Kumar used to eat 30 samosas in a month when the price of each samosa was ₹12. When the price of samosa increased to ₹15 per piece, he eats only 20 samosas a month. What is the price elasticity of demand for samosa by Kumar?
- (a)1·33
- (b)1·00
- (c)0·75
- (d)0·08
Correct — A, 1·33. Price elasticity of demand is the percentage change in quantity divided by the percentage change in price, taken as a magnitude. Quantity falls from 30 to 20, a change of 10 on a base of 30, which is 33·33 per cent. Price rises from ₹12 to ₹15, a change of 3 on a base of 12, which is 25 per cent. Dividing gives 33·33 ÷ 25 = 1·33. A cross-check confirms it: elasticity above 1 means demand is elastic, and elastic demand means a price rise cuts total spending — Kumar's outlay falls from 30 × 12 = ₹360 to 20 × 15 = ₹300, exactly as it should.
- (b)1·00 — Unit elasticity would need the two percentage changes to be equal. A 25 per cent price rise would then have cut consumption by 25 per cent, from 30 samosas to 22·5, and Kumar's monthly spending would have stayed at ₹360.
- (c)0·75 — This is the formula upside down — 25 ÷ 33·33 = 0·75. Dividing the price change by the quantity change instead of the other way round is the single commonest slip in elasticity arithmetic, and the examiner has priced the option to catch it.
- (d)0·08 — An elasticity of 0·08 would mean a 25 per cent price rise reduced demand by about 2 per cent, that is from 30 samosas to roughly 29. Kumar cut back by ten, so the answer has to be more than an order of magnitude larger.
Elasticity measures responsiveness in proportional terms, which is why it is a pure number with no units and can be compared across goods priced in different ranges. Demand is called elastic when the magnitude exceeds 1, unit elastic at exactly 1, and inelastic below 1. The link worth carrying into the hall is the one to spending — when demand is elastic a price rise lowers total expenditure, when it is inelastic a price rise raises it, and at unit elasticity expenditure does not move.
Two arithmetic decisions decide this item. The first is which base to use for the percentages; the standard school formula uses the original price and original quantity, which is what reaches 1·33. The midpoint or arc method, which divides by the average of the two values, gives about 1·8 here — and 1·8 is not among the options, which is the paper telling you which method it wants. The second decision is which quantity goes on top. Percentage change in quantity is the numerator; put price on top and you get 0·75, which is sitting in the options waiting. Note also that the elasticity is a magnitude — the raw ratio is negative because price and quantity move in opposite directions, and the minus sign is dropped by convention.
- Price elasticity of demand equals the percentage change in quantity demanded divided by the percentage change in price, reported as a magnitude.
- Here the changes are 10 on a base of 30, or 33·33 per cent, and 3 on a base of 12, or 25 per cent.
- A magnitude above 1 means elastic demand; between 0 and 1 means inelastic; exactly 1 means unit elastic.
- Elastic demand and a price rise together mean total expenditure falls, which is the fastest way to check an answer.
- The midpoint method, which uses the average of the two prices and quantities as base, gives about 1·8 for the same data and is not what this question wants.
Invert the division and you land on 0·75; use average bases instead of original ones and you land on 1·8, which is not offered.
- Dividing the price change by the quantity change instead of the other way round.
- Using the new price and new quantity as the base rather than the original ones.
- Reaching a negative number and treating the sign as an error rather than a convention to be dropped.
Elasticity items in this paper are arithmetic, not theory — the options are constructed from the specific wrong operations, so a spending cross-check is worth the ten seconds it takes.
Under normal downward sloping demand curve and fully elastic supply curve of a commodity, an exogenous decrease in demand would lead to
- (a) increase in equilibrium price and quantity
- (b) decrease in equilibrium price and quantity
- (c) decrease in equilibrium quantity and no change in price
- (d) increase in equilibrium price and no change in quantity
Answer(c) decrease in equilibrium quantity and no change in price
Elasticity applied to a market rather than to one buyer. It shows the same idea from the supply side — when one curve is fully elastic the whole adjustment falls on quantity and none of it on price.
How is the magnitude of price elasticity for an individual good determined? 1. By the degree to which the good is a necessity or luxury 2. By the extent to which substitutes are available 3. By the rate of income growth in the economy 4. By the relative importance of the good in the consumer's budget Select the correct answer using the code given below.
- (a) 1, 2 and 3
- (b) 1 and 4 only
- (c) 1, 2 and 4
- (d) 3 and 4
Answer(c) 1, 2 and 4
The theory behind this arithmetic. A samosa is a small part of anyone's budget but has close substitutes and is nobody's necessity, which is why a 25 per cent price rise could push Kumar's consumption down by a third.
- practice — not a real PYQ
The price of a good rises from ₹20 to ₹25 and the quantity demanded falls from 100 units to 80 units. The price elasticity of demand is
- (a)0·80
- (b)1·00
- (c)1·25
- (d)1·60
Answer(a) 0·80 — quantity falls by 20 per cent and price rises by 25 per cent, so 20 ÷ 25 = 0·8, and demand is inelastic.
- practice — not a real PYQ
If a rise in the price of a good raises the total expenditure of a consumer on that good, the demand for it is
- (a)elastic
- (b)unit elastic
- (c)inelastic
- (d)perfectly elastic
Answer(c) inelastic — quantity falls proportionately less than price rises, so the bill goes up.