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.
The Total Revenue Test formula
Calculator
Enter price and quantity before and after the change; get total revenue both ways and the verdict.
The price after the change (a cut from $10 to $8 in the example).
Try 110 for the inelastic case or 125 for the unit-elastic case.
Price fell while total revenue rose, opposite directions, so demand is elastic and the quantity effect wins.
- Total revenue before
- $1,000
- Total revenue after
- $1,120
- Change in total revenue
- $120
- Implied |PED| (midpoint)
- 1.5
How to calculate Total Revenue Test, step by step
- 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: Total Revenue Test
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.
Total Revenue Test 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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