Rice Price Rise and Household Demand in Kollam
The Raman household in Kollam has a monthly income of ₹30,000 and buys rice from the local ration-cum-market shop. In January the shop raised the price of rice from ₹40 to ₹50 per kg. The household's monthly purchase fell from 30 kg to 24 kg, while its total spending on rice remained ₹1,200. Other cereals and vegetables were available at unchanged prices. The household says it has 'not spent a rupee more on rice', but the shopkeeper reports that overall rice sales in the locality have fallen. The family also complains that it is buying more vegetables and less rice than before. A local cooperative bank economist is asked to explain the demand response using the arc elasticity method, and to advise the shop on whether the price rise has increased its rice revenue.
1. Calculate the arc price elasticity of demand for rice and classify the demand. Show the formula and all substitutions, and check your answer against the household's total expenditure on rice.
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Arc elasticity is calculated as:
e_d = |(ΔQ / ΔP) × ((P1 + P2) / (Q1 + Q2))|
Here ΔQ = 24 − 30 = −6 kg; ΔP = 50 − 40 = ₹10; P1 + P2 = 90; Q1 + Q2 = 54.
e_d = |(−6 / 10) × (90 / 54)| = 0.6 × 1.6667 = 1.0
Demand is unit elastic at this point, not elastic or inelastic. The total outlay check confirms this: before the price rise, expenditure = 30 × ₹40 = ₹1,200; after, 24 × ₹50 = ₹1,200. When price rises by 25 per cent and quantity falls by 20 per cent, the two percentage changes do not look equal because they use different bases; the arc formula avoids that base problem and gives unitary elasticity. For this household the shop's rice revenue is unchanged, but because other households also reduced purchases, the shopkeeper's total rice revenue may still have fallen.
2. The household claims it has not spent more on rice, yet it feels worse off. Explain this using the substitution effect, the income effect and consumer surplus. Is the claim that 'nothing has changed' correct?
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The claim is correct only about money spent on rice; it is not correct about welfare. When the price of rice rises, the budget line becomes steeper. The substitution effect makes rice relatively expensive compared with vegetables, so the household substitutes vegetables for rice and quantity falls. The income effect is also negative for a normal good: the higher price reduces real income, so the household buys less rice. Both effects work in the same direction, producing the fall from 30 kg to 24 kg.
Because demand is unit elastic, the percentage fall in quantity exactly offsets the percentage rise in price, leaving expenditure at ₹1,200. But the household's purchasing power has fallen: it now buys a less preferred bundle and has less real income for other goods. Its consumer surplus from rice is lower because it pays a higher price for each kilogram and consumes fewer kilograms. The correct conclusion is that rice expenditure is unchanged, but welfare is lower; unchanged expenditure is not the same as unchanged satisfaction.
3. Suppose the household's income rises to ₹36,000 and, at the unchanged price of ₹50, its rice purchase falls to 22 kg. Calculate income elasticity using the arc method and interpret the good. What happens to the demand curve for rice?
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Income elasticity using the arc method:
e_Y = (ΔQ / ΔY) × ((Y1 + Y2) / (Q1 + Q2))
ΔQ = 22 − 24 = −2 kg; ΔY = 36,000 − 30,000 = ₹6,000; Y1 + Y2 = 66,000; Q1 + Q2 = 46.
e_Y = (−2 / 6,000) × (66,000 / 46) = −0.000333 × 1,434.8 ≈ −0.48
The negative income elasticity means rice is an inferior good for this household over this income range: as income rises, it buys less rice, perhaps shifting to more expensive cereals, eggs or milk. Since the price is unchanged at ₹50, this is a movement of the whole demand curve, not a movement along it. The demand curve for rice shifts to the left at every price. A negative income elasticity does not by itself prove that rice is a Giffen good; that requires a positive price effect, which is not observed here.