Unit Elastic vs Inelastic Demand
Unit Elastic and Inelastic Demand are two Elasticity concepts in AP Economics that students often mix up. Unit elastic is when the percentage change in quantity demanded equals the percentage change in price. Inelastic demand is when the quantity demanded changes less than the price changes. Here is how they compare side by side.
In unit elastic demand, the percentage change in quantity demanded is equal to the percentage change in price. This means that the percentage change in total revenue from sales equals zero. Unit elastic is the midpoint between elastic and inelastic demand.
In inelastic demand, the percentage change in quantity demanded is less than the percentage change in price. This means that consumers are not very sensitive to price changes. Goods with few substitutes, such as necessities, often have inelastic demand.
Unit Elastic vs Inelastic Demand: The Break Even Point and Everything Below It
| Unit Elastic | Inelastic Demand | |
|---|---|---|
| Elasticity coefficient, absolute value | Exactly 1 | Between 0 and 1 |
| Size of the quantity response | The same percentage as the price change | A smaller percentage than the price change |
| Total revenue after a price rise | Unchanged | Rises |
| Total revenue after a price cut | Unchanged | Falls |
| Marginal revenue there | Zero | Negative |
| Position on a straight line demand curve | The midpoint, and nowhere else | The lower right stretch, below the midpoint |
| What it tells a seller about pricing | Revenue is at its peak, so look at costs instead | Raising the price raises revenue and cuts output, so profit rises too |
Watch the revenue figure and the two cases separate immediately
Start with an illustrative subscription priced at $10 with 60 buyers. Raise it to $12 and suppose 50 buyers stay. Using the midpoint method, price changes by 2 over the average of 11, which is 18.18 percent, and quantity changes by 10 over the average of 55, which is also 18.18 percent. The coefficient is exactly 1, so demand is unit elastic over that stretch. Revenue is unmoved: 10 times 60 is $600, and 12 times 50 is also $600. The seller has traded 10 of her 60 buyers for a fifth on the price and landed in precisely the same place. Now suppose only 6 buyers leave rather than 10, so quantity goes from 60 to 54. Quantity changes by 6 over the average of 57, which is 10.53 percent, against the same 18.18 percent price change, giving a coefficient of about 0.58. Demand is inelastic, and revenue rises from $600 to $648. The direction of the revenue figure is doing the work here, not its size, and the two rows of the table follow from that single arithmetic fact. Test other pairs at /calculate/midpoint-method.
Unit elastic is one point on a normal demand curve, not a description of it
Take demand given by quantity equals 120 minus 10 times the price, a straight line meeting the price axis at $12 and the quantity axis at 120 units. Its midpoint sits at a price of $6 and a quantity of 60, where revenue is $360. Move up to $7 and quantity falls to 50, giving $350. Move down to $5 and quantity rises to 70, giving $350 again. Revenue peaks at the midpoint and falls away on both sides, which is the signature of unit elasticity sitting at exactly one place. Above that price the curve is elastic, below it the curve is inelastic, and the coefficient runs all the way from very large near the price axis to nearly zero near the quantity axis. So a straight demand curve is never inelastic as a whole, and never unit elastic as a whole either. The only curve that is unit elastic everywhere is the one where price times quantity is constant, which bends rather than running straight. Whenever a question calls a demand curve inelastic, check which stretch it means. The revenue link is set out at /glossary/total-revenue-test.
Frequently asked questions
What is the difference between unit elastic and inelastic demand?
Unit elastic demand has a coefficient of exactly 1, so quantity changes by the same percentage as the price and total revenue stays flat, while inelastic demand has a coefficient between 0 and 1, so quantity moves less than the price and revenue follows the price. Unit elasticity is the dividing line and inelastic demand is everything below it. On a straight line demand curve the unit elastic case occupies a single point.
What happens to total revenue when demand is unit elastic?
Total revenue does not change, because the percentage gain from the new price exactly cancels the percentage loss in quantity. A seller raising the price loses just enough customers to offset the extra charged to those who remain. This makes the unit elastic point the peak of the revenue curve on a straight line demand curve.
Can a straight line demand curve be unit elastic everywhere?
No, a straight line is unit elastic only at its midpoint, elastic above it and inelastic below it. Constant slope does not mean constant elasticity, because elasticity compares percentage changes and the base values shift as you move along the line. A demand curve that is unit elastic at every point has to be curved.
Live Elasticity graph. Drag the curves, or open the full version.
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