Price Elasticity of Supply (PES) Calculator
This tool calculates the Price Elasticity of Supply (PES) using the percentage change in quantity supplied divided by the percentage change in price.
Enter the original and new price, and the original and new quantity supplied to find the PES value and determine if supply is elastic, inelastic, or unit elastic. All inputs must be non-negative numbers. Original Price and Original Quantity Supplied cannot be zero.
Enter Data
Understanding Price Elasticity of Supply (PES) & Formula
What is PES?
Price Elasticity of Supply (PES) measures the responsiveness of the quantity supplied of a good or service to a change in its price. It tells you how much producers change their output when the price of their product changes. A high PES means producers are very responsive to price changes; a low PES means they are not.
PES Formula
The formula for Price Elasticity of Supply is:
PES = (% Change in Quantity Supplied) / (% Change in Price)
Where:
% Change in Quantity Supplied = ((Q₂ - Q₁) / Q₁) * 100
% Change in Price = ((P₂ - P₁) / P₁) * 100
Substituting these gives:
PES = ((Q₂ - Q₁) / Q₁) / ((P₂ - P₁) / P₁)
This can be simplified to:
PES = ((Q₂ - Q₁) / (P₂ - P₁)) * (P₁ / Q₁)
Note: For supply, price and quantity usually move in the same direction, resulting in a positive PES value.
Interpreting the PES Value
- PES > 1: Elastic Supply. Suppliers can significantly increase output in response to a price rise.
- PES < 1: Inelastic Supply. Suppliers cannot easily change output in response to a price change.
- PES = 1: Unit Elastic Supply. Quantity supplied changes by the same percentage as the price.
- PES = 0: Perfectly Inelastic Supply. Quantity supplied does not change at all, regardless of price (e.g., fixed supply like land).
- PES = Infinite: Perfectly Elastic Supply. Suppliers can supply any amount at a certain price, but none below that price (theoretical).
Factors Affecting Price Elasticity of Supply
Several factors influence how elastic the supply of a good is. These include:
- Time Horizon: Supply is more elastic in the long run as producers have more time to adjust production capacity.
- Availability of Inputs: If inputs are readily available and easily sourced, supply is more elastic.
- Flexibility of Production: If firms can easily switch production between different goods, supply is more elastic.
- Storage Capacity: If goods can be easily stored, supply can be more elastic.
Uses of PES
Understanding PES is important for:
- Businesses: To predict how their supply will react to price changes or how market-wide supply will react.
- Government: To understand the impact of taxes, subsidies, or price controls on market supply.
Price Elasticity of Supply Examples
These examples demonstrate different PES values:
Example 1: Elastic Supply (PES > 1)
Scenario: The price of a new gadget increases, and manufacturers significantly ramp up production.
Known Values:
- Original Price (P₁) = $50
- New Price (P₂) = $60
- Original Quantity Supplied (Q₁) = 1000 units
- New Quantity Supplied (Q₂) = 1500 units
Calculation:
- % Change in Quantity = ((1500 - 1000) / 1000) * 100 = (500 / 1000) * 100 = 0.5 * 100 = 50%
- % Change in Price = ((60 - 50) / 50) * 100 = (10 / 50) * 100 = 0.2 * 100 = 20%
- PES = 50% / 20% = 2.5
Result: PES = 2.5
Conclusion: Since PES (2.5) is greater than 1, the supply of the gadget is **elastic**. Producers are quite responsive to the price change.
Example 2: Inelastic Supply (PES < 1)
Scenario: The price of ancient artifacts increases, but the quantity supplied cannot increase much.
Known Values:
- Original Price (P₁) = $1000
- New Price (P₂) = $1500
- Original Quantity Supplied (Q₁) = 50 pieces
- New Quantity Supplied (Q₂) = 55 pieces
Calculation:
- % Change in Quantity = ((55 - 50) / 50) * 100 = (5 / 50) * 100 = 0.1 * 100 = 10%
- % Change in Price = ((1500 - 1000) / 1000) * 100 = (500 / 1000) * 100 = 0.5 * 100 = 50%
- PES = 10% / 50% = 0.2
Result: PES = 0.2
Conclusion: Since PES (0.2) is less than 1, the supply of ancient artifacts is **inelastic**. The quantity supplied changed only a little despite a large price change.
Example 3: Unit Elastic Supply (PES = 1)
Scenario: A price change for a product leads to a proportional change in the quantity supplied.
Known Values:
- Original Price (P₁) = $20
- New Price (P₂) = $22
- Original Quantity Supplied (Q₁) = 400 units
- New Quantity Supplied (Q₂) = 440 units
Calculation:
- % Change in Quantity = ((440 - 400) / 400) * 100 = (40 / 400) * 100 = 0.1 * 100 = 10%
- % Change in Price = ((22 - 20) / 20) * 100 = (2 / 20) * 100 = 0.1 * 100 = 10%
- PES = 10% / 10% = 1.0
Result: PES = 1.0
Conclusion: Since PES (1.0) equals 1, the supply is **unit elastic**. The percentage change in quantity supplied is exactly equal to the percentage change in price.
Example 4: Perfectly Inelastic Supply (PES = 0)
Scenario: The price of land increases dramatically in a specific, limited area, but no more land can be created.
Known Values:
- Original Price (P₁) = $500,000
- New Price (P₂) = $750,000
- Original Quantity Supplied (Q₁) = 100 plots
- New Quantity Supplied (Q₂) = 100 plots
Calculation:
- % Change in Quantity = ((100 - 100) / 100) * 100 = (0 / 100) * 100 = 0%
- % Change in Price = ((750000 - 500000) / 500000) * 100 = (250000 / 500000) * 100 = 0.5 * 100 = 50%
- PES = 0% / 50% = 0
Result: PES = 0
Conclusion: Since PES is 0, the supply of land in this scenario is **perfectly inelastic**. The quantity supplied is fixed regardless of price.
Example 5: Supply response to a price decrease (Inelastic)
Scenario: The price of a perishable crop falls, and farmers can only slightly reduce the amount they bring to market in the short term.
Known Values:
- Original Price (P₁) = $5
- New Price (P₂) = $4
- Original Quantity Supplied (Q₁) = 500 kg
- New Quantity Supplied (Q₂) = 480 kg
Calculation:
- % Change in Quantity = ((480 - 500) / 500) * 100 = (-20 / 500) * 100 = -0.04 * 100 = -4%
- % Change in Price = ((4 - 5) / 5) * 100 = (-1 / 5) * 100 = -0.2 * 100 = -20%
- PES = -4% / -20% = 0.2
Result: PES = 0.2
Conclusion: Since the absolute value of PES (0.2) is less than 1, the supply of the crop is **inelastic** in the short term. The calculation gives a positive value, as expected for supply.
Example 6: Elastic Supply for Manufactured Goods
Scenario: The price of a popular toy increases, and the factory can easily run extra shifts to produce more.
Known Values:
- Original Price (P₁) = $15
- New Price (P₂) = $18
- Original Quantity Supplied (Q₁) = 2000 units
- New Quantity Supplied (Q₂) = 2800 units
Calculation:
- % Change in Quantity = ((2800 - 2000) / 2000) * 100 = (800 / 2000) * 100 = 0.4 * 100 = 40%
- % Change in Price = ((18 - 15) / 15) * 100 = (3 / 15) * 100 = 0.2 * 100 = 20%
- PES = 40% / 20% = 2.0
Result: PES = 2.0
Conclusion: Since PES (2.0) is greater than 1, the supply of the toy is **elastic**. Production can be significantly increased.
Example 7: Inelastic Supply for a Unique Service
Scenario: The price for a concert by a world-famous, unique performer increases, but they can only perform a fixed number of shows in a year.
Known Values:
- Original Price (P₁) = $200
- New Price (P₂) = $300
- Original Quantity Supplied (Q₁) = 10 shows/year
- New Quantity Supplied (Q₂) = 11 shows/year
Calculation:
- % Change in Quantity = ((11 - 10) / 10) * 100 = (1 / 10) * 100 = 0.1 * 100 = 10%
- % Change in Price = ((300 - 200) / 200) * 100 = (100 / 200) * 100 = 0.5 * 100 = 50%
- PES = 10% / 50% = 0.2
Result: PES = 0.2
Conclusion: Since PES (0.2) is less than 1, the supply of this unique service is **inelastic**. The ability to increase the number of shows is limited.
Example 8: Supply response to a price decrease (Elastic)
Scenario: The price of a non-essential manufactured good falls, and producers can easily divert resources to making something else, causing a large drop in supply.
Known Values:
- Original Price (P₁) = $25
- New Price (P₂) = $20
- Original Quantity Supplied (Q₁) = 500 units
- New Quantity Supplied (Q₂) = 300 units
Calculation:
- % Change in Quantity = ((300 - 500) / 500) * 100 = (-200 / 500) * 100 = -0.4 * 100 = -40%
- % Change in Price = ((20 - 25) / 25) * 100 = (-5 / 25) * 100 = -0.2 * 100 = -20%
- PES = -40% / -20% = 2.0
Result: PES = 2.0
Conclusion: Since the absolute value of PES (2.0) is greater than 1, the supply is **elastic**. Producers significantly reduced output in response to the price drop.
Example 9: Unit Elastic Supply with different numbers
Scenario: Another case where percentage changes are equal.
Known Values:
- Original Price (P₁) = $100
- New Price (P₂) = $90
- Original Quantity Supplied (Q₁) = 800 units
- New Quantity Supplied (Q₂) = 720 units
Calculation:
- % Change in Quantity = ((720 - 800) / 800) * 100 = (-80 / 800) * 100 = -0.1 * 100 = -10%
- % Change in Price = ((90 - 100) / 100) * 100 = (-10 / 100) * 100 = -0.1 * 100 = -10%
- PES = -10% / -10% = 1.0
Result: PES = 1.0
Conclusion: Since PES (1.0) equals 1, the supply is **unit elastic**. The percentage change in quantity supplied equals the percentage change in price.
Example 10: Perfectly Elastic Supply (Theoretical)
Scenario: A simplified model where producers will supply any amount at a specific price, but nothing below it. If the price increases even slightly, supply becomes undefined in simple percentage terms based on a single P1/Q1 point where Q1 could theoretically be 0 or very small.
Conceptual Idea: Imagine producers are willing to supply an infinite amount of bottled water at exactly $1 per bottle. If the price is $0.99, they supply zero. If the price goes to $1.01, they supply a massive quantity (theoretically infinite at that price). When Q₁ is 0, the standard percentage change formula becomes undefined due to division by zero. However, we can consider the case where P₁ and P₂ are very close, but P₁=0 is invalid for the formula. If P₁ > 0 and Q₁ > 0, but a tiny price change causes a massive quantity change, the denominator of the PES formula becomes very small relative to the numerator, making PES very large (approaching infinity).
Illustration (not calculable by tool with Q1>0, but shows concept): Price goes from $1.00 to $1.01. Quantity supplied goes from 1,000,000 to 10,000,000. %Change Q = 900%, %Change P = 1%. PES = 900. This is highly elastic, approaching infinite elasticity.
Conclusion: Perfectly elastic supply is a theoretical concept often represented by a horizontal supply curve. The PES is infinite because a tiny change in price leads to an infinitely large change in quantity supplied. It's difficult to calculate precisely using the standard formula with discrete price points unless Q1 is zero, which the calculator prevents due to division by zero.
Frequently Asked Questions about Price Elasticity of Supply
1. What is Price Elasticity of Supply (PES)?
PES measures how much the quantity supplied of a good changes when its price changes. It indicates the responsiveness of producers to price fluctuations.
2. What is the formula for PES?
The basic formula is: PES = (% Change in Quantity Supplied) / (% Change in Price).
3. What does a PES value greater than 1 mean?
A PES > 1 means supply is **elastic**. Producers can significantly increase the quantity supplied if the price rises. The percentage change in quantity supplied is greater than the percentage change in price.
4. What does a PES value less than 1 mean?
A PES < 1 means supply is **inelastic**. Producers cannot easily change the quantity supplied if the price changes. The percentage change in quantity supplied is less than the percentage change in price.
5. What does a PES value equal to 1 mean?
A PES = 1 means supply is **unit elastic**. The quantity supplied changes by the exact same percentage as the price.
6. What does a PES of 0 mean?
A PES = 0 means supply is **perfectly inelastic**. The quantity supplied remains constant regardless of the price change (e.g., unique historical artifacts, total amount of land).
7. What does an infinite PES mean?
An infinite PES means supply is **perfectly elastic**. Producers are willing to supply any amount at a specific price, but none below that price. This is often a theoretical concept.
8. Why is PES usually positive?
PES is usually positive because the supply curve slopes upward – as price increases, the quantity supplied typically also increases, and vice-versa. This means the percentage changes in quantity and price usually have the same sign, resulting in a positive ratio.
9. What factors affect the elasticity of supply?
Key factors include the time horizon (more time usually means more elastic supply), availability of inputs, flexibility of production, and ease of storage.
10. Why is knowing PES important?
It helps businesses understand how readily they can adjust production. It also helps economists and governments analyze market responses to price changes, taxes, and other policies.