Understanding how to calculate price elasticity of demand (PED) using numerical data is essential for analyzing how quantity demanded responds to price changes in real-world situations. This skill allows economists, businesses, and students to measure consumer responsiveness and apply this knowledge to pricing decisions.
What is price elasticity of demand?
Price elasticity of demand (PED) is a numerical measure that indicates how sensitive the quantity demanded of a good is to a change in its price. It helps to answer a fundamental economic question: If the price of a product changes, by how much will the quantity demanded change in response?
The general formula for PED is:
PED = (Percentage change in quantity demanded) ÷ (Percentage change in price)
This value is typically a negative number due to the law of demand—as price increases, quantity demanded usually decreases, and vice versa. However, when interpreting PED, we use the absolute value to classify elasticity.
In this section, we focus on how to calculate PED using numerical data, both from data sets and from graphs, and introduce the midpoint formula, which provides a more accurate calculation when prices and quantities change by larger amounts.
Calculating PED from numerical data
Often, you will be given two sets of data points: the original and the new price of a good, and the corresponding original and new quantity demanded. With this information, you can use the standard percentage change method to calculate PED.
Step-by-step method for the percentage change formula
Identify the initial and new prices (P1 and P2).
Identify the initial and new quantities demanded (Q1 and Q2).
Calculate the percentage change in quantity demanded:
(Q2 - Q1) ÷ Q1 × 100Calculate the percentage change in price:
(P2 - P1) ÷ P1 × 100Use the formula:
PED = (Percentage change in quantity demanded) ÷ (Percentage change in price)
Example using the percentage change formula
Suppose the price of a chocolate bar increases from 2.50, and as a result, the quantity demanded falls from 120 units to 100 units.
Step 1: Calculate the percentage change in quantity demanded:
(100 - 120) ÷ 120 × 100 = (-20 ÷ 120) × 100 = -16.67%Step 2: Calculate the percentage change in price:
(2.50 - 2.00) ÷ 2.00 × 100 = (0.50 ÷ 2.00) × 100 = 25%Step 3: Use the PED formula:
PED = -16.67 ÷ 25 = -0.67
Using the absolute value, PED = 0.67, which indicates that the demand is inelastic.
Why use the midpoint formula?
The basic percentage change formula has a major drawback: it gives different results depending on the direction of the change. For example, increasing price from 2.50 and decreasing from 2 can yield different elasticity values, even though it’s the same movement along the demand curve.
To avoid this inconsistency, economists use the midpoint formula. This approach uses the average of the initial and final values as the base when calculating percentage changes.
The midpoint formula for PED
The midpoint formula is written as:
PED = (Change in quantity demanded ÷ Average quantity demanded) ÷ (Change in price ÷ Average price)
Where:
Change in quantity demanded = Q2 - Q1
Average quantity demanded = (Q2 + Q1) ÷ 2
Change in price = P2 - P1
Average price = (P2 + P1) ÷ 2
This formula provides a consistent elasticity value regardless of whether price increases or decreases.
Example using the midpoint formula
Imagine the price of a movie ticket rises from 12, and the quantity demanded falls from 300 tickets to 250 tickets.
Change in quantity demanded = 250 - 300 = -50
Average quantity demanded = (250 + 300) ÷ 2 = 275
Change in price = 12 - 10 = 2
Average price = (12 + 10) ÷ 2 = 11
Now, apply the formula:
PED = (-50 ÷ 275) ÷ (2 ÷ 11)
PED = -0.1818 ÷ 0.1818 = -1
Taking the absolute value, PED = 1, indicating that demand is unit elastic.
Applying PED calculations to data scenarios
Let’s walk through another example with a different data set.
Suppose a bakery increases the price of a loaf of bread from 3.60, and the daily quantity demanded falls from 500 loaves to 440 loaves.
Change in quantity demanded = 440 - 500 = -60
Average quantity demanded = (500 + 440) ÷ 2 = 470
Change in price = 3.60 - 3.00 = 0.60
Average price = (3.60 + 3.00) ÷ 2 = 3.30
Now plug into the midpoint formula:
PED = (-60 ÷ 470) ÷ (0.60 ÷ 3.30)
PED = -0.1277 ÷ 0.1818 ≈ -0.70
Absolute value = 0.70, so the demand is inelastic.
This result indicates that consumers are not very responsive to the price change—demand decreases, but not drastically.
Calculating PED using graphs
Graphs are another common source for PED calculations. If a demand curve graph provides two points—each with a price and quantity combination—you can apply the midpoint formula the same way as with numerical data.
Step-by-step method using a demand curve graph
Identify two points on the demand curve:
Point A: Price = P1, Quantity = Q1
Point B: Price = P2, Quantity = Q2
Find:
Change in quantity demanded = Q2 - Q1
Average quantity demanded = (Q1 + Q2) ÷ 2
Change in price = P2 - P1
Average price = (P1 + P2) ÷ 2
Plug values into the midpoint formula.
Example from a demand graph
A demand curve shows that when the price of a T-shirt falls from 25, the quantity demanded increases from 100 to 140 units.
Change in quantity demanded = 140 - 100 = 40
Average quantity demanded = (140 + 100) ÷ 2 = 120
Change in price = 25 - 30 = -5
Average price = (30 + 25) ÷ 2 = 27.5
Now calculate PED:
PED = (40 ÷ 120) ÷ (-5 ÷ 27.5)
PED = 0.3333 ÷ -0.1818 ≈ -1.83
Absolute value = 1.83, so demand is elastic.
This means consumers are highly responsive to price changes—when the price drops, demand increases significantly.
FAQ
The midpoint formula is preferred because it eliminates the problem of getting different elasticity values depending on the direction of the price change. When using the basic percentage change method, if you calculate PED based on a price increase from $10 to $12, you get a different result than if you calculate PED based on a price decrease from $12 to $10. This inconsistency occurs because the basic method uses the original price and quantity as the base, which skews the percentage change depending on which point is chosen as the starting point. The midpoint formula solves this by using the average of the initial and final values for both price and quantity, which provides a consistent base regardless of the direction of the change. This makes it especially useful for analyzing large changes in price or quantity and ensures fairness and accuracy in elasticity comparisons. That’s why AP Microeconomics students are strongly encouraged to use it.
When a good has a price elasticity of demand equal to zero, it means that the quantity demanded does not change at all in response to a change in price. This is known as perfectly inelastic demand. From a data perspective, you could see a situation where the price of a good rises or falls, but the quantity demanded remains exactly the same. For example, if the price of insulin increases from $100 to $120, but the quantity demanded stays at 1,000 units, the change in quantity is zero. Using the formula PED = (change in quantity / average quantity) ÷ (change in price / average price), the numerator would be zero, which leads to a PED of 0. This tells us that consumers will buy the same amount regardless of price. Such cases usually apply to essential goods with no substitutes, and this concept is important when considering revenue effects or regulatory pricing decisions in necessary markets.
Yes, the price elasticity of demand can change for the same product depending on the price range or position on the demand curve. This happens because elasticity is not constant along a linear demand curve—it varies based on where you are measuring. At higher prices and lower quantities, consumers tend to be more sensitive to price changes, so elasticity is higher (more elastic). At lower prices and higher quantities, consumers are less sensitive to price changes, making elasticity lower (more inelastic). When using the midpoint formula to calculate PED over different intervals of a demand schedule or curve, you can observe how the value changes. For instance, reducing the price from $100 to $90 may produce a higher elasticity than reducing it from $30 to $20. Even though the slope of the curve might be constant, elasticity depends on relative percentage changes, so calculating it over different sections reveals varying consumer responsiveness at different price levels.
When using the midpoint formula, it does not matter which set of values you assign as Q1 and Q2 or P1 and P2, because the formula uses averages, making it direction-neutral. You can assign the original values as Q1 and P1, and the new values as Q2 and P2, or reverse them—it will produce the same final elasticity result. This is a key benefit of the midpoint method over the basic percentage change method. What’s important is being consistent in your calculation. For example, if you assign the starting price as P1 and the new price as P2, then you must assign the corresponding quantities correctly as Q1 and Q2. What’s being calculated is the relative change, not the absolute starting point. Always double-check the direction of the price and quantity change to make sure your signs make sense in intermediate steps, but remember: the final PED is interpreted using the absolute value.
A PED value between 0 and 1 indicates that the good is inelastic, meaning that quantity demanded is relatively unresponsive to price changes. In other words, a percentage change in price results in a smaller percentage change in quantity demanded. From a business perspective, this has important implications for pricing strategy. If a firm knows the demand for its product is inelastic, it can safely increase prices without losing a large portion of sales volume. This often leads to an increase in total revenue, because the smaller drop in quantity sold is outweighed by the higher price per unit. This type of elasticity is commonly found in necessities or goods with few substitutes. Businesses rely on elasticity calculations from market data or past sales to identify these situations. For example, if increasing price from $5 to $6 results in quantity falling from 1,000 to 950, the PED would be less than 1. This helps firms confidently adjust prices to maximize revenue.
Practice Questions
The price of a gym membership increases from 50 per month. As a result, the number of memberships sold falls from 200 to 160. Calculate the price elasticity of demand using the midpoint formula and classify the demand as elastic, inelastic, or unit elastic. Show your work.
To calculate PED using the midpoint formula:
Change in quantity = 160 - 200 = -40
Average quantity = (200 + 160) / 2 = 180
Change in price = 50 - 40 = 10
Average price = (50 + 40) / 2 = 45
PED = (-40 / 180) ÷ (10 / 45) = -0.222 ÷ 0.222 = -1
Taking the absolute value, PED = 1. Since PED equals 1, the demand is unit elastic. This means that the percentage change in quantity demanded is exactly proportional to the percentage change in price.
A streaming service decreases its monthly subscription fee from 9, and its number of subscribers increases from 10,000 to 13,000. Calculate the price elasticity of demand using the midpoint formula and explain what this implies about consumer responsiveness.
Change in quantity = 13,000 - 10,000 = 3,000
Average quantity = (13,000 + 10,000) / 2 = 11,500
Change in price = 9 - 12 = -3
Average price = (12 + 9) / 2 = 10.5
PED = (3,000 / 11,500) ÷ (-3 / 10.5) ≈ 0.2609 ÷ -0.2857 ≈ -0.91
Taking the absolute value, PED ≈ 0.91, which means demand is inelastic. This implies that consumers are somewhat responsive to the price change, but not enough for the percentage change in quantity to exceed the percentage change in price.
