Canteen Pricing: Elasticity, Cost-of-Living Bounds and a Combo Deal
A corporate campus canteen sells only two lunch items: a thali at ₹100 and a sandwich at ₹50. Meera, an analyst, has a lunch budget of ₹300 per working day, which she spends in full. At current prices she buys two thalis and two sandwiches. When the canteen raised the thali price to ₹120 and left the sandwich at ₹50, the till data show her buying one thali and, on average, 3.6 sandwiches a day - she still spends exactly ₹300.
Two months later the canteen introduces a combo: one thali plus two sandwiches for ₹200, against ₹220 à la carte. The manager has also noticed that regulars' average lunch spend fell after the combo launch even though they eat the same items. He wants to know how responsive thali demand is, whether Meera is materially worse off after the price rise, whether the combo is a pricing mistake, and how he should set prices for the next academic year.
1. Estimate the price elasticity of demand for thali from the two observations and state what it implies for thali revenue.
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Arc elasticity. P falls from... rather, P rises 100 → 120; Q falls 2 → 1.
Ed = (ΔQ/ΔP) × (average P / average Q) = (−1/20) × (110/1.5) = −3.67
Point elasticity at the original price. (ΔQ/ΔP) × (P/Q) = (−1/20) × (100/2) = −2.5.
Both exceed 1 in absolute value, so thali demand is elastic over this range. The revenue check confirms it without any elasticity formula: thali spending fell from ₹200 to ₹120, a 40% fall, after a 20% price rise.
Caveats before the manager acts.
- Two observations identify an arc, not a demand curve. If canteen footfall, incomes or the sandwich offering changed at the same time, the estimate is contaminated.
- The elasticity is large partly because a close substitute (the sandwich) sits right next to it. If the manager cuts the thali price, part of the volume gain is simply sandwiches switching back, so total canteen revenue may barely move even though thali revenue rises.
- The relevant elasticity for total revenue is the cross-price effect. Cutting thali price pulls sandwich sales; the manager should track revenue and contribution per cover, not thali revenue alone.
- At ₹100–120, a 20% price move is large relative to the likely noise in daily till data; re-estimate with at least a month of observations on both sides.
2. How much worse off is Meera after the price rise? Use revealed-preference bounds rather than asserting that she is worse off.
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Test 1 - is the old bundle still affordable? Old bundle (2 thalis, 2 sandwiches) at new prices: 2(120) + 2(50) = ₹340 > ₹300 budget. It is unaffordable, so her pre-rise consumption is out of reach. She is worse off.
Test 2 - was the new bundle affordable before? New bundle (1 thali, 3.6 sandwiches) at old prices: 1(100) + 3.6(50) = ₹280 ≤ ₹300. It was affordable and she did not choose it, which is consistent with the price change, not a preference reversal. This rules out the possibility that she simply changed tastes.
Bounding the welfare loss with index numbers.
- Laspeyres (upper bound): cost of the old bundle at new prices ÷ old cost = 340/300 = 1.133, i.e. a 13.3% rise in her cost of living.
- Paasche-type (lower bound): cost of the new bundle at new prices ÷ at old prices = 300/280 = 1.071, i.e. 7.1%.
Her true cost-of-living increase lies between 7.1% and 13.3% of her ₹300 lunch budget, roughly ₹21–40 a day, or ₹460–880 in a 22-day month.
Decomposition. The substitution effect dominates: thali became relatively expensive (up 20% versus 0% for sandwiches) and she shifted 1.6 units toward sandwiches. The income effect is small but works the same way for a normal good - her real lunch budget fell, reinforcing the cut in thali purchases. Thali is not a Giffen good.
3. Is the ₹200 combo a pricing mistake? Advise on pricing to maximise contribution, using the elasticity evidence.
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What the combo does. À la carte the bundle costs 120 + 2(50) = ₹220; the combo gives it for ₹200, a 9.1% discount. For a regular who already bought exactly that basket, nothing changes except that they pay ₹20 less: revenue and contribution per cover fall, quantity is unchanged. That is exactly why regulars' average spend dropped while their consumption did not - the combo transferred surplus to the canteen's least price-sensitive customers.
Break-even volume. If contribution per cover before the combo was ₹80 on ₹220 (36%) and ₹60 after, volume must rise by 80/60 − 1 = 33% to hold total contribution. A 9% discount on an already thin food margin rarely buys that much traffic from existing regulars; it can only work if it pulls in new customers or increases frequency.
Better design - second-degree price discrimination.
- Restrict the combo to a time window (2:30–4:00 pm), when the alternative is an empty table and the incremental cost is only the food cost.
- Make it ID-linked and non-transferable so staff on higher willingness to pay cannot arbitrage into it.
- Keep the à la carte thali at ₹120; the elasticity estimate (−3.67) tells you a general price cut would raise thali revenue, but a targeted discount captures the price-sensitive segment without giving away margin on the rest.
- Measure contribution per cover and per day-part, not revenue. Falling average spend with flat covers is a warning sign, not a success metric.
Recommendation. Keep a combo, but as a time-restricted, registered-only offer at ₹210, and re-test after four weeks against a control group of days.