Unitary Elasticity: When Price and Demand Move in Perfect Step
The Core Concept: What Does PED = 1 Really Mean?
To grasp unitary elasticity, we must first understand elasticity itself. Elasticity measures how much one thing changes when another thing changes. Price Elasticity of Demand specifically measures how sensitive the quantity demanded of a good is to a change in its price.
The formula is:
$ \text{PED} = \frac{\% \text{ Change in Quantity Demanded}}{\% \text{ Change in Price}} $
Economists calculate the percentage changes to compare them fairly, regardless of whether we talk about dollars or euros, kilograms or pounds. The result, the PED number, tells us the relationship:
- If PED > 1, demand is elastic (quantity changes more than price).
- If PED < 1, demand is inelastic (quantity changes less than price).
- If PED = 1, demand is unit elastic or has unitary elasticity.
When PED equals 1, the numerator and denominator in the formula are identical. For example, if the price of a notebook rises by 10%, and as a result, students buy 10% fewer notebooks, the PED is -10% / +10% = -1. Economists often use the absolute value (ignoring the negative sign) for simplicity, so we say PED = 1.
The Revenue Consequence: Why Unitary Elasticity is a Pivot Point
The most important practical implication of unitary elasticity concerns a seller's total revenue. Total Revenue (TR)[2] is simply the price of a good multiplied by the quantity sold: $ \text{TR} = \text{Price} \times \text{Quantity} $.
Let's see how TR behaves under different elasticities:
| Elasticity Type | If Price Increases... | If Price Decreases... | Effect on Total Revenue |
|---|---|---|---|
| Elastic (PED > 1) | Quantity demanded falls more than the price rise. | Quantity demanded rises more than the price fall. | TR falls when price rises. TR rises when price falls. |
| Unitary Elastic (PED = 1) | Quantity demanded falls exactly as much as the price rises. | Quantity demanded rises exactly as much as the price falls. | TR remains unchanged. |
| Inelastic (PED < 1) | Quantity demanded falls less than the price rise. | Quantity demanded rises less than the price fall. | TR rises when price rises. TR falls when price falls. |
Unitary elasticity is the precise turning point. If a business finds itself at PED = 1, changing the price will not increase total revenue. This makes it a key consideration for companies deciding whether to have a sale or increase prices. If demand is elastic, a sale makes sense. If it's inelastic, a price hike might. But if it's unitary, neither move will change the bottom line from sales.
Visualizing Unitary Elasticity on a Demand Curve
On a standard demand curve graph, which slopes downward from left to right, unitary elasticity does not occur at every point. For a straight-line demand curve, only one point is unit elastic!
Think of a demand curve for pizza slices at your school cafeteria. At very high prices, demand is usually elastic (a small price change causes a big drop in buyers). At very low prices, demand is often inelastic (even a big price change doesn't affect buyers much). The midpoint of the straight-line demand curve is where PED = 1.
A Real-World Scenario: The Magazine Subscription Experiment
Let's walk through a detailed, realistic example to see unitary elasticity in action.
Imagine "Science Today" magazine sells digital subscriptions. Their data shows that at a price of $10 per month, they have 1,000 subscribers. They decide to test the market by raising the price to $11. After the change, they track their subscribers and find they now have 900.
Let's calculate the PED step-by-step:
- Calculate Percentage Change in Price:
New Price = $11, Old Price = $10.
Change = $11 - $10 = $1.
Percentage Change = $ (\frac{1}{10}) \times 100 = 10\% $. - Calculate Percentage Change in Quantity Demanded:
New Quantity = 900, Old Quantity = 1,000.
Change = 900 - 1000 = -100.
Percentage Change = $ (\frac{-100}{1000}) \times 100 = -10\% $. - Apply the PED Formula:
$ \text{PED} = \frac{-10\%}{+10\%} = -1 $.
Taking the absolute value, PED = 1.
Now, let's check total revenue:
- Old Revenue: $10 \times 1,000 = $10,000$.
- New Revenue: $11 \times 900 = $9,900$.
The revenues are essentially identical (the slight $100 difference is due to rounding in our percentage calculations; theoretically, they should be exactly the same). The magazine's income from subscriptions did not meaningfully change because the loss in customers perfectly offset the gain from the higher price. The publisher is at a unitary elastic point on their demand curve.
Important Questions About Unitary Elasticity
Q1: Is unitary elasticity common in the real world?
It is relatively rare to find a product that always has a PED of exactly 1. More often, a product's elasticity is around 1, or it may be exactly 1 at a specific price point for a specific group of consumers. It's a useful theoretical benchmark that helps businesses understand they are at a revenue-maximizing price. Real-world examples might include certain branded clothing items, mid-range restaurant meals, or some streaming services where consumers have many comparable alternatives.
Q2: If revenue doesn't change, why would a business care about PED = 1?
Knowing you are at PED = 1 is incredibly valuable for strategy. It tells the business that price changes are not a tool for increasing revenue from this product. Instead, to grow, they must look at other factors: reducing costs, improving the product, or marketing to shift the entire demand curve outward (making more people want the product at every price). It stops them from wasting effort on ineffective price hikes or discounts.
Q3: Can government taxes be affected by unitary elasticity?
Yes, understanding elasticity is crucial for tax policy. If a government puts an excise tax on a good with unitary elastic demand, the tax will increase the price for consumers. Because PED = 1, the percentage drop in quantity sold will match the percentage price increase caused by the tax. This means the total spending by consumers on that good (and thus the pre-tax revenue for sellers) stays the same, but part of that money now goes to the government as tax. The burden of the tax is shared in a specific way between buyers and sellers.
Footnote
[1] PED (Price Elasticity of Demand): A measure of the responsiveness of the quantity demanded of a good to a change in its price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.
[2] Total Revenue (TR): The total income a firm receives from selling its goods or services. It is calculated as the price per unit multiplied by the number of units sold (Quantity).