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Quantitative Foundations: Elasticity & Margins
Course contents

Module · How customers respond

How much do they care?

Lesson 3 of 5 · 10 min

Everything so far has been about your costs. But a price change does something your costs cannot predict: it changes how many people buy. Put the price up 10% and you earn more per sale and make fewer sales. Which effect wins?

There is one number that decides it.

A ratio of two percentages

elasticity=% change in quantity% change in price\text{elasticity} = \frac{\%\ \text{change in quantity}}{\%\ \text{change in price}}
Both changes are percentages, so the ratio has no units at all.

If a 10% price rise costs you 20% of your customers, elasticity is 20 ÷ 10 = 2. If it costs you 5%, elasticity is 0.5.

It is a ratio of percentages rather than of amounts for a practical reason: that makes it unit-free. An elasticity of 2 means the same thing for a $4 coffee and a $400,000 machine, so the number travels between products, markets and currencies. "We lose 300 customers per dollar" does not.

Quantity moves the opposite way to price, so the ratio is technically negative. Everyone drops the sign and talks about its size — an elasticity of 2 means 2 in the direction demand always goes.

The only three cases

Take a 10% price rise and follow the money through:

Multiply what happens to price by what happens to quantity, and the product is what happens to revenue.

2.0

Name
elastic
Customers lost
20%
Revenue effect
1.10 × 0.80 = 0.88 → −12%
Verdict
the leavers win

1.0

Name
unit elastic
Customers lost
10%
Revenue effect
1.10 × 0.90 = 0.99 → about flat
Verdict
the effects cancel

0.5

Name
inelastic
Customers lost
5%
Revenue effect
1.10 × 0.95 = 1.045 → +4.5%
Verdict
the stayers win

So the rule that matters for revenue is short:

  • Elastic (above 1). Raising the price lowers revenue. Cutting it raises revenue.
  • Inelastic (below 1). Raising the price raises revenue. Cutting it lowers revenue.

The middle row is 0.99 rather than exactly 1.00, and that is not a rounding error — elasticity is defined for small changes, and 10% is not small. Over a 1% change the same calculation gives 1.0000. Treat unit elastic as "revenue barely moves", which is all anyone needs from it.

It is not a property of the product

Here is where most people go wrong. They label a product elastic or inelastic, as though it were printed on the box. It is not. Elasticity belongs to a price, and the same product has a different one at every price it could be sold at.

Below is an ordinary demand curve — a straight line. Every $1 you add to the price costs you exactly 2 customers, all the way along. Drag the price and watch the elasticity readout.

One product, one straight demand curve

027.55582.51101021.2532.543.7555Price ($)Units sold per month
Units sold
Units sold
80
Revenue
$1,600
Elasticity here
0.50
If you add $1
$38
The line is straight, the elasticity is not constant. Low prices sit on the inelastic half, high prices on the elastic half.

Three prices are worth stopping at:

Same product, same curve, same customers — three completely different pricing situations.

$20

Units
80
Elasticity
0.50
Add $1 to the price and revenue…
rises by $38

$30

Units
60
Elasticity
1.00
Add $1 to the price and revenue…
barely moves — it falls $2

$40

Units
40
Elasticity
2.00
Add $1 to the price and revenue…
falls by $42

At $20 you are underpriced: customers barely react, so the price can go up. At $40 you are overpriced: they react more than proportionally, so the price should come down. And at $30, elasticity is exactly 1 and revenue has stopped responding at all — which is not a coincidence, and is the subject of Where the money peaks.

So when someone hands you "our elasticity is 1.4", ask at what price. It is a local reading, like a speedometer — true where it was measured, and no promise at all about somewhere else on the road.

What makes customers react

You will rarely be handed an elasticity. You can usually reason your way to roughly the right one:

there is no substitute

Demand is elastic when…
a competitor is one click away

it is a small part of the buyer's budget

Demand is elastic when…
it is a big, visible line item

it is bought out of necessity or habit

Demand is elastic when…
the purchase can simply be delayed

someone else is paying (expensed, insured)

Demand is elastic when…
the buyer spends their own money

switching is expensive or slow

Demand is elastic when…
switching costs nothing

Two consequences fall straight out of that table.

  • Governments tax inelastic things. Fuel, tobacco and alcohol carry the heaviest duties in most countries, and the reason is arithmetic rather than morality: taxing something people keep buying raises money, while taxing something they can easily drop just stops the purchases and collects little.
  • Brand-building is elasticity work. Everything a strong brand does — being the default, being trusted, being the one there is no obvious substitute for — moves its demand toward the left-hand column. That is what it buys: the ability to raise a price without emptying the room.

What you now know

One number tells you which way revenue moves when the price moves, it is local rather than permanent, and you can estimate it from how easily a customer could say no.

But revenue is not the goal. Next we put costs back in — and find that the price which maximises revenue is the wrong price.