Perfectly Inelastic vs Unit Elastic
Perfectly Inelastic and Unit Elastic are two Elasticity concepts in AP Economics that students often mix up. Perfectly inelastic demand is when any change in price leads to no change in quantity demanded. Unit elastic is when the percentage change in quantity demanded equals the percentage change in price. Here is how they compare side by side.
In perfectly inelastic demand, consumers are completely insensitive to price changes. This means that changes in price have no effect on the quantity demanded. Perfectly inelastic demand is a theoretical concept that is not often observed in real markets.
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.
Perfectly inelastic demand vs unit elastic demand
| Feature | Perfectly Inelastic | Unit Elastic |
|---|---|---|
| Price elasticity of demand | Exactly 0 | Exactly 1 in absolute value |
| Shape of the curve | A vertical line sitting at one quantity | A curve bending toward both axes so price times quantity never changes |
| Quantity when price goes from $40 to $50 | Stays at 500 units | Falls from 500 units to 400 |
| Total revenue over that same rise | Climbs from $20,000 to $25,000 | Holds at $20,000 |
| Who carries a $5 per unit tax | Buyers pay the whole $5 and quantity holds steady | Buyers and sellers split it and quantity drops |
| Where you meet it | Short-run demand for a required medicine or a good with no substitute | The midpoint of a straight-line demand curve |
| Advice to a firm setting price | Raise the price and revenue follows it up | Price changes leave revenue where it is, so moving it gains nothing |
Zero response versus a matching response
Perfectly inelastic demand carries a price elasticity of 0, so quantity does not move at all when price changes. Unit elastic demand carries an elasticity of exactly 1, so quantity moves by the same percentage as price, in the opposite direction. That one number is the whole difference, and it drives everything else on this page. Run the same price change through both. A seller lifts price from $40 to $50. By the midpoint formula the percentage change in price is $10 over the average price of $45, which is 22.2%. On a perfectly inelastic curve, buyers take 500 units before and 500 units after, so the percentage change in quantity is 0 and the elasticity is 0 divided by 22.2%, or 0. On a unit elastic curve, quantity slides from 500 to 400. That 100 unit drop over an average quantity of 450 is also 22.2%, so the elasticity is 22.2% over 22.2%, or exactly 1. The two curves look nothing alike. Perfectly inelastic demand is a vertical line, because the same quantity clears at every price. Unit elastic demand bends toward both axes without touching them, because price times quantity has to hold constant along the entire curve.
Revenue and tax burden pull opposite ways
Revenue is the fastest way to tell them apart from a table of numbers. Perfectly inelastic demand hands the seller every cent of a price rise: 500 units at $40 brings $20,000, and the same 500 units at $50 brings $25,000. Unit elastic demand hands over nothing: 400 units at $50 is $20,000 again, the same total as before. Any price along a unit elastic curve returns identical revenue, which is why the unit elastic point on a straight-line demand curve marks the peak of the revenue hill. A per unit tax splits the same way. Levy $5 a unit on a good with perfectly inelastic demand and buyers swallow all $5, since they purchase 500 units whatever the price says. No sale disappears, so nothing is lost on the quantity side. Levy that same $5 on a unit elastic good and sellers give up part of it, because buyers walk away as the price climbs. Sales shrink, and the trades that vanish are the deadweight loss. Neither case describes a whole real curve. Perfect inelasticity is a short-run claim about a narrow price range for something a buyer cannot skip, such as a prescribed dose of medicine. Unit elasticity is a benchmark an ordinary demand curve passes through exactly once. The definition and worked figures sit at /glossary/unit-elastic.
Frequently asked questions
Can a real demand curve be perfectly inelastic at every price?
No. Buyers eventually run out of money or find a substitute, so a vertical demand curve is an approximation that holds over a limited price range and a short window. A medicine at $30 a vial and the same medicine at $900 a vial will not draw the same quantity. Treat perfect inelasticity as a claim about a range, not about the whole curve.
Is a unit elastic demand curve just a straight line?
No. A straight-line demand curve takes a different elasticity at every point: elastic above the midpoint, unit elastic exactly at the midpoint, inelastic below it. A curve that is unit elastic the whole way along has to bend toward both axes so that price multiplied by quantity stays constant.
How do I spot each one from a total revenue table?
Compare the direction of revenue with the direction of price. Revenue moving the same way as price means elasticity below 1, and 0 is the extreme version of that. Revenue holding steady while price moves means elasticity of exactly 1. Revenue moving the opposite way from price means demand is elastic.
Live Elasticity graph. Drag the curves, or open the full version.
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