A Muzaffarpur Sweet Shop Tests Two Prices Before the Festival Season
A sweet shop in Muzaffarpur sells peda and besan laddoo. In January the owner raised peda from ₹400 to ₹440 per kg, keeping laddoo at ₹300 per kg. Peda sales fell from 300 kg to 240 kg a month, while laddoo sales rose from 200 kg to 230 kg. In March, with peda back at ₹400, he tested laddoo at ₹330 per kg and sales fell from 200 kg to 194 kg. He must now fix both prices for the festival season, when customers are usually less price-sensitive, and a large sweet shop two lanes away sells peda at ₹430 per kg. Rent, staff and electricity cost ₹55,000 a month and are unaffected by these pricing decisions. The owner is tempted to raise both prices by 10 per cent because, as he puts it, "everyone pays more during festivals".
1. Calculate the price elasticity of demand for peda and for laddoo from these two experiments, using the percentage method, and classify each good. Mention whether a midpoint (arc) calculation would change your conclusion.
Read the worked answer
Peda: %ΔQ = (240 − 300)/300 × 100 = −20%; %ΔP = (440 − 400)/400 × 100 = +10%. So e_d = 20/10 = 2.0 - demand is elastic (greater than 1).
Laddoo: %ΔQ = (194 − 200)/200 × 100 = −3%; %ΔP = (330 − 300)/300 × 100 = +10%. So e_d = 3/10 = 0.3 - demand is inelastic (less than 1).
Midpoint check: peda %ΔQ = 60/270 = 22.2%, %ΔP = 40/420 = 9.5%, e_d ≈ 2.3. Laddoo %ΔQ = 6/197 = 3.05%, %ΔP = 30/315 = 9.5%, e_d ≈ 0.32. The classification is unchanged: peda is clearly elastic, laddoo clearly inelastic.
A careful candidate should note that these are measured elasticities over particular ranges, not permanent properties. The festival season and the rival's ₹430 price both affect peda's elasticity, so the January figure should be treated as evidence, not as a law.
2. Use the total outlay (total expenditure) method to work out what happened to the shop's revenue in January, and say whether the owner should carry out his plan of raising both prices by 10 per cent.
Read the worked answer
Before January: peda 400 × 300 = ₹1,20,000; laddoo 300 × 200 = ₹60,000; total ₹1,80,000.
After the peda rise: peda 440 × 240 = ₹1,05,600 (down ₹14,400); laddoo 300 × 230 = ₹69,000 (up ₹9,000); total ₹1,74,600 - a net fall of ₹5,400.
March laddoo test: 330 × 194 = ₹64,020 against ₹60,000, a rise of ₹4,020.
The total outlay rule explains both results: when demand is elastic, price and total revenue move in opposite directions; when demand is inelastic, they move together. The peda rise cut revenue because the 20% fall in quantity more than offset the 10% price rise. The laddoo rise added revenue because quantity barely moved.
The blanket 10% plan is therefore wrong. Raising laddoo is defensible - with e_d = 0.3 the revenue gain is small but positive, and festival demand is even less elastic. Raising peda is risky: he is already ₹30 below the rival, and a rise to ₹440 takes him above the rival's ₹430, which will make his demand more elastic than the January estimate. A price cut on peda is the revenue-raising direction if the elastic estimate holds.
3. Estimate the cross elasticity of demand between peda and laddoo from the January experiment and interpret it. Given that result, how much of the lost peda revenue did the shop actually recover?
Read the worked answer
Cross elasticity = %ΔQ of laddoo ÷ %ΔP of peda = [(230 − 200)/200 × 100] ÷ [(440 − 400)/400 × 100] = 15% ÷ 10% = +1.5.
The sign is positive, so the two sweets are substitutes: as peda became dearer, customers shifted part of their purchase to laddoo. A coefficient of 1.5 is fairly strong, so the shop is not losing the customer entirely - it is redirecting the purchase within its own counter.
The recovery, however, is only partial. The extra 30 kg of laddoo at ₹300 adds ₹9,000, while the peda revenue lost is ₹14,400, so the shop is still ₹5,400 poorer. This is exactly why the cross effect must be computed rather than assumed: a high cross elasticity feels reassuring but says nothing about whether the substitute's rupee value covers the loss. The cross estimate also rests on the assumption that nothing else changed in January - if laddoo's own price, festival demand or a competitor's action had moved at the same time, the +1.5 would be biased and the owner would need a cleaner test before relying on it.