A higher price can be outweighed by fewer sales.
Total revenue is price received multiplied by quantity sold; buyer expenditure uses the price paid. When buyers pay the same price that sellers receive, these totals are equal. Taxes, subsidies or fees can create a difference between those prices, sometimes called a price wedge. Along an unchanged demand relationship, a price rise reduces revenue when demand is elastic over the relevant change, and raises it when demand is inelastic. Reverse the directions for a price fall. Constant unit-elastic demand leaves revenue unchanged. For finite two-point data, calculate revenue directly and be clear about the elasticity method: midpoint elasticity gives a consistent interval comparison, while an original-base estimate of magnitude one need not mean unchanged revenue. Revenue is not profit.
- Revenue
- Revenue is price received x quantity sold. Buyer expenditure is price paid x quantity bought. They are equal when buyers pay the same price that sellers receive.
- Unchanged demand
- Price up: elastic demand lowers revenue; inelastic demand raises it over the relevant change.
- Profit
- Profit is revenue minus costs. A revenue rise does not guarantee higher profit if costs also rise.
Revenue rules and their limits
Price decreases
Along unchanged demand, a price cut raises revenue with elastic demand and lowers it with inelastic demand over the relevant change.
Unit elasticity
If demand stays unit elastic throughout, P x Q stays unchanged. A midpoint PED magnitude of 1 between two observations also means their revenue totals are equal; it does not prove unit elasticity everywhere between them.
Comparing two actual values
Equal and opposite percentages measured from original values do not cancel when multiplied. A 20% price rise gives a price factor of 1.20; a 20% quantity fall gives 0.80. Their product is 0.96, so revenue falls by 4%.
Shifts and different buyer/seller prices
If demand shifts, the observed points may not lie on one demand curve. If buyers and sellers face different prices, calculate expenditure and revenue separately.
| Demand | Price rises | Price falls |
|---|---|---|
| Elastic | Revenue falls | Revenue rises |
| Inelastic | Revenue rises | Revenue falls |
| Unit elastic under the stated comparison | Revenue unchanged | Revenue unchanged |
Worked example: Check the numbers before recommending a price rise
Weekly sales on unchanged demand: a ticket price rises from $10 to $12 and sales fall from 100 to 80. Buyers pay the same price that the seller receives; there are no taxes, commissions or other price differences. Use midpoint percentages to calculate PED between the two observations.
- Initial revenue is $10 x 100 = $1,000. New revenue is $12 x 80 = $960, a fall of $40.
- The midpoint PED is approximately -1.22, so the interval is elastic. The loss in quantity outweighs the higher price in the revenue calculation.
- Using original bases would give +20% price and -20% quantity, hence PED -1 under that method. But 1.20 x 0.80 = 0.96: revenue is 96% of its original value. Equal and opposite original-base percentages do not guarantee unchanged revenue.
- Costs might also change when fewer tickets are sold. The revenue decrease alone does not establish the size or direction of the profit change.
Watch out for this
Price rising while sales fall always raises revenue.
Compare the price and quantity effects. When actual values are supplied, calculate both P x Q totals.
Check your understanding
Along a constant unit-elastic demand relationship, price rises from $8 to $10 and quantity falls from 150 to 120. What happens to revenue?
- It stays at $1,200.
- It rises because each unit sells for $2 more.
- Profit must stay unchanged.