Unit Elastic
What is Unit Elastic?
Unit elastic is when the percentage change in quantity demanded equals the percentage change in price.
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.
Unit Elastic: a worked example
A theater sells 500 tickets at $20, so total revenue is 500 × $20 = $10,000. Drop the price to $16 and 625 tickets sell, giving 625 × $16 = $10,000 again. Confirm with the midpoint formula. Quantity changed by 125 over an average of (500 + 625) ÷ 2 = 562.5, which is 22.2 percent. Price changed by $4 over an average of ($20 + $16) ÷ 2 = $18, which is also 22.2 percent. The coefficient is 22.2 ÷ 22.2 = 1, so demand is unit elastic across this range, and revenue is unchanged at $10,000 exactly as a value of 1 predicts. Any two points where price times quantity gives the same product behave this way.
The mistake students make with unit elastic
Unit elastic gets treated as a label for an entire curve, so students write that a straight line demand curve is unit elastic throughout. Only one point on a downward sloping straight line is unit elastic, and that is the midpoint. Everything above it is elastic and everything below it is inelastic, because elasticity compares percentages while the slope stays fixed. The other slip is reading a coefficient of 1 as meaning quantity barely responds. Quantity responds fully, just in the same proportion as price, which is why revenue holds still.
Unit Elastic questions
What happens to total revenue when demand is unit elastic?
Total revenue holds still. At a coefficient of exactly 1 the percentage gain in quantity offsets the percentage loss in price, so a small price move leaves price times quantity where it started. That is precisely why the unit elastic point sits at the top of the total revenue hill: a seller standing there can gain nothing by nudging price in either direction. Cut price any further and the seller drops into the inelastic range, where the next price cut starts shrinking revenue.
Where is demand unit elastic on a demand curve?
The midpoint of a straight line demand curve is the unit elastic point. Prices above the midpoint sit in the elastic region, where a percentage price cut brings a larger percentage quantity gain. Prices below it sit in the inelastic region. Marginal revenue equals zero at that same midpoint quantity, which is why a firm facing a downward sloping demand curve never chooses to operate in the inelastic range.
Is unit elastic the same as perfectly elastic?
Unit elastic and perfectly elastic are different cases. Unit elastic means the coefficient equals 1, the two percentage changes match, and total revenue does not move. Perfectly elastic means the coefficient is infinite, the demand curve is horizontal, and any price rise at all wipes out every sale. Unit elastic demand still slopes downward on the graph, so buyers respond to price by degrees rather than abandoning the seller entirely.
Formula / Example
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Related terms
Common comparisons
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