The Notebook Shop: Elastic Demand but Higher Profit
A stationery shop sells 1,200 notebooks a month at ₹50 each. Variable cost is ₹30 per notebook and fixed costs are ₹20,000 a month. A supplier raises the wholesale price, so the owner considers raising the price to ₹55. A nearby market survey suggests quantity sold would fall to 1,020 notebooks a month; no other costs change. The owner says, 'A price rise always increases revenue, so it must increase profit.' The shop has spare shelf space and can handle either volume without new fixed cost. A competitor has not yet changed price, and the owner expects no change in the number of customers over the next six months. You are asked to evaluate the decision using elasticity and profit, not revenue alone.
1. Calculate the price elasticity of demand using the initial-value method and the arc method. Classify the demand and interpret the result.
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Initial-value method:
Percentage change in quantity = (1,020 − 1,200)/1,200 × 100 = −15%.
Percentage change in price = (55 − 50)/50 × 100 = +10%.
Ed = |−15%| / 10% = 1.5.
Arc (midpoint) method:
Average quantity = (1,200 + 1,020)/2 = 1,110. Change in quantity = 180.
%ΔQ = 180/1,110 × 100 = 16.22%.
Average price = (50 + 55)/2 = 52.5. Change in price = 5.
%ΔP = 5/52.5 × 100 = 9.52%.
Ed = 16.22/9.52 = 1.70.
Either way, Ed > 1, so demand is elastic in this price range. Quantity falls proportionately more than price rises. A 1% price increase reduces quantity demanded by about 1.5% to 1.7%. The owner cannot assume revenue will rise; with elastic demand, a price increase tends to reduce total revenue.
2. Compare total revenue and profit before and after the price rise. Explain why the owner's statement is wrong.
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Before the price rise:
Total revenue = 1,200 × ₹50 = ₹60,000.
Total variable cost = 1,200 × ₹30 = ₹36,000.
Total cost = ₹36,000 + ₹20,000 = ₹56,000.
Profit = ₹60,000 − ₹56,000 = ₹4,000.
After the price rise:
Total revenue = 1,020 × ₹55 = ₹56,100.
Total variable cost = 1,020 × ₹30 = ₹30,600.
Total cost = ₹30,600 + ₹20,000 = ₹50,600.
Profit = ₹56,100 − ₹50,600 = ₹5,500.
Revenue falls by ₹3,900, but profit rises by ₹1,500. The reason is the contribution margin per notebook: it rises from ₹50 − ₹30 = ₹20 to ₹55 − ₹30 = ₹25. Total contribution rises from 1,200 × ₹20 = ₹24,000 to 1,020 × ₹25 = ₹25,500. Fixed cost is unchanged at ₹20,000, so profit rises by ₹1,500.
The owner's statement is wrong because it confuses revenue with profit and ignores elasticity. A price rise can lower revenue when demand is elastic, but profit can still rise if the higher margin per unit outweighs the loss of volume. Here the margin effect dominates.
3. Recommend whether the shop should raise the price. State two conditions under which your recommendation would change.
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On the given survey and cost figures, the shop should raise the price if its objective is short-run profit: profit rises from ₹4,000 to ₹5,500, and spare shelf space means no extra fixed cost is needed. The price rise is not justified by higher revenue - revenue actually falls - but by the higher contribution per notebook.
The recommendation would change under at least two conditions:
If the competitor responds by holding or cutting price, the shop's customers may leave in larger numbers than the survey predicts. Demand would be more elastic than 1.5, and the profit gain could disappear.
If repeat customers matter over the longer run, a price rise may erode goodwill and future sales even if the six-month survey is accurate. The owner should also avoid assuming that further price rises will keep raising profit; once the margin gain is outweighed by volume loss, profit will fall.
If the owner's objective is market share or revenue rather than short-run profit, the recommendation would also change: keeping the price at ₹50 preserves revenue and customer traffic.