# Living Economics: Tools of the Trade

This is an introduction to the basic tools and resources kept in an economist’s toolbox for use in analyzing and identifying new data.

### Key Calculations

Some students will already be familiar with using a scientific calculator, but I often run into those who have never used the more advanced functions. Here is a brief refresher of two key functions.

### Parentheses

These two buttons enclosed in the red box below are as Parentheses.
( = Opening parentheses
) = Closing parentheses

For mathematical formulas, they always come together — you must have both opening and closing parentheses.

Use these for math equations requiring more than one action:

First, remember PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction). A formula should be completed in this order.

The calculator will complete the formula inside the parentheses before doing anything outside

Calculator: 2 + (5 ÷ 3)
2 + (1.66667) = 3.67

This formula is very useful for more difficult formulas . . . . for example %Δ

The price changes from \$5.00 to \$3.00, what is the %Δ?

Calculator: ((3.00 – 5.00) ÷ 5.00) x 100
= ((-2.00) ÷ 5.00) x 100
= -0.40 x 100
= Decrease of 40% or -40%

### Exponents

The next key tool on a calculator is the ability to complete “exponents” or xn . On a calculator, it often appears either as a button showing xy or as a button showing ^. The symbol ‘^’ is known as a Carat and is similar to an ↑.

To input on a calculator (25)

• Option 1 (xy)
• Input buttons in this order: 2 xy 5
• Option 2 (^)
• Input buttons in this order: 2 ^ 5
• *You can do this on a computer browser search bar too and it will calculate it for you.

### Graphs

Graphs are one of the most common tools for economists because they demonstrate the relationship between two factors (X and Y).

Every graph has two parts: X (Factor 1) and Y (Factor 2). X is always the horizontal line and Y is always the vertical line.

• Increasing X = Shifting right along the graph
• Increasing Y = Shifting upward on the graph

In basic economics courses, it is common for X to represent a Quantity (e.g. quantity produced, quantity demanded) and Y to represent the Price.

### Shape of the Graph

In general, all graphs are actually curved or ‘bowed’ in economics, but this is unnecessarily time consuming and we do not need to calculate the curves to make the point. So to simply our materials, we will primarily use straight line graphs.

Straight Line Graph

Curved Graph

### The Slope

The main difference between a curved line graph and a straight line graph is the slope.

The slope is a ratio that shows the Change in Y that results from ONE change in X.

Consider the following example:

In this graph, the company increases its production by 5Q every time the price increases by \$2.00.

The slope is calculated as a ratio of the change in Y over the change in X.

The simplicity of a straight line graphs is that the slope is always the same regardless of which two points you use to calculate the formula. I used (5Q, \$2) and (0Q, \$0), but it would have worked the same if I chose (10Q, \$4) and (0Q, \$0).

### Formula of a Line

A straight line uses the same formula every time:

Using the graph above, you can identify the formula of the line using any point on the graph (e.g. (10Q, \$4)) and the slope we calculated earlier:

• M = 0.40
• B = 0 →  when x = 0Q, y = \$0.

Y = MX + B
Formula of the Line:
Y = 0.40(X) + 0

### How Economists Use Graphs

Graphs are limited because you can only compare two things (X and Y) when reality shows there may be many factors.

In general we have three rules for graphs:

1. X changes and Y changes in a consistent pattern (e.g. a ‘line’ is formed), we might consider the two ‘related‘.
2. If X changes and Y does nothing, then we might consider whether the two are ‘unrelated‘.
3. If X changes and Y does nothing, then there must be another factor creating the change in X.

The goal of graphing data is to answer three primary questions:

1. Is there a relationship between X and Y — does a change in X create or cause a change in Y
2. What is the connection?
1. Is the relationship positive (Increase X = Increase Y)?
3. Is the relationship strong?
1. If X changes by 10,000,000 and Y only changes by 5. . . the relationship between the two is not strong.

### Quantity Shift v. Line Shift

A Quantity Shift occurs when X and Y are related (form a line) and we move from Point A to Point B on the line.

In the above graph, we shifted from point A to point B, but this is logical. We have remained on the line, so it appears the change in the price (\$2 up to \$6) is the result of a change in quantity produced.

A line shift occurs when X and Y may be related, but X is not the only factor causing a change in Y.

In the graph above, we have increased our quantity from 5Q to 10Q. We should then increase the price from \$2.00 to \$4.00. However, instead we move to point B (10Q, \$6.00). This change OFF OF THE LINE suggests that there is another factor causing the change in price.

### Inverse v. Direct

Lines in economics generally move in one of two directions:

## Direct Relationship

When the line move upwards from left to right, it means:

1. The Slope (M) is positive (+)
2. An increase in X = an increase in Y
3. This is called a direct relationship or a positive correlation

## Indirect Relationship

When the line move downwards from left to right, it means:

1. The Slope (M) is negative (-)
2. An increase in X = a decrease in Y

This is called a indirect relationship or a negative correlation