How to Use the Total Revenue Test for Elasticity
Total revenue test: if price and total revenue (P × Q) move in opposite directions demand is elastic; together, inelastic; if TR is unchanged, unit elastic.
Formula
Steps
- 1Compute total revenue before the price change. TR₁ = old price × old quantity sold.
- 2Compute total revenue after the price change. TR₂ = new price × new quantity sold.
- 3Compare the direction of P and TR. If price and TR moved in opposite directions, demand is elastic (|PED| > 1); if they moved together, inelastic (|PED| < 1).
- 4Check the unit-elastic case. If TR is exactly unchanged, demand is unit elastic (|PED| = 1) over that range.
Worked example
Price falls from $10 to $8 and quantity rises from 100 to 140: TR goes from 10 × 100 = $1,000 to 8 × 140 = $1,120. TR rose as price fell → elastic. If quantity had risen only to 110, TR = 8 × 110 = $880 — TR fell with price → inelastic. If quantity rose to 125, TR = 8 × 125 = $1,000, unchanged → unit elastic.
Frequently asked questions
Where is total revenue maximized on a linear demand curve?
At the midpoint of the demand curve, where demand is unit elastic. Above the midpoint demand is elastic (cutting price raises TR); below it demand is inelastic (cutting price lowers TR).
Why does raising price lower revenue when demand is elastic?
When demand is elastic, the percentage drop in quantity is larger than the percentage rise in price, so the quantity effect outweighs the price effect and P × Q falls.
Does the total revenue test give an exact elasticity number?
No — it only classifies demand as elastic, inelastic, or unit elastic over a price range. To get a number, use the midpoint formula: PED = %ΔQ ÷ %ΔP.
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