.

• Application: Used to analyze relationships such as production budget vs. box office revenue for movies.

• Interpretation: Patterns in the scatter diagram indicate the type of relationship (positive, negative, none).

Types of Relationships in Economic Data

Positive (Direct) Relationships

When two variables move in the same direction, the relationship is called positive or direct. On a graph, this is shown by an upward-sloping line.

• Linear Relationship: Shown by a straight line; the rate of change is constant.

• Example: As income increases, expenditure also increases.

Negative (Inverse) Relationships

When two variables move in opposite directions, the relationship is negative or inverse. This is represented by a downward-sloping line.

• Example: As the price of a good increases, the quantity demanded typically decreases.

Maximum and Minimum Relationships

Some relationships have a maximum or minimum point, meaning the relationship is positive over part of its range and negative over another part.

• Example: The relationship between output and cost may have a minimum cost at a certain output level.

Unrelated Variables

Variables may sometimes show no discernible relationship. In such cases, the graph does not display a clear pattern.

• Example: Inflation and unemployment may not always be related in a given dataset.

Slope in Economic Relationships

Definition and Calculation of Slope

The slope of a relationship measures the rate at which one variable changes in response to another. It is calculated as the change in the y-variable divided by the change in the x-variable.

• Formula:

$\text{Slope} = \frac{\Delta y}{\Delta x}$

• Δ (Delta): Represents "change in" a variable.

• Positive Slope: Upward-sloping line.

• Negative Slope: Downward-sloping line.

Slope of a Straight Line

The slope of a straight line is constant and can be calculated as "rise over run."

• Positive Slope: Indicates a direct relationship.

• Negative Slope: Indicates an inverse relationship.

Slope of a Curved Line

The slope of a curved line varies depending on the point of calculation. It can be determined at a specific point (using a tangent) or across an arc (using a secant).

• Slope at a Point: Equal to the slope of the tangent line at that point.

• Average Slope Across an Arc: Equal to the slope of the straight line joining two points on the curve.

Graphing Relationships Among More Than Two Variables

Ceteris Paribus and Multivariable Graphs

When analyzing relationships involving more than two variables, economists use the ceteris paribus assumption, meaning "all other relevant things remain the same." This allows for the isolation of the effect of one variable on another.

• Example: The quantity of ice cream consumed at different prices as temperature varies.

• By holding temperature constant, the relationship between price and quantity can be graphed.

• When temperature changes, the entire curve shifts, illustrating the effect of the third variable.

Table: Example of Multivariable Relationship (Inferred)

Price per Scoop ($)	Quantity Consumed (litres) at 21°C	Quantity Consumed (litres) at 32°C
2.75	10	20
3.00	8	16
3.25	6	12

Additional info: Table entries inferred for illustration based on context.

Summary of Key Concepts

• Graphs are used to visualize economic relationships.

• Scatter diagrams help identify the type and strength of relationships between variables.

• Slope quantifies the rate of change between variables and is central to interpreting graphs.

• Ceteris paribus is used to analyze the effect of one variable while holding others constant.