Elasticity was introduced as a property of demand, because that is where pricing power lives. Supply has an elasticity too, defined identically, and it is the half most analysts skip. Price elasticity of supply is Es = (dQs/dP)·(P/Qs), the percentage change in quantity offered for a one percent change in price, and it is positive because supply curves slope up. What makes it worth a section is that the split of any tax, subsidy or price control between buyers and sellers is decided by the ratio of the two elasticities and by nothing else.
Take the market from Practice Problem 1 and carry it through everything below, so that one set of numbers does all the work. Demand is Qd = 5,000 − 25P and supply is Qs = −1,000 + 50P, which clear at P* = ₹80 and Q* = 3,000. The choke price (where demand hits zero) is ₹200 and the supply curve leaves the axis at ₹20. Consumer surplus is ½(200 − 80)(3,000) = ₹1,80,000, producer surplus is ½(80 − 20)(3,000) = ₹90,000, and total surplus is ₹2,70,000.
At that equilibrium the two elasticities are Ed = −25 × (80/3,000) = −0.6667 and Es = 50 × (80/3,000) = +1.3333. Supply is twice as responsive as demand, which is the whole of what follows.
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Statutory incidence vs economic incidence
Statutory incidence is who writes the cheque. Economic incidence is who ends up poorer. They have nothing to do with each other, and the arithmetic proves it. Levy a specific tax of ₹15 per unit on sellers. Sellers now need ₹15 more per unit to offer any given quantity, so supply becomes Qs = −1,000 + 50(P − 15) = −1,750 + 50P. Solving against unchanged demand gives a buyer's price of ₹90 and a quantity of 2,750; sellers keep 90 − 15 = ₹75. Buyers pay ₹10 more than before and sellers receive ₹5 less, so buyers bear 66.67% of the tax and sellers 33.33%, despite sellers being the ones legally liable.
Now levy the identical ₹15 on buyers instead. Demand becomes Qd = 5,000 − 25(P + 15) = 4,625 − 25P, and solving gives a seller's price of ₹75, a buyer's all-in price of ₹90, and a quantity of 2,750. Every number is the same. The statute chose the payer and changed nothing else.
Tax incidence formula
The rule behind that result is worth memorising, because it answers a question analysts are asked constantly about excise duties, GST changes and carbon levies:
Buyers' share of a tax = Es / (Es + |Ed|)
Sellers' share of a tax = |Ed| / (Es + |Ed|)Here 1.3333 / (1.3333 + 0.6667) = 0.6667, matching the computed 66.67% exactly. The more inelastic side of the market bears more of the tax, because inelasticity is the formal statement of "cannot easily walk away". A cigarette tax lands almost entirely on smokers because their demand is close to vertical; a tax on a commodity with an elastic global supply and inelastic local demand lands on the local buyer. The corporate version of the same statement is the question every consumer-goods analyst asks after a duty change: can this company pass it through? The answer is not a matter of management's determination but of the elasticity ratio it faces, and the pass-through rate observed over the following two quarters is a direct measurement of that ratio.
What is the deadweight loss of a tax?
The tax's total cost exceeds its revenue, and the gap is deadweight loss. Revenue is 15 × 2,750 = ₹41,250. Consumer surplus falls to ½(200 − 90)(2,750) = ₹1,51,250, a loss of ₹28,750; producer surplus falls to ½(75 − 20)(2,750) = ₹75,625, a loss of ₹14,375. The two losses sum to ₹43,125, which is ₹1,875 more than the government collects. That residual is the deadweight loss, the value of the 250 units that were worth more to buyers than they cost sellers and which now do not get traded. Its shape is a triangle and its formula follows: DWL = ½ × tax × ΔQ = ½ × 15 × 250 = ₹1,875. Because ΔQ itself scales with the tax, deadweight loss grows roughly with the square of the tax rate, which is why doubling a levy more than doubles its economic cost, and why the efficiency case for taxation prefers broad low rates to narrow high ones.
What do price ceilings and price floors do?
A binding price ceiling destroys surplus without collecting anything in exchange. Impose a ceiling of ₹60, below the ₹80 equilibrium. Sellers now offer only −1,000 + 50(60) = 2,000 units while buyers want 5,000 − 25(60) = 3,500, a shortage of 1,500 units. Only 2,000 trade. Read the inverse demand curve at that quantity, P = 200 − Q/25, and the 2,000th unit is worth ₹120 to the buyer who gets it, against a controlled price of ₹60. Assuming the units go to the buyers who value them most (the friendliest possible assumption), consumer surplus is ₹2,00,000 and producer surplus is ₹40,000, for a total of ₹2,40,000 against ₹2,70,000 before. The deadweight loss is ₹30,000, sixteen times the loss from the ₹15 tax, and unlike the tax it funds nothing at all. Note also what happened to consumers as a group: their surplus rose, from ₹1,80,000 to ₹2,00,000, which is why ceilings are politically durable, and it rose only under the assumption that the 1,500 disappointed buyers are the ones who valued the good least. Relax that assumption toward random or queue-based rationing and the consumer gain shrinks or vanishes.
A binding price floor does the same damage from the other side. Impose a floor of ₹100, above equilibrium. Buyers take 2,500 units while sellers want to supply 4,000, an excess of 1,500 units, the classic agricultural surplus or the unemployment a minimum wage creates in the textbook model. Inverse supply, P = 20 + Q/50, says the 2,500th unit cost ₹70 to produce against the ₹100 received. Consumer surplus falls to ₹1,25,000 and producer surplus rises to ₹1,37,500, for a total of ₹2,62,500 and a deadweight loss of ₹7,500. Producers gain, buyers lose more than producers gain, and the same triangle formula gives the answer: ½ × (100 − 70) × (3,000 − 2,500) = ₹7,500.
How reliable are these calculations?
Two cautions before this machinery is used on a real policy. The triangles assume linear curves and no income effects, so they are order-of-magnitude devices rather than estimates; the elasticity ratio is far more robust than the deadweight number built on it. And the floor result above holds the demand curve fixed, which is exactly the assumption the empirical minimum-wage literature spends its time testing, so quote the model as a model and not as a finding.