Elasticity and the Total Revenue Test
A coffee shop raises its price from 4 to 5 dollars. Does total revenue go up or down?
Total revenueis the money the shop takes in — price times quantity. When the price goes up, two things happen at once: each unit sells for more (revenue up) but fewer units sell (revenue down). The winner of that tug-of-war depends on how price-sensitive customers are.
Price elasticity of demand measures that sensitivity. It is the percentage change in quantity demanded divided by the percentage change in price. If customers respond strongly to a price change (a small hike sends them packing), demand is elastic. If they barely respond, demand is inelastic.
The Total Revenue Test packages the tug-of-war into three rules:
- If a price hike raises total revenue, demand is inelastic at that price.
- If a price hike lowers total revenue, demand is elastic.
- If a price hike leaves total revenue unchanged, demand is unit elastic.
One tile of the full elasticity unit.
The course teaches elasticity interactively — drag the graphs, practice with feedback, and spaced reviews bring it back before you forget. Free.
Total revenue along a linear demand curve
What you are looking at
- Two graphs share the same horizontal axis: quantity .
- Top graph (demand): vertical axis is price . The demand line runs from top-left to bottom-right. The purple upper half is the elastic region (high prices, small quantities). The emerald lower half is the inelastic region. The midpoint is exactly unit elastic.
- The shaded rectangleon the demand graph is total revenue at the current price — literally as an area.
- Bottom graph (total revenue): vertical axis is . The inverted-U curve peaks at the same midpoint quantity, where elasticity equals one.
What to try
- Drag the price slider to move along the demand curve.
- Watch the revenue rectangle (top) change shape, and the dot on the inverted-U (bottom) trace out total revenue for each quantity.
- Notice: revenue is largest at the midpoint. From either corner, moving toward the middle always raises .
Worked example
Suppose linear demand is . Total revenue is .
At : ,
At (the midpoint): , — the peak.
At : ,
Moving from to (lowering price along the curve) raises — so demand was elastic in that range. Moving from to lowers — demand is now inelastic. The boundary is at the midpoint, where .
Common mistake
“A steeper demand curve is always more inelastic, so elasticity is the slope.” No — slope and elasticity are not the same thing. A straight line has constant slope but changing elasticity all along it. Elasticity compares percentage changes; slope compares unit changes. On a linear demand curve, elasticity is high near the top (small , tiny percentage changes go far) and falls to zero at the bottom.
Five practice questions
Pick an answer, then click Check answer to see the explanation.
Question 1 of 5
Demand for a product has elasticity (inelastic). The firm raises its price by 10%. What happens to total revenue?
Question 2 of 5
Along a linear (straight-line) demand curve, where is demand unit elastic?
Question 3 of 5
The total revenue test says: if a price increase RAISES total revenue, demand is ___.
Question 4 of 5
Insulin has very inelastic demand. A monopolist selling insulin can increase total revenue by:
Question 5 of 5
At the quantity where total revenue is maximized along a linear demand curve, the elasticity of demand is:
What the course adds
Beyond this one page
The elasticity unit teaches the midpoint and point methods, then walks through cross-price, income, and price elasticity of supply — each with interactive graphs and adaptive practice that catches the slope-vs-elasticity confusion students keep making.
Spaced reviews
FSRS brings every concept back right before you'd forget. ~50% better retention than re-reading.
Per-concept mastery
Performance Factor Analysis tracks each sub-skill separately — you see which version of the idea is still wobbly.
Diagnostic placement
A short test skips you past what you already know. No re-learning the basics.
For instructors
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Want the full elasticity unit?
The Econ Academy elasticity unit covers arc and point methods, cross-price elasticity, income elasticity, and elasticity of supply — with interactive graphs and spaced reviews tuned to you.