## Price Elasticity of Demand Formula

The price elasticity of demand measures the sensitivity of the quantity demanded of a good or service to a change in its price. In other words, it quantifies how changes in price affect the demand for a product.

The formula for calculating the price elasticity of demand is:

Price Elasticity of Demand = % Change in Quantity Demanded / % Change in Price

Where:

- % Change in Quantity Demanded is the percentage change in the quantity of the good or service demanded
- % Change in Price is the percentage change in the price of the good or service

The resulting number, the elasticity, will be a negative number due to the law of demand – as price increases, quantity demanded decreases (and vice versa). But it’s often reported in absolute terms (i.e., as a positive number) for simplicity.

- If the price elasticity of demand is greater than 1, demand is considered to be “elastic.” This means consumers’ purchasing quantity is quite sensitive to price changes. Luxury goods often fall into this category.
- If the price elasticity of demand is less than 1, demand is considered to be “inelastic.” This means consumers’ purchasing quantity is not very sensitive to price changes. Necessity goods often fall into this category.
- If the price elasticity of demand equals 1, demand is considered to be “unit elastic.” Here, the percentage change in quantity demanded is exactly the same as the percentage change in price.

Remember that numerous factors can influence the price elasticity of demand, including the availability of substitutes, the proportion of income spent on the good, and whether the good is considered a necessity or a luxury.

## Example of the Price Elasticity of Demand Formula

Suppose you are a business owner selling headphones. Last month, you sold 100 units at a price of $50 each. This month, you decide to increase the price to $60. As a result, your sales drop to 80 units.

First, calculate the percentage change in price. The price went from $50 to $60, so:

% Change in Price = ((New Price – Old Price) / Old Price) * 100

% Change in Price = (($60 – $50) / $50) * 100 = 20%

Next, calculate the percentage change in quantity demanded. The quantity demanded went from 100 units to 80 units, so:

% Change in Quantity Demanded = ((Old Quantity – New Quantity) / Old Quantity) * 100

% Change in Quantity Demanded = ((100 – 80) / 100) * 100 = 20%

Finally, calculate the price elasticity of demand:

Price Elasticity of Demand = % Change in Quantity Demanded / % Change in Price

Price Elasticity of Demand = 20% / 20% = 1

In this case, the price elasticity of demand is 1, so demand is unit elastic. This means that a 20% increase in price led to a 20% decrease in the quantity demanded.

This is a simple example, but remember that in the real world, many factors can influence demand, so changes in quantity demanded might not be solely due to changes in price. Also, this calculation assumes a linear demand curve, while in reality, the demand curve could have a different shape which could lead to different elasticity at different price points.