Price Elasticity of Demand: How to Compute and Read It

Price elasticity of demand is one number: the percentage change in quantity bought divided by the percentage change in price, both measured along a single unchanged demand schedule. Take the size and ignore the sign. Below one, buyers barely move and the good is inelastic. Above one, they move sharply. The minus sign only repeats that quantity falls when price rises.

Computed on two observations already held

The panel above at its opening setting states the whole of what follows in ordinary words. The two observations are Rs 1,800/- with 105 lakh quintals and Rs 2,200/- with 95 lakh quintals. On the midpoint basis the quantity moved minus 10.00 per cent, the price moved 20.00 per cent, and the elasticity is minus 0.50. Moving the basis to the first observation returns minus 0.43 from the same four figures; moving it to the second returns minus 0.58. The revenue reconciliation holds in all three cases because it never consults the elasticity at all: the higher price adds Rs 380 crore on the 95 lakh quintals still bought, the 10 lakh quintals no longer bought give up Rs 180 crore at the old price, and the net of Rs 200 crore is exactly Rs 2,090 crore less Rs 1,890 crore.

Here is the machinery underneath that panel. A demand schedule is a list of pairs: at this price, that quantity. Elasticity takes any two of those pairs and asks a single question. Did the quantity move by more, or by less, in percentage terms than the price did? Everything else in this guide is bookkeeping around that comparison: how to take the percentages so the answer does not depend on which row the count started from, how to read the result once it is in hand, and how to test the result a second way before it is used.

A demand schedule slopes downward, and a movement along it is a different event from a shift of the whole thing. Both of those matter here, and both are covered separately. The computation now comes apart step by step: how the two percentages are taken, how to read the result, why the choice of base changes it, how the revenue test confirms it independently, and where the two rows would come from outside a teaching example.

What are the two rows the computation starts from?

The Sankhya onion market, an invented country's invented trade, supplies the one schedule everything below is computed from. Quantity is in lakh quintals a year and price is in rupees for each quintal. A reader who loses the unit has lost the schedule, so both units sit beside every figure.

An elasticity computed across two different schedules is not an elasticity of anything, so both rows must be read off one schedule. That sounds like a technicality and it is the single most common way the computation goes wrong. Price elasticity of demandThe percentage change in the quantity bought divided by the percentage change in the price that caused it, measured between two points on one unchanged demand schedule. is a measure of how buyers respond to a price, holding everything else about those buyers still. If incomes changed between the two readings, or the price of something people eat instead of onions changed, then the second reading came off a different schedule and the resulting ratio is a mixture of two events with no name.

Reading two rows off one schedule works like a household weighing itself. A step on the scale in the morning and another in the evening, and the difference says something. A step on a different scale in the evening, and the difference says something about the scales instead. Two rows of one schedule are one scale, read twice.

How is the percentage change in quantity computed?

Take the two rows chosen above, Rs 1,800/- with 105 lakh quintals and Rs 2,200/- with 95 lakh quintals. The change in quantity is 95 less 105, or minus 10 lakh quintals. Minus 10 is a percentage of what? That question decides the whole method.

The midpoint methodA way of taking percentage changes in which each change is divided by the average of the two readings rather than by one of them, so the answer does not depend on which reading is called the start. divides by the average of the two quantities rather than by either one of them. The average of 105 and 95 is 100 lakh quintals. So minus 10 divided by 100 is minus 0.10, or minus 10 per cent. Dividing by the average rather than by the starting figure is the one decision that makes this method different from every other way of taking the same percentage. It is the setting the panel above calls the basis, and moving that control to either single reading is what the next two sections are about.

How is the percentage change in price computed?

Exactly the same way, on the other column. The change in price is Rs 2,200/- less Rs 1,800/-, or Rs 400/-. The average of the two prices is Rs 2,000/-. So 400 divided by 2,000 is 0.20, or 20 per cent. A ratio of two numbers computed on different bases is a ratio of nothing, so the two percentages must be taken by the same rule as each other. If the quantity change is divided by an average and the price change by a starting figure, the answer is a mongrel and it will not match anybody else's.

Notice what has just happened to the units. The quantity change was in lakh quintals and the price change was in rupees per quintal, and both have been turned into bare percentages. Lakh quintals cancels out of the top and rupees per quintal cancels out of the bottom. Elasticity therefore has no unit at all. A number computed on onions can be set beside a number computed on anything else without a conversion.

What does the division give on the Sankhya rows?

Divide the first percentage by the second. Minus 10 per cent divided by 20 per cent is minus 0.50. Sankhya onion demand between those two prices comes out at minus 0.50, meaning quantity moves half as far in percentage terms as the price that moved it. Every step of the arithmetic is set out below, so each division can be checked rather than the result taken on trust.

What does the number actually mean?

The result splits into two parts, and they carry completely different amounts of information. The size is 0.50 and the sign is negative, and only one of those says anything that was not already known.

The size answers the question the measure exists for. A size below one means quantity moved by less, in percentage terms, than the price did, and the good is inelasticA price elasticity whose size is below one. Buyers change the quantity they take by a smaller percentage than the price changed. over that range. A size above one means quantity moved by more and the good is elasticA price elasticity whose size is above one. Buyers change the quantity they take by a larger percentage than the price changed.. A size of exactly one is unit elasticA price elasticity whose size is exactly one. The percentage change in quantity matches the percentage change in price., and it is the hinge that the next two sections both turn on. At 0.50 the Sankhya onion market sits well inside the inelastic half, exactly where a staple food should sit. People who cook with onions keep cooking with onions when the price moves, and they adjust at the edges rather than walking away.

The minus sign is the law of demand showing up again rather than a finding about these particular buyers, and it carries almost no information. The law of demandThe general observation that a higher price is associated with a smaller quantity bought, everything else about the buyers held still. already said that quantity falls when price rises, so a negative elasticity is what every ordinary good produces and a positive one is a signal that something has gone wrong with the measurement. Practitioners therefore drop the sign in conversation and say the elasticity is 0.50 when the computed figure is minus 0.50. Dropping the sign is harmless as long as everyone at the table knows it was dropped rather than never computed.

Why use the midpoint method rather than simple percentage change?

Dividing by the average rather than by a starting figure now earns its explanation. The simple percentage method divides each change by the starting figure instead, and the same two Sankhya rows go through it in both directions.

Going up from Rs 1,800/-, the quantity change of minus 10 is measured against 105, or minus 9.52 per cent, and the price change of Rs 400/- against Rs 1,800/-, or 22.22 per cent. The division gives minus 0.43. Coming down from Rs 2,200/- instead, the quantity change of plus 10 is measured against 95, or 10.53 per cent, and the price change of minus Rs 400/- against Rs 2,200/-, or minus 18.18 per cent. The division gives minus 0.58.

The same two rows have just produced minus 0.43 and minus 0.58 depending only on which one was called the start, and the midpoint method returns minus 0.50 in either direction. That is the whole reason the midpoint method exists. The midpoint method is not a refinement and not a convention. It removes a genuine ambiguity that would otherwise let two careful people compute two different elasticities from one identical pair of rows and both be right.

There is a sharper version of this failure, and it is worth seeing because it shows the ambiguity is not merely cosmetic. Extend the same straight schedule upward, purely as the arithmetic of the line, to Rs 2,800/- with 80 lakh quintals and Rs 3,200/- with 70 lakh quintals. The simple method started from Rs 2,800/- returns 0.88 in size, a reading of inelastic. Started from Rs 3,200/- it returns 1.14, a reading of elastic. The two directions of the simple method do not merely differ by a decimal there; they land on opposite sides of the one boundary on the scale that changes what the number means. The midpoint method returns exactly 1.00 for that pair, and the next section shows why 1.00 is the answer that survives an independent test.

What does elasticity say about what happens to revenue?

Total revenueThe price multiplied by the quantity sold at that price. For a whole market it is what all buyers together hand over. in this market is the price per quintal multiplied by the quantity of quintals bought. Because the price rises while the quantity falls, revenue is a tug of war between the two, and elasticity is exactly the number that says which side wins.

Work it on the Sankhya rows at three prices, holding money in whole rupees and converting to crore only for reading. At Rs 1,800/- the quantity is 105 lakh quintals, or 1,05,00,000 quintals, and the revenue is Rs 18,90,00,00,000, or Rs 1,890 crore. At Rs 2,000/- the quantity is 1,00,00,000 quintals and the revenue is Rs 20,00,00,00,000, or Rs 2,000 crore. At Rs 2,200/- the quantity is 95,00,000 quintals and the revenue is Rs 20,90,00,00,000, or Rs 2,090 crore.

Revenue rises from Rs 1,890 crore to Rs 2,090 crore as the price rises. An elasticity of 0.50 in size predicts exactly that, and the agreement is the check. The rule in general form is short. If demand is inelastic, revenue moves the same way as price. If demand is elastic, revenue moves the opposite way. If demand is unit elastic, revenue does not move at all. Here the elasticity computation said inelastic and the revenue arithmetic, computed from the same rows but never referring to the elasticity, said revenue rises with price. Two routes, one conclusion.

An agreement that happens by luck is not a check at all, so why two independent computations agree is worth asking. The reason is short enough to follow. The midpoint test says the good is inelastic when the quantity change over the average quantity is smaller than the price change over the average price. Multiplying both sides out cancels the halves in the two averages, and expanding the brackets cancels the cross terms too. What is left is that the price times the quantity at the lower row is less than the price times the quantity at the higher row. The revenue comparison says the same thing word for word. The midpoint test rearranges into the revenue test, so the two routes must agree, and computing both is a real check on the arithmetic rather than a second opinion. If one of them is wrong the two will disagree, which is exactly what a check is for.

Why is elasticity different at different points on the same curve?

Take the four adjacent pairs on the Sankhya schedule and run the midpoint computation on each one. Every pair is a Rs 200/- step in price and a 5 lakh quintal step in quantity, so the raw movements are identical all the way down. The elasticities are not.

The size climbs steadily from 0.40 to 0.62 while the schedule itself never changes. The reason is in the two middle columns and it is purely arithmetic. The same Rs 200/- is a smaller percentage of a high price than of a low one, so the denominator shrinks with each step up. The same 5 lakh quintals is a larger percentage of a small quantity than of a big one, so the numerator grows. Both movements push the ratio the same way. Elasticity is therefore a property of a point or a range on a schedule, never a property of a good, and a sentence that says onions are inelastic without naming a price range has left out the part that made it true.

Follow the same straight line far enough and it must eventually cross into the elastic half. The Sankhya schedule sits on a line with simple arithmetic: every Rs 40/- on the price takes one lakh quintal off the quantity, and that line reproduces all five published rows exactly. Continue that line, purely as its own arithmetic and not as any additional Sankhya reading, and the point where the size reaches exactly one is Rs 3,000/- at 75 lakh quintals. Everything below that price is inelastic and everything above it is elastic, and all five rows of the Sankhya schedule sit in the lower part. Point elasticityThe elasticity measured at a single point on a schedule rather than across a range between two rows, found as the slope of the schedule scaled by the price and quantity at that point. answers at one spot rather than over a stretch, and it makes the crossing point exact rather than approximate.

Choose Rs 2,800/- and Rs 3,200/- and the midpoint elasticity lands on exactly minus 1.00 while both revenue totals read Rs 2,240 crore: the price moved and the market handed over the same amount of money. Choose Rs 3,200/- and Rs 3,600/- and the size passes one, the verdict turns elastic, and revenue falls for the first time. The boundary at a size of one is the same boundary as the point where revenue stops rising and starts falling. The two routes are one test wearing two faces.

Where would a reader find the quantities to compute it?

Sankhya offers a tidy schedule because it was built to. A real market offers transaction records and a statistical publisher, so the field notes below say where each input to this computation is physically found rather than what it means.

Why does a lender care which side of one a borrower sits on?

Picture two shops on the same street. One sells rice and dal, the other sells decorated gift boxes. Both borrow to hold stock. A bad season arrives and costs go up for both of them. The first shop raises its prices, loses a little volume and takes more money over the counter than before. A gift box is a purchase anybody can postpone, so the second shop raises its prices and watches customers simply not buy. Same street, same shock, same rupee rise in cost, and two completely different outcomes on the takings.

A lender assessing either shop is not really asking what the elasticity number is. The lender is asking what happens to the money coming in when the borrower is forced to move its price. The money coming in is what services the loan. An inelastic seller can pass a cost rise into its price and come out with more revenue. An elastic seller passing the same rise comes out with less, and the same shock reaches the two loans in opposite directions. That is why a lender looking at a borrower whose product competes on price will assume much less room to raise prices than one looking at a borrower selling something people buy in any case.

Two cautions belong with that, and both are limits of the tool. First, revenue is not profit: a seller whose revenue rises while its costs rise faster is worse off, and elasticity says nothing about the cost side at all. Second, the elasticity that matters to one shop is the elasticity of demand for that shop's own goods. A buyer who will not stop eating onions may very well cross the street to a different seller of them, so a single shop's elasticity is usually far higher in size than the elasticity of demand for the whole product across the market.

Sankhya and its onion trade are invented.
Educational material. Not advice on any investment, tax, budget or market position.