# Using Slope in Economics

## Introduction

The slope of a line is a numeric value that describes both its direction and steepness. Slope helps economists understand the relationship between two variables. For example, it can show the relationship between income and spending in an economy.

• The sign of slope shows direction; a positive slope reflects an upward sloping line, and a negative slope reflects a downward sloping line.
• The magnitude of slope shows steepness. A larger magnitude indicates a steep slope. A lower magnitude indicates a gradual slope.

## How do I calculate slope?

Slope is measured by the rise divided by the run. The slope of a line is a rate of change that tells us how much the variable on the vertical axis changes while the variable on the horizontal axis changes by one unit.

\s\l\o\p\e = (\r\i\s\e)/(\r\u\n)

#### Steps to calculate slope

1. Subtract the starting value on the horizontal axis from the ending value on the horizontal axis. This is the run, the change in income.
2. Subtract the starting value of on the vertical axis from the ending value on the vertical axis. This is the rise, the change in spending.
3. Divide the result from step 2, the rise, by the result from step 1, This is the slope.

### For example:

In 2008 U.S. households received tax rebates ranging from $300 to$1200. One study found that spending increased as shown below:

1. The run is $1200 -$300 = $900. 2. The rise is$400- $100 =$300
3. The slope is $300/$900 = 1/3, showing that 1/3 of the additional income was spent. (In this case, the remainder of the rebate (2/3) was saved or used to pay off debt.)

## Where is slope used in Macroeconomics?

In macroeconomics, slope is useful for examining how economic variables change in response to other economic variables.

## Where is slope used in Microeconomics?

In microeconomics, we calculate slope for a wide variety of things including demand, supply, production possibility frontiers, budget constraints, production functions, and cost functions.

### ✓ Final thoughts on slope

• Whatever line or curve we are dealing with, the operation for calculating its slope does not change. It is always rise over run, or ΔX/ΔY.
• Often economists go one step beyond slope, measuring the ratio of the percent changes --- a concept called elasticity. This calculation uses changes in each variable, but then divides by the absolute numbers involved to arrive at a percentage. For example, in the case of our hypothetical Surfzup corporation, the price changed by -40% and the quantity sold changed by 33%. The ratio --- the elasticity --- is 33%/-40% = -0.83.