Price Elasticity Of Demand Calculator

The same price change, measured twice, two answers

You drop the price from 200 to 160 and sales go from 1,000 units to 1,400. How sensitive is your demand?

The obvious approach is to work out both percentage changes and divide one by the other. Quantity rose 400 on a base of 1,000, so 40 percent. Price fell 40 on a base of 200, so 20 percent. Forty divided by twenty is 2, and demand is elastic.

Now measure the identical change backwards. Price went from 160 to 200, a rise of 25 percent. Quantity went from 1,400 to 1,000, a fall of 28.6 percent. That gives 1.14.

Two answers, from one price change, depending only on which end you called the start.

Nothing about the market changed. What changed is the denominator: percentage changes are always relative to wherever you started, and a rise from a small base looks bigger than the equivalent fall from a large one.

That is not a rounding nuisance. On these numbers one answer says demand is highly elastic and the other says it is barely elastic at all, and those imply different pricing decisions.

How the midpoint fixes it

The fix is to stop measuring from either end and measure from the middle of the two.

PED = [ (Q2 - Q1) / average Q ] / [ (P2 - P1) / average P ]

Both percentage changes are expressed against the average of the starting and ending values rather than against the start. Since the average does not care which point you called first, the answer no longer does either.

This is what our calculator does, and it goes by two names. Midpoint method describes the mechanics. Arc elasticity describes what it measures, which is an average across the stretch between two points rather than the sensitivity at any single price.

Run our example through it. Quantity change is 400 over an average of 1,200, which is 33.33 percent. Price change is minus 40 over an average of 180, which is minus 22.22 percent. Divide and you get -1.50.

Measure it backwards and you get -1.50 again. That symmetry is the whole reason the method exists.

The reasoning is not new. Lipsey put it that when elasticity is measured between two separate points on a demand curve, the best approximation to the correct measure is obtained by defining price and quantity as the averages of the two points. Averages give you a neutral reference that direction cannot disturb.

There is a trade-off and it is worth stating. Your answer is an average across the whole range, so it does not tell you the elasticity at any particular price inside it. On a straight line demand curve elasticity changes continuously along its length, being high at the top and low at the bottom, so an average across a wide stretch can hide a lot of variation. Use narrow ranges where you can.

Worth noting that our price elasticity of supply calculator offers both methods with a selector and defaults to the standard one. The two tools take different views, which is a fair thing to know if you are using them together.

The rule that makes this worth calculating

Elasticity is an abstraction until you connect it to money, and there is exactly one connection that matters.

Cutting the price raises total revenue when demand is elastic, and lowers it when demand is inelastic.

Which is why the calculator shows you initial revenue, final revenue and the percentage change alongside the elasticity figure. Those four numbers together answer the only question a business actually has.

The logic is a tug of war. Every price cut loses you money on the units you were already selling, and wins you money on the extra units it brings in. Which side wins depends entirely on how many extra units arrive, and that is what elasticity measures.

One caution before anybody reprices anything. This is about revenue, not profit. Selling 40 percent more units means making or buying 40 percent more units, and that costs something. A price cut can lift revenue and reduce profit at the same time. Our profit calculator is where the cost side belongs, and the two need reading together.

Three price cuts, three outcomes

Same starting point in all three: price 200, quantity 1,000, revenue 200,000. Same price cut to 160 each time. Only the response differs.

The middle row is the one to look at hardest. A twenty percent price cut that brought in a quarter more customers left revenue exactly where it started. Not approximately. Exactly zero change, and the elasticity is exactly minus one.

That is not a coincidence engineered for a worked example. Unit elasticity is defined as the point where the two effects cancel, so revenue must be unchanged whenever the figure is one, and any pair of numbers producing minus one will do it.

Which gives you a check you can run on your own data. If you have historical figures from a real price change, compute the elasticity and then look at what revenue actually did. If the sign of the revenue move disagrees with what the elasticity implies, something is wrong with one of the four inputs.

The bottom row is the one that catches people. Sales rose by ten percent and revenue fell by twelve. A price cut can be followed by more customers, more units out of the door, a busier shop, and less money.

Why the answer comes out negative

Every result from this calculator has a minus sign in front of it, and that is correct rather than a display quirk.

Demand curves slope downward. Price up, quantity down, or price down, quantity up. One of the two changes is always negative, so dividing them always gives a negative number. The sign is telling you the relationship is inverse, which for demand it essentially always is.

Now, a great many textbooks and analysts drop the sign and quote elasticity as an absolute value, so you will see the same figure written as 1.5 in one place and -1.5 in another. Both refer to identical behaviour, and mixing the conventions is harmless as long as you know which you are looking at.

Where it stops being harmless is in comparisons. Ranking products by elasticity while some figures carry signs and others do not will put the most sensitive product at the wrong end of the list. Pick one convention and hold it across everything you compare.

When people say demand is more elastic they always mean the magnitude is larger, so -2.0 is more elastic than -1.2, even though it is the smaller number.

The thresholds, stated once in signed terms: below -1 is elastic, exactly -1 is unit elastic, and between -1 and 0 is inelastic.

Why it insists the two move in opposite directions

Enter a price rise together with a quantity rise and the calculator stops, saying that if price decreases quantity must increase and the other way round.

That guard exists because the overwhelming majority of the time, price and quantity moving together means something other than elasticity is happening, and computing a positive elasticity would attach a precise number to a misunderstanding.

Three things that produce that pattern in real data.

The demand curve moved. Elasticity describes movement along a fixed demand curve. If incomes rose, a competitor closed, a season turned or an advertisement worked, the whole curve shifted and your two observations sit on different curves. This is easily the most common explanation and it is not elasticity at all.

Something else changed at the same time. You raised the price and also improved the product, extended the warranty, or moved to a better location.

The good is genuinely unusual. Economists do recognise cases where higher prices raise demand, either because the price itself signals quality or status, or because of an income effect on a staple food. These exist, they are rare, and they are not what most upward sloping data is.

So when the tool refuses, the useful response is not to force the numbers through. It is to ask what else moved between your two observations, because that is where the real answer is.

Two other things this figure cannot see, worth holding in mind. It is historical, describing a change that already happened rather than forecasting the next one. And elasticity is not fixed: it changes with the time horizon, because customers who cannot switch this week frequently can switch by next year. The same logic runs on the supply side, and our supply elasticity calculator goes into it.

Hope that makes a pricing decision a bit easier to weigh. If a figure here does not match what your own sales data did, do tell us, since that mismatch is usually informative in itself.

Questions people ask

Which formula does this use?

The midpoint method, also called arc elasticity, where both percentage changes are measured against the average of the two values rather than against the starting one. It gives the same answer whichever direction you measure.

Why is my answer negative?

Because demand curves slope down, so price and quantity always move in opposite directions and the division produces a negative number. Many sources quote the absolute value instead. Both describe the same behaviour.

What counts as elastic?

A magnitude above 1. Below 1 is inelastic, exactly 1 is unit elastic. On a signed figure, anything below -1 is elastic.

Will cutting the price raise my revenue?

If demand is elastic, yes. If it is inelastic, no, revenue falls. If it is unit elastic, revenue does not move at all. Remember this is revenue rather than profit, since more units cost more to supply.

Why will it not accept my numbers?

It requires price and quantity to move in opposite directions. If yours moved together, something other than a movement along the demand curve happened, most often a shift in the whole curve.

What is point elasticity?

Elasticity measured at a single price rather than across a range, using the standard percentage change from a base value. It is what most advanced work uses, and it is the version that gives different answers depending on direction.

Does the size of the price change matter?

Yes. Elasticity varies along a demand curve, so a figure computed across a wide range is an average that may hide considerable variation. Narrower ranges give more useful answers.

References

A note on the sources. The choice between the midpoint and point methods is not a matter of one being right, and the peer reviewed article cited below examines how inconsistently introductory economics texts handle the two, which is precisely why a calculator ought to say which it uses. The argument for averaging the two endpoints, rather than anchoring to either, is Lipsey's and is the standard justification for arc elasticity. The relationship between elasticity and total revenue is standard microeconomics and is set out in the texts below.

1. Kachaturov, R., Point Elasticity Versus Arc Elasticity: On Different Approaches to Teaching Elasticity in Principles Courses, Journal of Economics and Economic Education Research, Volume 18, Issue 2, 2017, on the inconsistent treatment of point and arc elasticity across principles textbooks. https://www.abacademies.org/articles/Point-Elasticity-Versus-Arc-Elasticity-1533-3604-18-2-111.pdf
2. Lipsey, R.G., An Introduction to Positive Economics, on measuring elasticity between two points by defining price and quantity as the averages of the two points.
3. Pindyck, R.S., and Rubinfeld, D.L., Microeconomics, Pearson, chapters on elasticity of demand, arc elasticity and the relationship between elasticity and total revenue.