Price Elasticity

Worked example

Raising the price from $10 to $12 lost 150 of 1,000 sales — an elasticity of −0.89, just inside inelastic. Revenue rose from $10,000 to $10,200. Had sales fallen to 800 instead, elasticity would be −1.22, revenue $9,600, and the rise a mistake.

How to work it out yourself

1. 1.Use the midpoint method, which is what this computes. Dividing by the starting value gives a different elasticity depending on which direction you measure, and the midpoint form gives the same answer both ways.
2. 2.Read the sign as a check, not as information. Demand elasticity is almost always negative because price and quantity move opposite ways; a positive figure means something else changed at the same time.
3. 3.Compare the absolute value to 1. Below 1 is inelastic and a price rise raises revenue; above 1 is elastic and a price rise lowers it. That crossing point is the only thing the number is for.
4. 4.Isolate the price change. Elasticity measured across a period when you also advertised, changed packaging, or hit a season is not measuring price.

Elasticity as the units sold after the rise vary

Revenue turns where absolute elasticity passes 1. Below that the price rise wins; above it the lost volume costs more than the higher price brings in, and revenue falls despite charging more.

The formula

1. Change in quantity, midpoint method(850 - 1000) / ((850 + 1000) / 2) * 100
2. Change in price, midpoint method(12 - 10) / ((12 + 10) / 2) * 100
3. Price elasticity of demand-16.216216 / 18.181818
4. Revenue before10 * 1000
5. Revenue after12 * 850
6. Change in revenue10200 - 10000

Source: US Bureau of Labor Statistics — consumer expenditure and price response data, Federal Reserve Bank of St. Louis, FRED — price and quantity series for elasticity work, OECD — glossary of statistical terms, price elasticity of demand

Questions people actually ask

What is price elasticity of demand?

The percentage change in quantity demanded divided by the percentage change in price. An elasticity of −0.89 means a 1% price rise costs 0.89% of unit sales.

What is the midpoint method and why use it?

It divides each change by the average of the before and after values rather than by the starting one. Without it, a price rise from $10 to $12 and a fall from $12 to $10 give different elasticities for the same pair of points, which is plainly wrong.

What does elastic and inelastic mean?

Elastic is an absolute elasticity above 1: buyers are sensitive, and raising the price loses more volume than it gains in margin. Inelastic is below 1 — insulin, petrol, cigarettes — where a price rise raises revenue. Exactly 1 is unit elastic, and revenue does not move.

How do I use elasticity to set a price?

If demand is inelastic you are leaving money on the table; if it is elastic, raising the price shrinks revenue. Note that revenue is not profit — with elastic demand, a price rise can cut revenue while raising profit, because you are also selling fewer units to make.

What makes demand elastic?

Substitutes above all. One brand of soap is elastic because another sits beside it; soap in general is not. Necessity, the share of income a purchase takes, and how long buyers have to react all push the same way — elasticity is always higher over a longer horizon.

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