Wheat Price Rise in a Kanpur Household: Elasticity, Substitution and Income Effects
A family in Kanpur spends its entire monthly food budget of ₹8,000 on wheat flour and rice. In January, wheat flour costs ₹30 per kg and rice ₹50 per kg, and the family buys 160 kg of wheat and 64 kg of rice. In February the price of wheat flour rises to ₹33 per kg while rice stays at ₹50; the family's money income is unchanged. In February the family buys 150 kg of wheat and 61 kg of rice, spending exactly ₹8,000. A local college survey then asks a hypothetical question: if the family were given an extra ₹480 per month - enough to buy its original 160 kg of wheat at the new price - how much wheat would it buy? The family answers 156 kg, with rice back at 64 kg. The survey team wants to use these three observations to separate the two forces behind the fall in wheat purchases, and to advise the district supply office on whether a wheat price rise will cut consumption appreciably.
1. Compute the price elasticity of demand for wheat between January and February by the percentage method. State whether demand is elastic, unit-elastic or inelastic, cross-check your answer against the family's total spending on wheat, and explain why the two must agree.
Read the worked answer
Calculation.
- Percentage change in quantity = (150 − 160)/160 × 100 = −6.25%
- Percentage change in price = (33 − 30)/30 × 100 = +10%
- Price elasticity e = −6.25 ÷ 10 = −0.625, so |e| = 0.625 < 1: demand is inelastic.
Cross-check with expenditure.
- January: 30 × 160 = ₹4,800
- February: 33 × 150 = ₹4,950
Spending on wheat rose by ₹150 (about 3.1%). This is exactly what an elasticity below one predicts: when price rises proportionally faster than quantity falls, the price effect on expenditure outweighs the quantity effect. If spending had fallen, |e| would necessarily have exceeded 1. The two findings are not independent facts but two ways of stating the same relationship.
Implication for policy. A 10% price rise removes only 6.25% of purchases, so using price to cut wheat consumption by, say, 10% would require a very large rise. The inelasticity is explained by wheat being a staple with few close substitutes in this household's food basket, and by the fact that the family has already cut rice (64 → 61 kg) to protect wheat consumption.
2. Split the 10 kg fall in wheat purchases into a substitution effect and an income effect, and explain what the ₹480 compensation in the survey represents.
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What the ₹480 means. ₹480 = 160 kg × ₹3, the extra money needed to buy the January bundle (160 kg wheat plus 64 kg rice) at February prices. It is the compensating variation: it restores the family's original purchasing power, so a purchase decision taken with it reflects only the change in relative prices, not the change in real income.
Decomposition.
- Total effect: 160 → 150 kg = −10 kg
- Substitution effect (with ₹480 compensation): 160 → 156 kg = −4 kg. Wheat has become dearer relative to rice, so even at unchanged real income the family replaces some wheat with rice.
- Income effect (removing the compensation): 156 → 150 kg = −6 kg. The price rise has made the family poorer in real terms; wheat is a normal good, so the fall in real income reduces quantity demanded further.
Interpretation. Both effects work in the same direction, which is why ordinary demand curves slope downward. Here the income effect (−6 kg) dominates the substitution effect (−4 kg) because wheat absorbs a large share of a small food budget - a price rise of this kind is felt as a real income cut, not merely as a change in relative prices. Note that the family is worse off even though its money income never changed; the ₹480 was hypothetical, and the actual February basket (150 kg wheat, 61 kg rice) yields less satisfaction than the January basket.
3. The district supply office wants wheat purchases by such households to fall by 10 per cent. Using your elasticity, estimate the price rise needed, and give two reasons why that estimate could be unreliable at such a large price change.
Read the worked answer
Estimate. Required %ΔQ = −10%. With |e| = 0.625, %ΔP = 10 ÷ 0.625 = 16%, i.e. wheat would have to rise from ₹30 to about ₹34.80 per kg.
Why the estimate is fragile.
- Elasticity is not constant along a demand curve. The 0.625 was measured over a small 10% price change on a linear demand curve, where elasticity rises as we move up the price axis. At higher prices the same 10% quantity cut would need a smaller price rise than 16%, so a naive linear extrapolation overstates the required increase.
- The measurement is one household's behaviour, not a market response. Other households may have different budget shares, and at higher prices families may switch to coarse grains, to the public distribution system, or to rationed wheat - responses that were not available in the observed range.
Judgement. A price instrument aimed at a staple is a blunt and regressive tool: the 10% quantity cut is achieved by making a necessity expensive for exactly the households that spend the largest share of income on it. A quantity instrument (targeted PDS allocation, procurement diversion to deficit districts) would achieve the same reduction in consumption with a smaller welfare loss.