Econ Lab · Markets

Elasticity

Raise the price of coffee by ten percent. Do buyers shrug and keep drinking, or do half of them walk away? That responsiveness is elasticity, and it decides almost everything practical about a market: who absorbs a tax, whether a price rise helps or hurts a cafe's takings.

Drag the dot down the demand curve and watch the number change.

024680100200300400
Cups of coffee\text{Cups of coffee}
Price per cup ($)\text{Price per cup (\$)}
revenue\text{revenue}
DD
140140
$5.20\$5.20

Elasticity measures how sharply quantity answers to price: the percentage change in cups divided by the percentage change in price. On a straight demand curve it is not one fixed number, it falls steadily as you slide down the line. The shaded box is revenue, price times quantity.

High on the curve demand is elastic, elasticity 1.861.86 at 140140 cups. Quantity reacts more than price does, so a price rise loses cups faster than it gains margin. Push the price up here and the box gets shorter and much narrower, revenue, now about 728728 dollars, falls. To earn more in this region you cut the price, not raise it.

Drag the dot along the demand curve, or use the slider. The shaded box is the cafe's revenue.

A ratio of percentages

Elasticity is built from percentage changes, not raw units, so it does not care whether you measure coffee in cups or in litres.

e=%ΔQ%ΔPe = \left| \frac{\%\,\Delta Q}{\%\,\Delta P} \right|

Above one, demand is elastic: buyers are touchy, and a small price rise drives a big drop in cups. Below one it is inelastic: buyers are stuck, and quantity barely moves.

It changes as you slide

Here is the surprise. A straight demand curve does not have one elasticity, it has a different one at every point. High up, where coffee is dear and few cups sell, a small price change is a big percentage, so demand is elastic. Low down it is inelastic. Exactly in the middle it passes through one.

Why a cafe cares

The shaded box is revenue, price times quantity. Watch it as you drag. Where demand is elastic, pushing the price up loses so many customers that revenue falls. Where it is inelastic, the price rise sticks and revenue grows. The takings peak right at the middle, where elasticity is one. That single fact is why knowing elasticity is worth real money.

What you just did

You measured responsiveness and saw it move. Hold on to it, because when the coffee tax came back, elasticity was the hidden hand deciding how much of it landed on buyers versus cafes. The steeper, less elastic side always carries more.

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