What decides the elasticity of demand, and the price rise needed to cut the use of good X by 20 per cent

What decides how elastic demand is. Price elasticity of demand measures how strongly buyers change the quantity they buy when the good's own price changes. How strongly they react depends on how easily they can do without the good, or with less of it. Five influences matter most; the examples are our own.

• Time to adjust. Buyers react little at first and more as time passes, so demand is less elastic in the short run than in the long run. Purchases that can be put off respond more than purchases that cannot. When petrol becomes dearer, commuters keep riding their motorcycles for the first few weeks; over a few years some switch to electric scooters or the metro.
• Share of the budget. A good that takes a tiny part of a buyer's income has relatively inelastic demand, because even a large rise in its price hardly dents the budget; a good that takes a large share has more elastic demand. A rise in the price of a ₹2 shampoo sachet changes few plans; a similar rise in the price of a two-wheeler makes many families wait.
• Closeness of substitutes. The more easily buyers can turn to similar goods, the more elastic the demand; a good with no close substitute has inelastic demand. One brand of packaged drinking water loses many buyers to rival brands if it alone raises its price; the demand for insulin barely falls when its price rises.
• Necessity or luxury. Necessities are bought in roughly the same amounts whatever their price, so their demand is inelastic; goods people can do without, or can postpone, have elastic demand. A family keeps buying rice after a price rise but may drop a holiday abroad.
• Number of uses. A good with many uses has more elastic demand, because a price rise leads buyers to give up its less important uses; a good with only one main use has less elastic demand. When milk becomes dearer, a household may stop making sweets and curd at home but keep the milk for children.

The price rise needed. By definition:

eD = (% change in quantity demanded) ÷ (% change in price).

The government wants quantity to fall by 20%, and the elasticity (in absolute value) is 0.2. So the required change in price is

% change in price = 20 ÷ 0.2 = 100%.

A 100% rise in the present price of 50 is 50 × 100 / 100 = 50, which takes the price from 50 to 100. Since demand for X is very inelastic, a large rise in price is needed for a modest cut in consumption.

The other reading: the mid-point method. The calculation above measures each change against its starting value, as the simple formula does. A change as large as a doubling of the price gives a noticeably different answer when both changes are measured against their averages, the mid-point method:

• A 20% cut takes the quantity from 100 to 80 (per 100 units now bought); on the average of 90 this is a change of 20 / 90 = 22.22%.
• The price change needed is then 22.22 ÷ 0.2 = 111.11% of the average price.
• With P1 as the new price, (P1 – 50) ÷ [(P1 + 50) / 2] = 1.1111, which gives P1 = 175, a rise of 125.

The gap between the two readings shows that an elasticity figure of roughly 0.2 is a guide for small changes; for a change this large the answer depends on the method used.

Answer. Using the usual percentage method, the government must raise the price of X by 100%, that is by 50, from 50 to 100, to cut its consumption by 20%. (Measured by the mid-point method throughout, the price would have to rise to 175.)