Price Elasticity of Demand Calculator

How to calculate the price elasticity of demand

The formula for the price elasticity of demand is:

where:

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:

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.

We will learn more about the Midpoint Method below.

Percentage change in price

Let’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.

$\textrm{Percentage change in price} = \left( \frac{\textrm{\$6} - \textrm{\$4}}{\textrm{\$4}}\right) \times 100 = 50\%$

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:

$\textrm{Percentage change in price} = \left( \frac{\textrm{Final price} - \textrm{Initial price}}{\textrm{Initial price}}\right) \times 100$

$\textrm{Percentage change in price} = \left( \frac{\textrm{\$4} - \textrm{\$6}}{\textrm{\$6}}\right) \times 100 = -33\%$

The percentage change is −33%.

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

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.

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:

$\textrm{Percentage change in price} = \left( \frac{\textrm{Final price} - \textrm{Initial price}}{\textrm{(Final price + Initial price)} \div 2}\right) \times 100$

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

$\textrm{Percentage change in price} = \left( \frac{\textrm{\$6} - \textrm{\$4}}{\textrm{(\$6 + \$4)} \div 2}\right) \times 100 = 40\%$

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

$\textrm{Percentage change in price} = \left( \frac{\textrm{\$4} - \textrm{\$6}}{\textrm{(\$4 + \$6)} \div 2}\right) \times 100 = -40\%$

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%.

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

Let’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. The percentage change in quantity demanded using the Midpoint Method is:

$\textrm{Percentage change in quantity} = \left( \frac{175 - 50}{(175+50) \div 2}\right) \times 100 = 111\%$

Demand elasticity

When we look at demand elasticity, we use the absolute value, or the magnitude of the calculate price elasticity of demand. This allows us to look at how responsive quantity is to a change in price.

For example, the percentage change in quantity can be greater than, equal to, or less than the percentage change in price.

• Elastic demand: The percentage change in quantity demanded is greater than the percentage change in price. What does this mean? This means that when there is a small change in price, there is a big change in the quantity demanded. Let’s say the item of a cupcake dropped by 5%. If demand for cupcakes is elastic, then the quantity demanded will increase by more than 5%. People will be buying a lot more cupcakes.
• Unit elastic demand: The percentage change in quantity demanded is equal to the percentage change in price.
• Inelastic demand: The percentage change in quantity demanded is less than the percentage change in price.

This means that when there is a big change in price, there is a small change in the quantity demanded. An example might be the cost of milk. When the price of milk doubles, you might decrease your consumption by a little, but not significantly since milk might be a staple in your home.

To determine if demand is elastic or inelastic, take the absolute value of the calculated price elasticity of demand and use the following table.

Factors influencing the price elasticity of demand

What determines whether the demand for a good is elastic or inelastic? There are several factors that influence demand elasticity.

Availability of substitutes

Demand for a good will be elastic if there is an abundance of substitutes available. For example, if the price of an ice coffee goes up at Starbucks, but does not at Dunkin’ Donuts, you might just go to Dunkin’ Donuts for your coffee fix.

If substitutes are very hard to find, then the demand for a good will be inelastic. Water, electricity, accessing the internet, and gasoline are inelastic goods because there are few alternatives.

The amount of time to find a substitute also affects the demand elasticity. If a substitute can be found easily and quickly, then demand will be elastic. If it takes a long time to find a substitute and you need the good immediately, then demand will be inelastic.

Soft drinks have elastic demand because there is an abundance of substitutes that can be found quickly — usually in the same aisle at the supermarket.

Necessity or luxury?

Necessities, such as food, water, and housing, usually have inelastic demand, whereas luxuries, items that you want but don’t need to have, tend to have more substitutes and generally has elastic demand.

Percentage of income spend on the good

Goods that cost a small fraction of your income tend to be inelastic. Examples are pens and salt. The reason is because if the price of salt doubles, the impact on your income is very little since the item cost very little to begin with.

Price of the good

Relatedly, high priced goods tend to have elastic demand and low priced goods generally have inelastic demand.

In summary

To summarize the factors influencing demand elasticity, here are the cases when demand is more elastic and when demand is less elastic.

Examples of price elasticity in real life

Now that we know how price elasticity is calculated in theory, what is the price elasticity of some real life goods? A group of scholars from the Mackinac Center for Public Policy collected data to determine the elasticity of a number of goods.