Matching a Rival's Price Cut: Elasticity Versus Margin
Rohan Fans Pvt Ltd makes ceiling fans and sells about 8,000 units a month at ₹2,400 each in a single regional market. Variable cost is ₹1,800 per fan and monthly fixed cost is ₹28 lakh, so the firm currently earns a profit of ₹20 lakh. An imported rival has just cut its retail price by 8%. The marketing head wants Rohan to match with a 10% cut to ₹2,160, arguing that sales will jump and turnover will grow. A consultant's estimate puts Rohan's own-price elasticity of demand at about −1.8 in this price range, and the cross-price elasticity with the rival's brand at +0.9. Rohan's finance manager is unconvinced by the turnover argument but has no counter-analysis. The board meets next week, and the sales team has already told two large dealers that a price cut is 'likely'. Rohan cannot quickly change its factory layout or renegotiate the imported-component contract that sets most of its variable cost.
1. Quantify the effect of the proposed 10% price cut on monthly quantity, turnover, contribution and profit, assuming the elasticity estimate holds. What should the board decide?
Read the worked answer
Step 1 - Quantity effect. % change in quantity = elasticity × % change in price = (−1.8) × (−10%) = +18% New volume = 8,000 × 1.18 = 9,440 fans
Step 2 - Turnover. Before: 2,400 × 8,000 = ₹1,92,00,000 After: 2,160 × 9,440 = ₹2,03,90,400 (up ₹8,39,400, about +4.4%)
Step 3 - Contribution and profit. Contribution per fan before = 2,400 − 1,800 = ₹600; total = ₹48,00,000. After the cut it is 2,160 − 1,800 = ₹360; total = 360 × 9,440 = ₹33,98,400. Profit before = 48,00,000 − 28,00,000 = ₹20,00,000. Profit after = 33,98,400 − 28,00,000 = ₹5,98,400.
Decision rule. The right test is contribution, not turnover. A firm with |e| > 1 does raise revenue by cutting price, which is exactly why the marketing head's turnover argument looks persuasive - but here each extra fan earns ₹240 less than before, and the volume gain is nowhere near enough. To hold contribution at ₹48,00,000 the firm would need 48,00,000 ÷ 360 = 13,333 fans, a rise of 66.7%, implying an elasticity near 6.7. That is not credible for ceiling fans.
Recommendation: reject the 10% cut. Profit would fall by about ₹14 lakh even though turnover rises.
2. If Rohan holds its price, use the cross-price elasticity to estimate the volume it loses. Compare the resulting profit with the price-cut outcome, and explain why a point elasticity of −1.8 may mislead for a move of this size.
Read the worked answer
Volume lost if Rohan does nothing. % change in Rohan's demand = cross elasticity × rival's % price change = 0.9 × (−8%) = −7.2% Volume = 8,000 × 0.928 = 7,424 fans Contribution = 7,424 × 600 = ₹44,54,400; profit = 44,54,400 − 28,00,000 = ₹16,54,400.
Comparison.
| Option | Volume | Profit |
|---|---|---|
| Cut price 10% | 9,440 | ₹5,98,400 |
| Hold price | 7,424 | ₹16,54,400 |
| Holding price is better by about ₹10.56 lakh. Matching the rival gives away ₹240 of margin on all 9,440 units to win 2,016 units that contribute only ₹360 each; the arithmetic cannot work unless demand is far more elastic than estimated. |
Why −1.8 may mislead. It is a point estimate, valid for small changes around ₹2,400. A 10% move should strictly be assessed with arc elasticity, which is usually smaller in magnitude on a linear demand curve. The cross elasticity of +0.9 is also an average that may not hold when a rival makes a large, visible cut, and it says nothing about a second round of cuts.
Judgement: hold the list price and respond through dealer margins, warranty and service turnaround, while tracking monthly volume against the 7,424 benchmark. If volume falls materially below it, the elasticity assumption - not the pricing logic - needs revisiting.