Canteen Price Revision at a Government Arts College
The students' canteen at a government arts college in Tiruchirappalli sells samosas at ₹20 each and tea at ₹10 a cup. In the first week of July, after maida and cooking oil prices rose, the canteen committee raised the samosa price to ₹25 and left the tea price unchanged. Over the next ten days, average daily samosa sales fell from 600 to 510, while tea sales fell from 800 cups to 720. One committee member argues that a fall of only 90 samosas "proves demand is not responsive to price" and proposes a further increase to ₹30. Another member says the tea figures have nothing to do with samosa prices. In the same week a rumour spread in the college that the frying oil was being reused. The canteen's licence fee of ₹18,000 a month is fixed by the college, and the committee must submit a written note to the Principal explaining the price change and recommending whether to go ahead with the ₹30 price.
1. Calculate the price elasticity of demand for samosas by the percentage (proportionate) method and state its type. Verify your answer by the total outlay method.
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Percentage method
Ed = (ΔQ ÷ Q) ÷ (ΔP ÷ P), using the original price and quantity as base.
- ΔQ = 510 − 600 = −90; Q = 600 → −90/600 = −15%
- ΔP = 25 − 20 = ₹5; P = ₹20 → 5/20 = +25%
- Ed = −15 ÷ 25 = −0.6, i.e. |Ed| = 0.6
Since 0.6 < 1, demand is inelastic (less than unitary elastic): quantity falls proportionately less than price rises.
Total outlay check
- Before: ₹20 × 600 = ₹12,000
- After: ₹25 × 510 = ₹12,750
Expenditure on samosas rises when the price rises. A price and total outlay moving in the same direction is the outlay-method signature of inelastic demand, so the two methods agree.
Robustness check (arc method)
- ΔQ ÷ average Q = 90/555 = 16.2%
- ΔP ÷ average P = 5/22.5 = 22.2%
- Ed = 0.73
Still below one, so the conclusion does not depend on which base is chosen - although the exact value does, which is itself a point worth noting in the note.
2. The member proposes raising the price further to ₹30. Using your calculation and the cautions in the data, advise the committee on what to recommend.
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The direction of the argument is defensible, but the member's reasoning is not.
What the number supports. Because |Ed| = 0.6 < 1, a price rise increases total outlay. That happened: revenue rose by ₹750 a day. Since the ingredient cost per samosa did not change and 90 fewer samosas were fried, total variable cost also fell, so the contribution to the fixed licence fee rose by more than ₹750. On the same logic a further rise would raise revenue as long as demand remains inelastic at the new price.
What the member gets wrong. "Only 90 samosas" is not evidence of anything by itself; the elasticity figure, not the absolute fall, is the evidence. A small fall on a small base can mean elastic demand. Also, elasticity is not constant along a straight-line demand curve: at ₹30 the canteen moves towards the elastic range, and students who buy two or three samosas may drop to one.
The contaminated data. The oil rumour is a non-price determinant that shifts the demand curve left. Part of the 90-samosa fall is therefore not a price effect, so the true price elasticity is smaller than 0.6 - which strengthens the case for the hike, but weakens any inference from a single ten-day observation.
Recommendation. Do not fix ₹30 permanently on this evidence. Record a clear denial of the rumour, observe sales for two to three more weeks, and treat ₹30 as a trial. Report the elasticity, the outlay figures and the caveat to the Principal rather than claiming the demand is simply 'unresponsive'.
3. Explain the fall in tea sales with the help of cross elasticity of demand, and comment on the second member's statement that the tea figures have nothing to do with samosa prices.
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Cross elasticity of demand measures the responsiveness of the demand for one good to a change in the price of another:
Ec = (% change in quantity of tea) ÷ (% change in price of samosa)
- % change in tea = −80/800 = −10%
- % change in samosa price = +25%
- Ec = −10 ÷ 25 = −0.4
The negative sign identifies tea and samosa as complements - they are consumed together, so a rise in the samosa price reduces the quantity of samosas bought and drags tea down with it.
Change in quantity demanded versus change in demand. The price of tea itself did not change, so this is not a movement along the tea demand curve. Samosa price is a non-price determinant of tea demand, so the tea demand curve has shifted to the left - a decrease in demand, not a decrease in quantity demanded.
On the second member. She is wrong in principle: the samosa price is a determinant of tea demand through complementarity, and the negative cross elasticity measures exactly that link. She is right only in a narrower sense - the observed 80-cup fall mixes two causes, since the oil rumour also drives students away from both items. To isolate the price effect one would compare tea sales on days when samosas were unavailable with normal days, or re-measure after the rumour is publicly denied.