Price Elasticity of Supply (PES) can be calculated using numerical data to determine how responsive quantity supplied is to changes in price.
Understanding the calculation of PES
Price Elasticity of Supply (PES) is a critical concept in microeconomics that helps us understand how much the quantity supplied of a good changes in response to a change in price. Unlike demand, which focuses on consumers, PES focuses on the behavior of producers and how they adjust their production levels based on price movements.
The calculation of PES involves numerical values from either tables, graphs, or word problems. The basic formula gives the percentage change in quantity supplied relative to the percentage change in price. However, for consistency and accuracy, especially when calculating using discrete data points, we use the midpoint formula.
The basic formula for PES is:
PES = (percentage change in quantity supplied) / (percentage change in price)
This tells us, for instance, whether a 10% increase in price will lead to a more than, less than, or equal 10% increase in quantity supplied.
The midpoint formula for PES
To avoid inconsistencies depending on whether prices are increasing or decreasing, economists often use the midpoint method. This method averages the starting and ending values when calculating percentage changes. The midpoint formula is especially useful when working with limited or discrete data points.
The midpoint formula for PES is:
PES = (Q2 - Q1) / [(Q2 + Q1) / 2] ÷ (P2 - P1) / [(P2 + P1) / 2]
Where:
Q1 is the initial quantity supplied
Q2 is the new quantity supplied
P1 is the initial price
P2 is the new price
This formula can also be expressed as:
PES = (change in quantity supplied / average quantity supplied) ÷ (change in price / average price)
This format helps break the formula into clear, manageable parts and is often more intuitive for students.
The result of this calculation gives a numerical value that tells us whether supply is elastic (PES > 1), inelastic (PES < 1), or unit elastic (PES = 1).
Step-by-step method to calculate PES
Step 1: Identify the initial and new values
The first step in calculating PES is to extract the necessary values from the data provided. This can come from a table, graph, or a written scenario. You need to find:
The initial price (P1) and the new price (P2)
The initial quantity supplied (Q1) and the new quantity supplied (Q2)
Example:
P1 = 10 dollars
P2 = 12 dollars
Q1 = 100 units
Q2 = 140 units
Step 2: Calculate the changes
Next, calculate the change in quantity supplied and the change in price.
Change in quantity supplied = Q2 - Q1 = 140 - 100 = 40 units
Change in price = P2 - P1 = 12 - 10 = 2 dollars
Step 3: Calculate the averages
Now, calculate the average quantity supplied and average price.
Average quantity supplied = (Q1 + Q2) / 2 = (100 + 140) / 2 = 120 units
Average price = (P1 + P2) / 2 = (10 + 12) / 2 = 11 dollars
Step 4: Plug into the midpoint formula
Now use the formula:
PES = (change in quantity supplied / average quantity supplied) ÷ (change in price / average price)
Substitute the values:
PES = (40 / 120) ÷ (2 / 11)
First calculate the individual ratios:
40 / 120 = 0.333
2 / 11 ≈ 0.1818
Then divide:
0.333 ÷ 0.1818 ≈ 1.83
Step 5: Interpret the result
The PES value is 1.83, which is greater than 1. This indicates that supply is elastic, meaning producers are relatively responsive to changes in price.
Using graphs to estimate PES
Sometimes, data is presented visually using supply curves. In these cases, PES can be estimated by selecting two points on the curve and applying the midpoint formula using the price and quantity coordinates from those points.
Steps for reading PES from graphs:
Choose two points on the supply curve.
Determine the price and quantity supplied at each point.
Use these values to calculate PES using the midpoint method.
Even though a graph may look steep or flat, it’s important to remember that PES is not the same as the slope. While slope measures the change in quantity relative to price in absolute units, PES looks at percentage changes, making it a better tool for comparing different products or markets.
Additional examples
Example 1: Inelastic supply
A producer supplies 200 units at a price of 15 dollars. When the price increases to 16 dollars, the quantity supplied rises to 210 units.
Step-by-step:
Q1 = 200, Q2 = 210
P1 = 15, P2 = 16
Change in Q = 10
Change in P = 1
Average Q = (200 + 210) / 2 = 205
Average P = (15 + 16) / 2 = 15.5
PES = (10 / 205) ÷ (1 / 15.5)
PES ≈ 0.0488 ÷ 0.0645 ≈ 0.76
Interpretation: PES < 1, so supply is inelastic. A change in price leads to a smaller proportional change in quantity supplied.
Example 2: Unit elastic supply
Let’s modify the values so the change in quantity matches the percentage change in price.
P1 = 20, P2 = 24
Q1 = 100, Q2 = 120
Change in Q = 20
Change in P = 4
Average Q = 110
Average P = 22
PES = (20 / 110) ÷ (4 / 22)
PES ≈ 0.1818 ÷ 0.1818 = 1.0
Interpretation: PES = 1, so supply is unit elastic. The change in quantity supplied is proportional to the change in price.
Common mistakes to avoid
When learning to calculate PES, students often run into a few common errors. Avoiding these can help improve accuracy and understanding.
Not using averages: The midpoint formula relies on averaging to provide accurate results. Using only initial values can skew the percentage change.
Reversing Q1 and Q2 or P1 and P2: While it doesn’t matter which value you treat as initial or final, consistency is essential. Always subtract in the same direction.
Confusing PES with slope: Remember, slope is not elasticity. PES deals with percentage changes, which is why two supply curves with different steepness can have the same elasticity over a given range.
Forgetting to divide correctly: Ensure you divide the change by the average in both the numerator and the denominator before computing the final ratio.
Mixing up supply and demand formulas: This section focuses on supply, not demand. Be careful to apply the correct formula to the correct side of the market.
Why the midpoint formula is preferred
The midpoint formula is widely used in economics for the following reasons:
Prevents direction bias: It gives the same elasticity value regardless of whether the price is increasing or decreasing.
Ensures consistency: Using averages produces more balanced results across various data sets.
Enhances clarity: It provides a step-by-step way to calculate elasticity that avoids errors associated with calculating percent changes based on starting values alone.
Practice problem
Try this problem using the step-by-step method:
A firm’s product increases in price from 20 dollars to 25 dollars. As a result, the quantity supplied rises from 500 units to 650 units.
Step 1:
Change in Q = 650 - 500 = 150
Change in P = 25 - 20 = 5
Step 2:
Average Q = (500 + 650) / 2 = 575
Average P = (20 + 25) / 2 = 22.5
Step 3:
PES = (150 / 575) ÷ (5 / 22.5)
150 / 575 ≈ 0.2609
5 / 22.5 ≈ 0.2222
Step 4:
PES = 0.2609 ÷ 0.2222 ≈ 1.18
Interpretation: PES is greater than 1, indicating an elastic supply. The quantity supplied is relatively responsive to price changes.
How to interpret PES values
After calculating PES, it is important to understand what the number tells us. Here is a guide to interpreting different PES values:
PES > 1: Supply is elastic. A change in price results in a more than proportional change in quantity supplied.
PES < 1: Supply is inelastic. A change in price results in a less than proportional change in quantity supplied.
PES = 1: Supply is unit elastic. A change in price results in a proportional change in quantity supplied.
PES = 0: Supply is perfectly inelastic. Quantity supplied does not respond at all to price changes.
PES = infinity: Supply is perfectly elastic. Any small change in price results in an infinite change in quantity supplied.
These extreme cases are mostly theoretical but are helpful in analyzing special situations such as short-term supply constraints or perfectly competitive markets.
Tips for mastering PES calculations
Practice regularly: Try using different numbers and scenarios to get familiar with the formula.
Label every step: Clearly marking each stage of the process helps track your logic and avoid errors.
Understand the concept behind the math: Don’t just memorize the formula—know what it represents.
Double-check calculations: Small mistakes in averaging or dividing can lead to incorrect PES values.
Use real-world examples: Think of agricultural products, technology goods, or labor-intensive industries to understand how PES applies to different contexts.
FAQ
PES values should always be reported as positive numbers, even though mathematically, a negative value may appear if the direction of change is calculated incorrectly. This confusion often arises when students subtract the new quantity from the old one or the new price from the old in reverse order. However, by convention in economics, elasticity of supply is always positive because there is a direct relationship between price and quantity supplied. As price increases, quantity supplied typically increases, and as price decreases, quantity supplied decreases. If you obtain a negative result, double-check the order of your inputs in the formula. Make sure that the change and average values are correctly calculated, and always report the absolute value of PES. The sign does not affect whether supply is elastic or inelastic—it’s the magnitude of the result that determines elasticity.
When calculating PES over a large price range, the percentage changes in price and quantity supplied are more substantial, which can affect the accuracy of the results if you don’t use the midpoint formula. Larger intervals may include segments where elasticity varies, especially if the supply curve is non-linear. In such cases, the elasticity may shift from inelastic to elastic as price and quantity increase, making it an average elasticity over that range rather than a point-specific measure. For small price ranges, PES tends to be more precise and representative of local responsiveness, especially on linear supply curves. Smaller intervals better reflect producer behavior around a particular price level. That’s why economists often use point elasticity (calculated with derivatives) for theoretical work and midpoint elasticity for real-world, discrete data. Using small intervals generally yields more accurate insights into producer responsiveness in a given market situation.
If either the initial or new value of price or quantity supplied is zero, calculating PES becomes mathematically problematic, particularly with the midpoint formula, because you would be dividing by zero when finding the average. This leads to undefined or misleading results. Economists avoid calculating elasticity from or to zero because a zero price or zero quantity implies an extreme or theoretical condition (like a perfectly elastic or inelastic supply), which is rare in real-world markets. In practical analysis, PES should be calculated between two positive, non-zero values. If you encounter a zero in the data, consider whether the good is newly introduced, discontinued, or subject to a market failure. In those cases, the elasticity concept still applies, but it’s better addressed through qualitative analysis or by using approximate values rather than direct computation. Always ensure values used are realistic and interpretable in economic context.
Two goods can have the same PES value even if they come from different industries because elasticity depends on relative responsiveness, not the absolute quantity or price. PES measures the percentage change in quantity supplied relative to the percentage change in price, so the scale of the market or product doesn’t matter as much as the behavior of producers. For example, a tech company and a clothing manufacturer might both have a PES of 1.5 if each increases supply by 15% in response to a 10% price increase. Despite differences in production processes, capital requirements, or market structure, they are similarly responsive to price changes. This is why PES allows economists to compare producer behavior across industries. However, while the values may match, the reasons behind their elasticity may differ significantly due to factors like production flexibility, input availability, or inventory capacity.
PES is not fixed for a good—it can change over time due to shifts in production conditions, technology, input availability, or market expectations. In the short run, supply is often more inelastic because producers have limited flexibility to adjust inputs like labor, machinery, or raw materials. However, in the long run, firms can invest in capacity expansion, adopt new technologies, or enter/exit the market, making supply more elastic. For example, farmers may not be able to increase crop production instantly, but over several seasons they can plant more land or switch crops. Understanding how PES evolves matters for policy decisions and business strategy. For instance, if supply is expected to become more elastic over time, a temporary price spike may not justify long-term investment. Similarly, governments may delay taxes or subsidies if they expect producers to adjust more effectively later. PES is dynamic, and analyzing its changes helps anticipate market behavior under different time frames.
Practice Questions
A firm increases the price of its product from 12, leading the quantity supplied to rise from 100 units to 130 units. Using the midpoint formula, calculate the price elasticity of supply (PES), and identify whether the supply is elastic, inelastic, or unit elastic.
To calculate PES, use the midpoint formula: PES = (change in quantity supplied / average quantity supplied) ÷ (change in price / average price). The change in quantity is 30, average quantity is 115, change in price is 2, and average price is 11. PES = (30 / 115) ÷ (2 / 11) = 0.2609 ÷ 0.1818 ≈ 1.43. Since PES is greater than 1, supply is elastic. This means that the quantity supplied is relatively responsive to changes in price, indicating that producers are able to adjust output efficiently in response to price changes within this range.
Explain why the midpoint formula is used when calculating the price elasticity of supply rather than a simple percentage change formula.
The midpoint formula is preferred because it avoids directional bias by calculating percentage changes using the average of the starting and ending values. A simple percentage change depends on whether the price increases or decreases, leading to inconsistent PES values for the same data. The midpoint method ensures that the elasticity remains consistent regardless of the direction of change. This provides a more accurate and objective measure of responsiveness, especially when analyzing data from two distinct points. It standardizes the calculation, making comparisons between different goods, time periods, or markets more reliable and fair.
