Canteen Pricing at a School
A school canteen in Patiala sells samosas at ₹15 each and cold drinks at ₹20 per bottle. On a typical day it sells 120 samosas and 80 drinks. The owner’s son, a commerce student, estimates from a trial week that if the samosa price rises to ₹18, samosa sales fall to 100 per day and drink sales fall to 72. Separately, when teachers’ salaries were raised by 10% last year, samosa sales rose by 4% while drink sales fell by 1%. The canteen has a fixed monthly contract with the supplier and no close competitors within the school. The owner wants to raise the samosa price to ₹18 to cover rising costs but is worried about overall revenue. The student is asked to use elasticity concepts rather than intuition.
1. Calculate the price elasticity of demand for samosas using the percentage-change method and state whether demand is elastic, inelastic or unit elastic.
Read the worked answer
Using initial values:
- % change in quantity = (100 − 120)/120 × 100 = −16.67%
- % change in price = (18 − 15)/15 × 100 = +20%
- Price elasticity = −16.67/20 = −0.83, so the absolute value is 0.83.
Since 0.83 < 1, demand is inelastic over this range: a 20% price rise reduces quantity by a smaller percentage. Revenue does not automatically rise, however. Here samosa revenue before is 15 × 120 = ₹1,800 and after is 18 × 100 = ₹1,800, so it is unchanged. The owner must therefore also examine the drink market rather than rely on elasticity alone.
2. Calculate the cross elasticity of demand between samosas and drinks, and the income elasticity of demand for each good. What do the signs tell the canteen owner?
Read the worked answer
Cross elasticity:
- % change in drink quantity = (72 − 80)/80 × 100 = −10%
- % change in samosa price = +20%
- Cross elasticity = −10/20 = −0.5
A negative cross elasticity means the goods are complements: raising the samosa price also reduces drink sales. Income elasticity:
- Samosa = 4%/10% = +0.4
- Drink = −1%/10% = −0.1
Samosa is a normal necessity (positive but less than one); the drink is inferior for this group (negative). The trial week is small, so these are indicative estimates, but the signs are useful for pricing.
3. Should the owner raise the samosa price to ₹18? Use total revenue and the elasticity/complementarity results to justify.
Read the worked answer
Total revenue before = (15 × 120) + (20 × 80) = 1,800 + 1,600 = ₹3,400. Total revenue after = (18 × 100) + (20 × 72) = 1,800 + 1,440 = ₹3,240.
Revenue falls by ₹160. Samosa revenue alone is unchanged because the inelastic demand and the price rise exactly offset. The fall comes entirely from the complementarity: fewer samosas sold means fewer drinks sold. The owner should also compare the variable cost saved by making 20 fewer samosas with the ₹160 lost drink revenue. On the given data, the price rise is not clearly profitable. A better judgement may be to keep the samosa price and bundle a drink offer, or raise the price only if cost savings exceed ₹160 per day.