Suppose the GST rate on small cars falls from 28% to 18% and a carmaker passes it on fully. With demand elasticity of 1.2, what happens to prices, volumes and the carmaker's profit?

The buyer's price falls about 7.8% and volumes rise about 9.4%. The tax-inclusive price moves from 128 to 118 per 100 of ex-tax price, a cut of 10 over 128. At an elasticity of 1.2, volumes rise 1.2 times that. Chalvik's ex-tax price is unchanged, so its revenue rises 9.4% to Rs 32,812 crore, and with a 20% contribution on each extra car, EBIT rises about 23%.

Because the tax is charged on top of the ex-tax price, and the buyer sees the total. A shopkeeper who used to add 28 rupees of tax to a 100 rupee item and now adds 18 has cut the till price from 128 to 118, which is 7.8%, not 10%. A tax cut passed on works like a price cut sized by the tax-inclusive price: 10 points off 128. For Chalvik's car, Rs 7,68,000 becomes Rs 7,08,000, a fall of Rs 60,000.

The price elasticityThe percentage change in quantity demanded for a one per cent change in price. An elasticity of 1.2 means a 1% price cut lifts volumes 1.2%. of 1.2 turns a 7.8% price cut into 9.4% more cars. Chalvik's own price has not changed, so its revenue rises by the full volume gain, and because most of its costs are fixed, profit rises much faster. Revenue goes from Rs 30,000 crore to Rs 32,812 crore. Each extra rupee of revenue brings 20 paise of contribution, so EBIT rises from Rs 2,400 crore to Rs 2,962 crore, about 23%.

Three things. An elasticity measured on small price moves may not hold for a large one, and part of the demand may be buyers bringing forward a purchase rather than new buyers. Supply can bind: if plants run near capacity, Chalvik cannot sell 9% more cars this year. And carmakers do not always pass on a tax cut in full; keeping part of it raises Chalvik's margin but shrinks the volume gain. The candidate who uses 10% gets 12% more volume, overstating the volume gain by more than a quarter.