As demonstrated in visual economic models like price-elasticity-of-demand-curve.png, the slope of the curve visualizes consumer sensitivity to price changes.
Perfectly Inelastic (PED = 0): A vertical line. Consumers buy the exact same quantity regardless of price.
Inelastic (PED < 1): A steep slope. Price changes cause smaller percentage changes in quantity.
Elastic (PED > 1): A flatter slope. Price changes cause larger percentage changes in quantity.
How much will customer demand change if a business raises or lowers its prices? A small price increase might have little effect on sales for one product, while the same increase could cause a sharp decline in sales for another. Understanding this relationship helps businesses make better pricing decisions, economists study consumer behaviour, and students solve microeconomics problems.
A Price Elasticity of Demand Calculator measures how sensitive the quantity demanded of a product or service is to a change in its price. By entering the original and new prices alongside the corresponding quantities demanded, users can estimate the strength of the relationship and determine whether demand is elastic, inelastic, or unit elastic.
This calculator is useful for pricing analysis, revenue planning, market research, and academic calculations. The midpoint method is particularly helpful when comparing two price-and-quantity observations because it uses average values as the reference point.
What Is Price Elasticity of Demand?
Price elasticity of demand (PED) is an economic measure of the responsiveness of quantity demanded to a change in price, assuming other relevant factors remain reasonably constant.
For example, suppose a coffee shop raises the price of a drink from $4 to $4.50. If the number of drinks customers purchase falls only slightly, demand is relatively inelastic. If sales decline substantially, demand is relatively elastic.
Price elasticity is generally negative because price and quantity demanded tend to move in opposite directions: when price rises, quantity demanded usually falls, and when price decreases, quantity demanded usually rises. However, results are often interpreted using the absolute value of elasticity so that the degree of responsiveness is easier to classify.
Price Elasticity of Demand Formula
The basic formula is:
Price Elasticity of Demand = Percentage Change in Quantity Demanded ÷ Percentage Change in Price
To compare two observations, many economics courses use the midpoint formula, also called the arc elasticity formula.
The percentage terms in the formula can both be multiplied by 100, but the factors cancel when one percentage is divided by the other.
The midpoint method uses the average of the two prices and the average of the two quantities as the reference values. Consequently, it produces the same elasticity magnitude when comparing the same two observations in reverse order.
Worked Example: Calculating Price Elasticity of Demand
Suppose a retailer sells 200 units of a product each week at $10 per unit. After increasing the price to $12, weekly sales decline to 160 units.
The input data is:
Variable
Original
New
Price
$10
$12
Quantity demanded
200 units
160 units
Step 1: Calculate the percentage change in quantity using the midpoint method.
[ \frac{160-200}{(160+200)/2}\times100 ]
[ =\frac{-40}{180}\times100=-22.22% ]
Step 2: Calculate the percentage change in price.
[ \frac{12-10}{(12+10)/2}\times100 ]
[ =\frac{2}{11}\times100=18.18% ]
Step 3: Calculate price elasticity of demand.
[ E_d=\frac{-22.22%}{18.18%}\approx-1.22 ]
The signed elasticity is approximately −1.22, and its absolute value is 1.22.
Interpretation: Demand is elastic over this price range because the quantity demanded changed proportionally more than the price. The example suggests that customers are relatively responsive to the price increase.
Types of Price Elasticity of Demand
The absolute value of the calculated elasticity determines the usual classification.
Absolute elasticity
Type
Meaning
Greater than 1
Elastic demand
Quantity demanded responds proportionally more than price
Between 0 and 1
Inelastic demand
Quantity demanded responds proportionally less than price
Equal to 1
Unit elastic demand
Quantity demanded changes proportionally by the same amount as price
Equal to 0
Perfectly inelastic demand
Quantity demanded does not change in response to price
Approaches infinity
Perfectly elastic demand
Demand is infinitely responsive at a particular price in the idealized model
In practical markets, demand is rarely perfectly elastic or perfectly inelastic. Most products fall somewhere between these theoretical extremes, and elasticity can vary across different prices and market conditions.
Price Elasticity and Total Revenue
Total revenue is calculated as:
[ TR=P\times Q ]
Where (TR) is total revenue, (P) is price, and (Q) is quantity sold.
Using the retailer example:
Original revenue: $10 × 200 = $2,000
New revenue: $12 × 160 = $1,920
Revenue decreases by $80, or 4%, after the price increase. This is consistent with elastic demand over the observed range: the percentage decline in quantity was greater than the percentage increase in price.
This comparison illustrates why a business should examine both customer response and revenue rather than assuming a higher selling price automatically produces more sales income. Revenue is also different from profit, which depends on expenses and other operating costs.