# Midpoint Formula

Definition: Midpoint formula is a mathematically equation used to measure the halfway point between two data points. The study of economics uses this calculation to find the coefficient of elasticity, either demand or supply, by measuring the average of the two points. In other words, it’s used to calculate how consumer habits change as price, quantity demanded, and quantity supplied changes.

## What Does A MidPoint Mean?

Typically this equation is used to solve the elasticity of demand and supply in different models or scenarios. The key characteristic of this equation is that it calculates the percentage changes based on the difference between the beginning and the ending values.

Here is the standard Mid Point Formula:

Midpoint = (b2 - b1 ) / ( b2 + b1 / 2 ) / ( a2 - a1 ) / ( a2 + a1 / 2 )

Where:

- A1 = the initial value of good A
- A2 = the ending value of good A
- B1 = the initial value of good B
- B2 = the ending value of good B

Let’s look at an example.

## Example

Peter wants to calculate the average change in the elasticity of two goods A and B. The price of good A increases from $8 to $12. The price of good B changes from $5 to $8.

Using the traditional method, Peter gets a change of $12 / $8 - 1 x 100 = 50% for good A and a change of $8 / $5 - 1 x 100 = 60% for good B.

Using the midpoint formula, he gets:

Good A: ( $12 - $8 ) / ( $12 + $8 ) /2 = $4 / $10 = 0.46 = 46%

Good B: ($8 - $5) / ($8 + $5) / 2 = $3 / $6.5 = 0.4 = 40%

Midpoint = ( b2 - b1 ) / ( b2 + b1 / 2 ) / ( a2 - a1 ) / ( a2 + a1 / 2 ) = 0.46 / 0.4 = 1.15

The price of good A decreases from $12 to $8. The price of good B decreases from $8 to $5.

Using the traditional method, Peter gets a change of $8/$12-1*100 = -66.6% for good A and a change of $5/$8-1*100 = -37.5% for good B.

Using the midpoint formula, he gets:

Good A: ( $8- $12 / ( $8 + $12 ) / 2 = -$4 / $10 = -0.46 = -46%

Good B: ( $5 - $8 ) / ($5 +$8) / 2 = -$3 / $6.5 = -0.4 = -40%

Midpoint = -0.46 / 0.4 = -1.15

Therefore, by using the midpoint equation, the results are more accurate as percentage change is calculated as an average of the initial and the ending value.

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