Canteen Prices, Elasticity and a Hosteller's Budget
A women's hostel canteen in Mangaluru sells coffee at ₹20 a cup and a packaged cold drink at ₹40 a bottle. Last term it raised the coffee price to ₹25 and daily coffee sales fell from 400 cups to 340. In the same term it cut the cold drink price to ₹36 and daily sales rose from 250 to 300 bottles. The warden reads this as proof that 'students are price-sensitive about everything' and proposes a further ₹5 rise in coffee to cover rising milk costs; the students' council demands a cut in both prices. The canteen's fixed costs are unchanged, and the warden wants the price changes that leave the largest daily receipts. Separately, a hosteller with a ₹100 daily budget is buying 3 coffees and 2 snacks; the last coffee gives her 60 units of utility and the last snack, priced at ₹10, gives 40 units.
1. Compute the price elasticity of demand for coffee and for the cold drink using the percentage method, and say which demand is elastic.
Read the worked answer
Coffee: % change in quantity = (340 − 400)/400 × 100 = −15%; % change in price = (25 − 20)/20 × 100 = +25%. Taking absolute values, e = 15/25 = 0.6.
Cold drink: % change in quantity = (300 − 250)/250 × 100 = +20%; % change in price = (36 − 40)/40 × 100 = −10%. e = 20/10 = 2.0.
So cold-drink demand is elastic (e > 1) and coffee demand is inelastic (e < 1) in the ranges observed.
The warden's inference is wrong: the two goods do not have the same sensitivity. Note the measurement caveat - each figure is a single arc between two points, so it is an average elasticity over that range, not a permanent constant.
2. Use the total expenditure method to check both decisions, then judge whether the proposed further ₹5 rise in coffee is justified.
Read the worked answer
Coffee receipts: 400 × ₹20 = ₹8,000 → 340 × ₹25 = ₹8,500. Receipts rise when price rises, which independently confirms inelastic demand.
Cold-drink receipts: 250 × ₹40 = ₹10,000 → 300 × ₹36 = ₹10,800. Receipts rise when price falls, which confirms elastic demand.
Both past decisions were right on revenue grounds. For the further rise to ₹30 (a 20% increase), if e remained 0.6, quantity would fall about 12% to roughly 299 cups and receipts would be about 299 × ₹30 ≈ ₹8,970, still above ₹8,500. But this is arithmetic on a borrowed assumption: the 0.6 was measured over one small arc, at a price where 340 cups are still sold, and a second rise of the same size may push students to tea or water, moving demand into the elastic range. Since fixed costs are unchanged, revenue equals contribution, but the gain at stake (₹500 a day on the first rise) is small relative to that risk. Judgement: a small rise with weekly monitoring of cups sold is defensible; a confident forecast of higher receipts is not.
3. Using the hosteller's marginal utilities, state what she should change and the condition she should satisfy at her optimum.
Read the worked answer
Compare marginal utility per rupee, not marginal utility:
- Coffee: MU/P = 60/20 = 3 utils per ₹1
- Snack: MU/P = 40/10 = 4 utils per ₹1
The last rupee spent on snacks is giving more utility, so she should buy more snacks and fewer coffees, shifting money until the ratios are equal:
MU(coffee)/P(coffee) = MU(snack)/P(snack), with total spending = ₹100.
This is the law of equi-marginal utility. As she buys more snacks, the law of diminishing marginal utility pulls MU(snack) down; as she buys fewer coffees, MU(coffee) is pushed up; the two ratios meet and total utility is maximised. Note that the rule is not 'spend equally on both goods' and not 'equalise total utilities' - the comparison must be at the margin and per rupee, because the two goods have different prices.