Elastic Demand vs Unit Elastic
Elastic Demand and Unit Elastic are two Elasticity concepts in AP Economics that students often mix up. Elastic demand is when the quantity demanded changes more than the price changes. 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 elastic demand, the percentage change in quantity demanded is greater than the percentage change in price. This means that consumers are very sensitive to price changes. Goods with many substitutes, such as luxury goods, often have elastic demand.
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.
Elastic Demand vs Unit Elastic: One Number Apart, Two Different Revenue Answers
| Elastic Demand | Unit Elastic | |
|---|---|---|
| Coefficient | Absolute value of price elasticity greater than 1, quantity responds proportionally more than price | Absolute value of exactly 1, the two percentage changes match |
| What a price change does to total revenue | Total revenue moves opposite to price, a cut raises it and a rise lowers it | Total revenue does not move in either direction, which is what makes this the peak |
| Where it sits on a straight demand curve | The upper left stretch, every point above the midpoint | The midpoint alone, one point rather than a range |
| Marginal revenue there | Positive, so selling one more unit still adds revenue | Exactly zero, which is why total revenue is at its maximum |
| Whole curve version | Only a horizontal demand curve is elastic at every point, any downward sloping straight line turns inelastic below its midpoint | A rectangular hyperbola with price times quantity constant, never a straight line |
| Where a monopolist operates | Always somewhere in this range, since marginal cost is positive and must equal a positive marginal revenue | Only at the boundary, and only in the special case of zero marginal cost, where marginal revenue of zero is optimal |
Unit elastic is a single point, elastic is a stretch of the curve
Students treat the two as parallel categories, but they behave differently on a graph. Take the linear demand curve P = 20 minus Q. Its slope is constant everywhere, and yet its elasticity is not. High up, at a price of 16 and a quantity of 4, selling one more unit is a 25 percent move in quantity against a 6.25 percent move in price, so demand is elastic there. Low down, at a price of 4 and a quantity of 16, that same one-unit change is a 6.25 percent move in quantity against a 25 percent move in price, so demand is inelastic. Unit elastic occurs at exactly one place on that line, the midpoint at a price of 10 and a quantity of 10. Elastic demand therefore names a whole region of a curve, while unit elastic names the single crossing point between two regions. The same arithmetic is why steepness never settles the question. Slope and elasticity are different quantities, and one downward sloping straight line holds elastic points, a unit elastic point, and inelastic points without its slope changing once.
The total revenue test separates them faster than the formula does
Keep the demand curve P = 20 minus Q and compute revenue at three prices. At a price of 12 the quantity is 8 and total revenue is 96. At a price of 10 the quantity is 10 and total revenue is 100. At a price of 8 the quantity is 12 and total revenue is 96 again. Revenue rose when price fell from 12 to 10, so demand was elastic over that stretch. Revenue fell when price dropped further from 10 to 8, so demand had turned inelastic. Right at a price of 10 revenue peaks, and that peak is the unit elastic point. The pattern generalizes cleanly. If price and total revenue move in opposite directions, demand is elastic. If they move together, demand is inelastic. If revenue does not budge, demand is unit elastic. When a multiple-choice question hands you a before and after price along with the matching revenues, you can answer it without computing a single percentage change, which usually saves a minute you need elsewhere.
A monopolist never chooses the inelastic range, and the boundary is the unit elastic point
Marginal revenue is positive where demand is elastic, zero where demand is unit elastic, and negative where demand is inelastic. A profit-maximizing firm produces where marginal revenue equals marginal cost, and marginal cost is positive, so marginal revenue at the chosen output has to be positive too. That pushes the firm into the elastic region of its demand curve. The unit elastic point is the exact boundary it will not cross, because beyond it another unit sold lowers total revenue while still adding cost. On the curve P = 20 minus Q, marginal revenue is 20 minus 2Q, which reaches zero at a quantity of 10, the same midpoint where revenue peaks at 100. Only a firm with zero marginal cost would produce that last unit and land exactly on the unit elastic point. A recurring exam setup gives a monopolist an elasticity below one and asks whether it is maximizing profit. The answer is no, and the correction is to raise price, since that cuts quantity and increases total revenue at the same time, which is only possible in the inelastic range.
Frequently asked questions
How do I tell elastic from unit elastic without calculating elasticity?
The total revenue test separates elastic demand from unit elastic demand in one step. Compare total revenue before and after a price change. If revenue moves in the opposite direction from price, demand is elastic over that range. If revenue does not move at all, demand is unit elastic. On the demand curve P = 20 minus Q, cutting price from 12 to 10 lifts revenue from 96 to 100, so that stretch is elastic. Cutting further from 10 to 8 pushes revenue back down to 96, so that stretch is inelastic, and the unit elastic point sits at the peak between them.
Is a unit elastic demand curve a straight 45 degree line?
Unit elastic demand across an entire curve traces a rectangular hyperbola, not a straight line, because price times quantity has to stay constant at every point on it. A quantity of 4 at a price of 30, a quantity of 6 at a price of 20, and a quantity of 12 at a price of 10 all yield revenue of 120, and plotting them produces a curve that bends toward both axes without touching either. A straight downward sloping line is unit elastic at exactly one point, its midpoint, elastic above it and inelastic below it.
Why does a monopolist avoid the inelastic part of its demand curve?
A monopolist maximizes profit where marginal revenue equals marginal cost, and marginal cost is never negative, so marginal revenue at the chosen output cannot be negative either. Marginal revenue turns negative only in the inelastic range, which rules that range out entirely. The firm stops at or before the unit elastic point, where marginal revenue equals zero. If a question states that a monopolist faces an elasticity of 0.6, the correct response is that the firm should raise its price, because doing so would cut quantity and increase total revenue at once.
Live Elasticity graph. Drag the curves, or open the full version.
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