Price elasticity of demand (PED) measures how much the quantity demanded of a good changes in response to a change in its price.
What is price elasticity of demand?
Price elasticity of demand (PED) is a fundamental concept in microeconomics used to understand consumer behavior in response to changes in prices. It refers to the degree of responsiveness or sensitivity of quantity demanded when there is a change in the price of a good or service.
Economists use PED to analyze how consumers react when prices increase or decrease. If a small change in price causes a large change in quantity demanded, the demand is said to be elastic. On the other hand, if quantity demanded changes only slightly when price changes, demand is considered inelastic.
PED is a crucial tool for businesses when making pricing decisions and for governments when considering taxation policies. By examining elasticity, firms can estimate how a change in price might impact their total revenue, and policymakers can anticipate how consumers will respond to price-based interventions.
The formula for price elasticity of demand
The basic formula used to calculate price elasticity of demand is:
PED = (Percentage change in quantity demanded) ÷ (Percentage change in price)
This can be written as:
PED = (%ΔQd) ÷ (%ΔP)
Where:
%ΔQd = Percentage change in quantity demanded
%ΔP = Percentage change in price
Since price and quantity demanded are inversely related due to the law of demand, PED values are usually negative. However, economists typically refer to the absolute value of PED to simplify interpretation. This means we ignore the negative sign and focus on the magnitude of responsiveness.
Example:
Suppose the price of a concert ticket increases from 22, and as a result, the quantity of tickets demanded decreases from 100 to 80.
Step 1: Calculate the percentage change in quantity demanded
%ΔQd = [(80 - 100) ÷ 100] × 100 = (-20 ÷ 100) × 100 = -20%
Step 2: Calculate the percentage change in price
%ΔP = [(22 - 20) ÷ 20] × 100 = (2 ÷ 20) × 100 = 10%
Step 3: Plug into the PED formula
PED = (-20%) ÷ (10%) = -2
PED = 2 (in absolute value)
This means that demand is elastic, and consumers are highly responsive to the price increase.
Why elasticity is not the same as slope
Although elasticity and slope both relate to the relationship between price and quantity, they are not the same thing. It's important to understand the distinction, especially when analyzing demand curves.
Slope:
Measures the rate of change between price and quantity.
Calculated as: Slope = Change in price ÷ Change in quantity (ΔP ÷ ΔQ)
Depends on the units used for price and quantity.
Remains constant along a linear demand curve.
Elasticity:
Measures the percentage change in quantity relative to a percentage change in price.
Is unit-free because it uses percentages, making it useful for comparing different goods or markets.
Varies along a demand curve, even if the curve is a straight line.
Because elasticity uses relative (percentage) changes instead of absolute changes, it provides a more accurate picture of how responsive consumers are at different price levels.
Example:
Suppose the price of a product increases by 10, the percentage change is 10%.
If the original price was 1,200. A 400, a 10 to $12. It expects that quantity demanded will drop from 1,000 tickets per day to 800.
%ΔQd = [(800 - 1,000) ÷ 1,000] × 100 = -20%
%ΔP = [(12 - 10) ÷ 10] × 100 = 20%
PED = (-20%) ÷ (20%) = -1 (or 1 in absolute value)
This means demand is unit elastic. A price increase will cause total revenue to remain unchanged, since the percentage decrease in quantity exactly offsets the percentage increase in price.
If the estimated PED had been greater than 1 (elastic), raising the price would reduce total revenue. If it had been less than 1 (inelastic), raising the price would increase total revenue.
Businesses routinely use such calculations to determine how to maximize revenue and set prices that match consumer responsiveness.
FAQ
Economists use percentage changes instead of absolute changes when calculating price elasticity of demand because percentage changes provide a unit-free measure that allows for meaningful comparisons across different goods, markets, and currencies. Absolute changes can be misleading since the same price or quantity change can represent very different levels of responsiveness depending on the base value. For instance, a $1 change in price is far more significant for a product that originally costs $2 than one that costs $100. By using percentage changes, economists ensure that the measurement of responsiveness accounts for the size of the initial price and quantity, making elasticity a more consistent and accurate indicator of consumer behavior. This approach avoids distortions caused by the units of measurement and allows elasticity to serve as a universal tool for analyzing demand sensitivity, regardless of the product type or economic context.
On a nonlinear (curved) demand curve, the elasticity still changes at different points along the curve, but unlike a linear demand curve, the slope is not constant. This means both the rate of change in price relative to quantity and the percentage changes vary throughout the curve. Typically, at the upper left portion of a curved demand curve, where the price is high and quantity is low, demand is elastic, just like in a linear curve. As we move down and to the right, elasticity decreases, and demand becomes inelastic. However, because the curve is not straight, the transition from elastic to inelastic may occur more gradually or unevenly, depending on the curvature. Calculating elasticity on a curved demand curve requires taking smaller intervals or using calculus in advanced economic analysis. For AP-level purposes, it’s important to recognize that elasticity can still be analyzed on a curved curve—it just won’t follow the consistent midpoint seen in linear demand curves.
Economists use the absolute value when interpreting price elasticity of demand to simplify analysis and focus on the magnitude of consumer responsiveness, rather than the direction of the change. The law of demand tells us that there is an inverse relationship between price and quantity demanded—meaning that as price increases, quantity demanded decreases, and vice versa. This inverse relationship causes the calculated PED to be negative in most cases. However, the negative sign is predictable and doesn't add much informational value when analyzing elasticity. Instead, what matters most is how large or small the change in quantity is relative to the change in price. Using the absolute value allows economists, businesses, and students to easily interpret elasticity as elastic (PED > 1), inelastic (PED < 1), or unit elastic (PED = 1) without being distracted by negative signs. This convention improves clarity when comparing elasticity across different goods or market situations.
Yes, a product can have different price elasticities of demand at different times of the year or in different markets due to changes in consumer behavior, market conditions, and availability of substitutes. For example, ice cream may have more inelastic demand in summer, when it’s in higher demand and consumers are less price-sensitive due to the weather. The same product might have more elastic demand in winter, when it’s considered a luxury or less essential, and consumers are more responsive to price changes. Similarly, the elasticity of a product like gasoline might differ between rural and urban areas. In rural areas, where there are fewer transportation alternatives, demand is more inelastic. In urban areas with access to public transportation, demand can be more elastic. These variations highlight that elasticity is not just about the product itself—it also depends on the context in which the product is being sold and consumed.
The definition of the market has a significant impact on the measured price elasticity of demand for a good because broader or narrower market definitions change the availability of substitutes. When a market is defined narrowly, such as "organic Fuji apples," there are many close substitutes (other apple varieties or fruit types), making demand more elastic. Consumers can easily switch if the price rises. In contrast, a broadly defined market like "fruit" includes many products and therefore has fewer close substitutes for the entire category, making demand more inelastic. The more specific the market definition, the more likely it is that the product will face competition from similar goods, increasing consumer responsiveness to price changes. This principle is important when businesses set pricing strategies or when governments assess the potential impact of taxation. It shows that the scope of the market under consideration directly affects how consumers respond to price fluctuations.
Practice Questions
A local coffee shop raises the price of its signature latte from 5.00. As a result, the quantity demanded falls from 200 to 150 cups per day. Calculate the price elasticity of demand and explain whether the demand is elastic, inelastic, or unit elastic. Show your work and interpret your result.
To calculate the price elasticity of demand (PED), use the formula: PED = (% change in quantity demanded) ÷ (% change in price). Quantity falls from 200 to 150, so %ΔQd = (-50 / 200) × 100 = -25%. Price increases from 5, so %ΔP = (1 / 4) × 100 = 25%. PED = -25% ÷ 25% = -1. Taking the absolute value, PED = 1. This means the demand is unit elastic, where the percentage change in quantity equals the percentage change in price. In this case, total revenue remains unchanged because the decrease in quantity offsets the price increase.
Explain why the price elasticity of demand varies along a straight-line (linear) demand curve even though the slope is constant.
The price elasticity of demand varies along a linear demand curve because elasticity is based on percentage changes in price and quantity, not on the slope itself. Even though the slope (change in price over change in quantity) is constant on a straight-line demand curve, the base values of price and quantity change at different points. At higher prices and lower quantities (upper portion), a small change in price leads to a large percentage change in quantity, making demand elastic. At lower prices and higher quantities (lower portion), the same price change causes a smaller percentage change in quantity, making demand inelastic.
