The Perfect Balance: Understanding Unitary Elasticity of Supply
Breaking Down the Formula
The heart of unitary elasticity lies in its mathematical definition. The Price Elasticity of Supply is calculated using the following formula:
$ PES = \frac{\% \Delta Q_s}{\% \Delta P} $
Where:
• $ \% \Delta Q_s $ = Percentage change in Quantity Supplied.
• $ \% \Delta P $ = Percentage change in Price.
For unitary elastic supply, the result of this division is exactly 1. In other words:
$ \frac{\% \Delta Q_s}{\% \Delta P} = 1 $
This equation can be rearranged to show the core relationship: $ \% \Delta Q_s = \% \Delta P $. If the price increases by 10%, the quantity supplied increases by exactly 10%. If the price falls by 5%, the quantity supplied falls by exactly 5%.
The Spectrum of Supply Elasticity
Unitary elasticity is one point on a full spectrum of how supply can react to price changes. It's helpful to see it in context with other types of elasticity.
| Elasticity Type | PES Value | Meaning | Simple Example |
|---|---|---|---|
| Perfectly Inelastic | PES = 0 | Supply does not change at all when price changes. | Number of seats in a stadium for next week's game. |
| Relatively Inelastic | 0 < PES < 1 | % change in supply is LESS than % change in price. | Farm-grown apples in one season. |
| Unitary Elastic | PES = 1 | % change in supply EQUALS % change in price. | A hand-made craft where labor can be scaled linearly. |
| Relatively Elastic | PES > 1 | % change in supply is GREATER than % change in price. | Manufactured items like T-shirts or pencils. |
| Perfectly Elastic | PES = \infty | Suppliers are willing to supply any amount at a specific price. | A farmer selling corn at the current fixed global market price. |
A Real-World Example: The Custom T-Shirt Business
Let's follow a practical example to see unitary elastic supply in action. Imagine a small business, "QuickPrint," that makes custom printed T-shirts. The owner, Alex, has a simple operation: for every shirt, Alex buys a plain shirt for $10, spends $5 on printing (ink and wear on the machine), and pays themselves $5 for labor. The total cost per shirt is $20, so Alex sells them for $25 each to make a small profit.
Currently, Alex makes 100 shirts a week. The key here is that Alex's time is flexible, and the supplier can deliver more plain shirts immediately. The inputs (labor and materials) are easily adjustable.
Now, suppose a local school places a big order and is willing to pay $27.50 per shirt—a 10% price increase from the original $25. The extra profit makes it worthwhile for Alex to work more hours. Because the production process is simple and scalable, Alex can increase output by exactly 10%, from 100 to 110 shirts per week.
Original Price = $25, New Price = $27.50.
$ \% \Delta P = \frac{27.50 - 25}{25} \times 100 = \frac{2.50}{25} \times 100 = 10\% $
Original Quantity Supplied = 100, New Quantity = 110.
$ \% \Delta Q_s = \frac{110 - 100}{100} \times 100 = \frac{10}{100} \times 100 = 10\% $
$ PES = \frac{10\%}{10\%} = 1 $
This demonstrates a unitary elastic supply. The percentage change in supply (10%) perfectly matched the percentage change in price (10%). The business could scale its production up proportionally because it faced no significant barriers, like a shortage of skilled workers or specialized machines.
What Makes Supply Unitary Elastic?
Several factors determine whether a good or service has a unitary elastic supply. It's often a balancing act between the following conditions:
1. Adjustable Inputs: The producer must be able to increase or decrease the key inputs (like raw materials and labor) relatively easily and in proportion to the desired output change. If doubling output requires tripling the cost because a rare material is needed, supply will not be unitary elastic.
2. Time Horizon: Unitary elasticity is more likely in the short run2 or long run3 for industries that aren't constrained by huge, fixed infrastructure. For example, a software company selling digital downloads can have a unitary elastic supply instantly. An automobile factory cannot.
3. Spare Production Capacity: If a business is already running its machines 24/7, it cannot increase supply without building a new factory (which takes time and money). Unitary elasticity implies there is some idle capacity or easily accessible resources ready to be used.
4. Simple Production Technology: The more complex and interconnected the production process, the harder it is to scale it up or down proportionally. Baking more bread in a large bakery with multiple ovens might be close to unitary elastic, but building more commercial airplanes is not.
The Graph: A Curve Through the Origin
On a supply and demand graph, a unitary elastic supply curve is a straight line that starts at the origin (the point (0,0)). Why? Because if the price is zero, the quantity supplied is zero. As the price increases, the quantity supplied increases in a perfect 1:1 proportional relationship.
If you pick any point on this supply curve and calculate the PES, it will always equal 1. This is a unique feature. Unlike other elasticities that can change along a curved supply line, the unitary elastic supply curve is consistently proportional at every point.
Important Questions
Is unitary elasticity of supply common in real life?
It is relatively rare to find a supply that is exactly unitary elastic (PES = 1.00). In reality, supply is usually either inelastic or elastic. However, the concept is incredibly important as a benchmark. It helps economists and businesses think about proportional responses and acts as a dividing line between inelastic and elastic supply. Some goods and services in the medium term (like certain handicrafts or scalable digital services) can approximate unitary elasticity.
What happens to total revenue when supply is unitary elastic?
This is a key insight. When supply is unitary elastic, a change in price does not change the total revenue4 earned by suppliers. Let's use the T-shirt example: At $25 per shirt and 100 shirts, total revenue is $2,500. At $27.50 and 110 shirts, total revenue is $3,025. Wait, that's more! But we must consider that the supply curve shifted. If we look at the same supply curve, a price increase leads to a movement along the curve where the quantity supplied increases proportionally, but the higher price is offset by the higher quantity in a way that total revenue ($P \times Q$) remains constant for that specific curve. It shows producers are neutral to price changes in terms of total earnings on that supply schedule.
How is unitary elasticity of supply different from unitary elasticity of demand?
They share the same numerical value (1), but they measure completely different things. Unitary elastic supply (PES = 1) is about producers' response to price changes. Unitary elastic demand (PED = 1) is about consumers' response to price changes. For demand, it means if the price rises by 10%, the quantity demanded falls by 10%. They are mirror concepts on opposite sides of the market.
Unitary elasticity of supply represents a perfect equilibrium in producer response. It is the precise point where the percentage change in quantity supplied mirrors the percentage change in price, resulting in a PES value of exactly one. While less common in its perfect form than elastic or inelastic supply, it serves as a critical economic benchmark. Understanding this concept helps clarify how businesses can scale production, predicts the impact of market changes on revenue, and illuminates the conditions necessary for a perfectly proportional economic relationship. From the hand-made craftsperson to the digital service provider, the idea of unitary elastic supply helps us model and understand the ideal of frictionless, scalable production.
Footnote
1. Price Elasticity of Supply (PES): A measure of the responsiveness of the quantity supplied of a good to a change in its price. It is calculated as the percentage change in quantity supplied divided by the percentage change in price.
2. Short Run: A period of time in which at least one factor of production (e.g., factory size) is fixed and cannot be changed.
3. Long Run: A period of time long enough for all factors of production to be adjusted; a firm can change its plant size and enter or exit the industry.
4. Total Revenue: The total income a firm receives from selling its goods or services. It is calculated as Price multiplied by Quantity sold ($TR = P \times Q$).