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Initial revenue | $400 | |

Final revenue | $300 | |

Percentage change in revenue | -25% |

The formula for the price elasticity of demand is:

**Price elasticity of demand = Percentage change in quantity demanded Ã· Percentage change in price**

where:

**Percentage change in quantity demanded**

= (Final quantity âˆ’ Initial quantity) Ã· ((Final quantity + Initial quantity) Ã· 2)

= (Final quantity âˆ’ Initial quantity) Ã· Average quantity

**Percentage change in price**

= (Final price âˆ’ Initial price) Ã· ((Final price + Initial price) Ã· 2)

= (Final price âˆ’ Initial price) Ã· Average price

Using this formula, we can calculate the price elasticity of demand.

**Percentage change in quantity demanded**

= (Final quantity âˆ’ Initial quantity) Ã· ((Final quantity + Initial quantity) Ã· 2)

= (100 âˆ’ 50) Ã· ((100 + 50) Ã· 2)

= 66.67%

**Percentage change in price**

= (Final price âˆ’ Initial price) Ã· ((Final price + Initial price) Ã· 2)

= ($3 âˆ’ $8) Ã· (($3 + $8) Ã· 2)

= -90.91%

**Price elasticity of demand **

= Percentage change in quantity demanded Ã· Percentage change in price

= 66.67% Ã· -90.91%

= -0.733

## What is price elasticity of demand?

The price elasticity of demand measures how responsive is the quantity demanded of a good or service to a change in its price.

For example, a coffee shop knows that if it raises the price of an ice coffee then the quantity of coffee sold will decrease. How much will it decrease? This depends on how much the quantity demanded responds to a change in price. The price elasticity of ice coffee determines this.

## Price elasticity of demand formula

The price elasticity of demand formula compares the percentage change in quantity demanded to the percentage change in price.

where:

You might notice that the calculation of percentage change does not use the initial price or quantity as the base, but rather the average of the initial and finance price or quantity. This is known as the Midpoint Method and its purpose is to adjust for rises and falls in prices.Â

We will learn more about the Midpoint Method below.

## Percentage change in price

Letâ€™s say that a coffee shop raises the price of an ice coffee from $4 to $6. The percentage change is calculated by the following formula.

In this case, the percentage change would be 50%.

Now, imagine that the coffee shop lowers the price of an ice coffee from $6 to $4. The percentage change would be:

The percentage change is âˆ’33%.

The price change in both scenarios is the same â€” $2, but the percentage change is different because the initial price is different in each scenario.Â We want a percentage change that is not dependent on the direction of the price change, which brings us to the Midpoint Method.Â

## The Midpoint Method

The Midpoint Method divides the change in price by the average price rather than the initial price. The average price is in the middle of the initial and final price, which is why it is called the Midpoint Method.

The formula for the percentage change in price based on the Midpoint Method is:

Using the Midpoint Method, the percentage change in price for a given dollar change in price will be the same regardless of direction.Â

In the previous examples where the ice coffee price change was $2 and the initial and final prices were $4 and $6, the percentage change using the midpoint method is:

The percentage change when the price of an ice coffee rises from $4 to $6 is:

The percentage change when the price of an ice coffee falls from $6 to $4 is:

The average price is the same whether the price rises or falls and so the ** magnitude** of the percentage change for the same dollar change is the same. Here, it is 40%.Â

The Midpoint Method is used to calculate both the percentage change in price and the percentage change in quantity demanded.

## Percentage change in quantity demanded

Letâ€™s say that when the price of an ice coffee falls from $6 to $4, the quantity demanded increases from 50 cups a day to 175 cups a day.Â The percentage change in quantity demanded using the Midpoint Method is: