How To Calculate Price Elasticity Of Demand

Price elasticity of demand is the ratio of how much quantity moves to how much price moved. It is normally negative, because raising a price usually reduces how much people buy, and the size of that negative number is what matters.

An elasticity between 0 and minus 1 is called inelastic: quantity moves less than price, in percentage terms. Raising price then raises total revenue, because the margin on each unit grows faster than the volume shrinks.

Below minus 1 is elastic: quantity moves more than price. Raising price in that region destroys revenue, and cutting price wins more than enough extra volume to pay for the lower margin.

Exactly minus 1 is the boundary, and revenue is at its maximum there. That is the practical reason to care about the number: it tells you which side of the revenue peak your current price sits on.

The sign convention varies. Economists often quote the absolute value and say demand is elastic when it exceeds one. Engineers and analysts more often keep the minus sign so the direction is unambiguous. Both appear in the literature.

The simplest version uses two observed points. Compute each percentage change against its own starting value, then divide. That is fine for small changes and is what most people mean by the term.

Its weakness is asymmetry: going from 20 to 22 is a 10 percent rise, but coming back from 22 to 20 is only a 9.0909 percent fall, so the same pair of prices gives different answers depending on direction.

The arc elasticity fixes that by measuring both changes against the midpoint rather than the endpoints. On the same data it gives minus 1.3404 against the minus 1.2 of the endpoint method, which is a material difference.

Which one you use should be stated. For pricing decisions over a modest range the difference rarely changes the conclusion, but for large moves it can, and mixing the two across a series makes the numbers incomparable.

Elasticity is not a constant of nature. It varies along the demand curve, differs by customer segment, and changes with the time allowed for buyers to adjust, so a figure measured over one period is only valid near it.

Time is the most underrated factor. Immediately after a price rise demand often looks inelastic because buyers have not yet found substitutes; over a year the same change can look considerably more elastic.

For the running example, price goes from 20 to 22, a rise of 10 percent, and units fall from 1,000 to 880, a fall of 12 percent.

Dividing gives minus 1.2, which is elastic. Revenue confirms it: 20,000 before and 19,360 after, a fall of 3.2 percent.

That revenue check is the practical test. Whatever the elasticity says, if total revenue falls after a price increase, the price increase lost money at these margins and volumes.

The arc version gives minus 1.3404 on the same data, which is more elastic still, and both numbers point the same way here. When they disagree, prefer the arc measure for larger price moves.