Enter a price and the units sold at it, then a second price and its units. You get price elasticity of demand, whether demand is elastic or inelastic, and whether the price change raised or lowered gross profit.
The calculator uses the midpoint method, which gives the same answer whether you move the price up or down. The simple percentage change does not, and a price that falls ten percent and then rises back does not rise ten percent, it rises eleven.
Elasticity is almost always negative, because people buy less when price rises. The sign is dropped in conversation and the size is what gets discussed.
Above 1, elastic. Quantity moves proportionally more than price. A discount raises revenue.
Below 1, inelastic. Quantity moves less than price. A price rise raises revenue.
Exactly 1, unit elastic. Revenue stays flat whichever way you move.
That is the textbook reading and it is incomplete, because it is about revenue. The question a business actually cares about is gross profit, and the threshold for profit is far steeper than the threshold for revenue. In the worked example, demand is elastic, the discount raised revenue by $606, and gross profit fell by $2,193. The textbook says the discount worked. The bank account says otherwise.
| Gross margin | 10% discount needs volume up by | Implied elasticity needed |
|---|---|---|
| 20% | 100% | about -6.3 |
| 30% | 50% | about -3.8 |
| 42% | 31% | about -2.6 |
| 50% | 25% | about -2.1 |
| 70% | 17% | about -1.5 |
The table is the reason low-margin businesses should almost never discount. At 20 percent margin, a ten percent price cut has to double unit sales just to keep gross profit flat. Very few products have demand that responsive, and the ones that do tend to be commodities where competitors match the cut within a week.
High-margin products have more room, which is why software and cosmetics discount freely and grocery rarely does except as a loss-leader designed to sell something else.
The calculator needs two price points and the quantity sold at each. Getting those two numbers honestly is harder than the arithmetic.
The quantities have to come from comparable periods. A discount that ran in December against a full price that ran in February measures seasonality, not price response. The cleanest method is a split test, with the two prices shown to comparable traffic at the same time, which the A/B test calculator and sample size calculator are built for.
Advertising has to be held constant. If the discount was also promoted with extra spend, some of the volume came from the promotion rather than the price. Measure it that way and you will conclude demand is far more elastic than it is, and discount again next time.
Short periods overstate it too. A sale pulls forward purchases that would have happened later at full price. Measure the month after the promotion as well, and if sales dipped below normal, part of the lift was borrowed rather than earned.
Elastic demand means a discount raises revenue. It says nothing about whether it raises profit, and usually it does not.
The largest trap is optimising revenue. Elasticity is taught as a revenue concept, and a business that discounts whenever demand is elastic will grow its top line while shrinking its profit. Always check the gross profit row, not the revenue row.
The second is assuming elasticity is fixed. It changes with price level, with season, and with what competitors are doing. A figure measured at $60 tells you little about $40 or $90.
The third is ignoring what discounting teaches customers. A product discounted regularly trains its buyers to wait, which raises measured elasticity over time because the full-price buyers disappear. The short-term number looks like price sensitivity. It is partly a habit you created.
The last is forgetting the cost of acquisition. If each sale carries an advertising cost, that cost does not fall when the price does, and the margin that pays for it shrinks. Check the result against the break-even ROAS calculator before running the discount on paid traffic.
There is no good or bad value, only what it implies. Above 1 in size, a discount raises revenue; below 1, a price rise does. For profit the threshold is much steeper and depends on your gross margin.
Because price and quantity usually move in opposite directions. The sign is normally dropped when people discuss it, and the size is what matters.
Not necessarily. Elastic demand means revenue rises with a discount. Gross profit only rises if elasticity is steep enough to overcome the margin you gave away, which at 42 percent margin means around -2.6 for a 10 percent cut.
Test two prices on comparable traffic at the same time, hold advertising constant, and check the period after the change for pulled-forward demand. Comparing different months measures seasonality instead.
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