9 min readConcept sheetOften a 5-mark calculation or a 10-mark essay

Tax incidence, consumer surplus and producer surplus

Whoever is less responsive to price bears more of a tax. Consumer and producer surplus measure the gains from trade, which a tax partly destroys.

Tax incidenceWho really bears a tax

RuleThe less elastic side pays more

Consumer surplusWilling to pay − price paid

Producer surplusPrice received − minimum acceptable

Impact and incidence of a tax

The impact of a tax is on whoever hands the money to the government, usually the seller. The incidence is on whoever finally bears the cost. A specific tax of Rs. t per unit shifts the supply curve up by t. Buyers then pay a higher price and sellers keep a lower price; the gap between the two is the tax. The share paid by consumers is Es ÷ (Es + |Ed|) and by producers |Ed| ÷ (Es + |Ed|). So the side with the lower elasticity carries the larger burden.

How a tax on sellers works through the market

Worked example 1: who pays a Rs. 25 tax?

Problem

Coconut market: Qd = 6,000 − 20P and Qs = 30P − 1,500 (equilibrium Rs. 150, 3,000 nuts). The government levies Rs. 25 per nut on sellers. Find the new prices, quantity, tax revenue and each side's burden.

Working

Sellers now keep (P − 25), so supply becomes Qs = 30(P − 25) − 1,500 = 30P − 2,250.
6,000 − 20P = 30P − 2,250 → 8,250 = 50P → buyers' price P = Rs. 165.
Q = 6,000 − 20 × 165 = 6,000 − 3,300 = 2,700. Sellers keep 165 − 25 = Rs. 140 (check: 30 × 140 − 1,500 = 2,700 ✓).
Consumer burden = 165 − 150 = Rs. 15 per nut (15 ÷ 25 = 60%). Producer burden = 150 − 140 = Rs. 10 per nut (40%).
Tax revenue = 25 × 2,700 = Rs. 67,500 a day: consumers pay 15 × 2,700 = 40,500 and producers 10 × 2,700 = 27,000.
Check with elasticities at the old equilibrium: |Ed| = 20 × 150 ÷ 3,000 = 1; Es = 30 × 150 ÷ 3,000 = 1.5. Consumer share = 1.5 ÷ (1.5 + 1) = 0.6 = 60%. ✓

Answer

Buyers pay Rs. 165, sellers keep Rs. 140, 2,700 nuts are sold. Consumers bear 60% (Rs. 15) and producers 40% (Rs. 10); revenue is Rs. 67,500 a day.

Elasticity decides who pays

Situation	Who bears most of the tax	Example
Demand inelastic, supply elastic	Consumers	Cigarettes, liquor, fuel
Demand elastic, supply inelastic	Producers	A product with many substitutes made in fixed capacity
Demand perfectly inelastic	Consumers bear all of it	An essential medicine in the short run
Supply perfectly inelastic	Producers bear all of it	A fixed stock that must be sold, such as land

Consumer surplus and producer surplus

Consumer surplusThe difference between the most a buyer is willing to pay and the price actually paid. If you would pay Rs. 500 for a book but buy it for Rs. 350, your surplus is Rs. 150. On a diagram it is the area below the demand curve and above the price.

Producer surplusThe difference between the price a seller receives and the lowest price it would accept (its marginal cost). On a diagram it is the area above the supply curve and below the price.

Consumer surplus + producer surplus = total gains from trade. It is largest at the free-market equilibrium.

Worked example 2: surplus before and after the tax

Problem

In the coconut market, demand meets the price axis at Rs. 300 (Qd = 0) and supply starts at Rs. 50 (Qs = 0). Calculate consumer surplus (CS) and producer surplus (PS) at the free equilibrium and after the Rs. 25 tax, and the deadweight loss.

Working

Before tax: CS = ½ × 3,000 × (300 − 150) = ½ × 3,000 × 150 = Rs. 225,000.
Before tax: PS = ½ × 3,000 × (150 − 50) = ½ × 3,000 × 100 = Rs. 150,000. Total = Rs. 375,000.
After tax: CS = ½ × 2,700 × (300 − 165) = ½ × 2,700 × 135 = Rs. 182,250.
After tax: PS = ½ × 2,700 × (140 − 50) = ½ × 2,700 × 90 = Rs. 121,500. Tax revenue = Rs. 67,500.
Total after tax = 182,250 + 121,500 + 67,500 = Rs. 371,250.
Deadweight loss = 375,000 − 371,250 = Rs. 3,750. Check: ½ × 25 × (3,000 − 2,700) = ½ × 25 × 300 = 3,750. ✓

Answer

CS falls from Rs. 225,000 to Rs. 182,250 and PS from Rs. 150,000 to Rs. 121,500. The government collects Rs. 67,500, and Rs. 3,750 a day of gains from trade is lost (deadweight loss).

In Sri Lankan business

Excise taxes on cigarettes, liquor and fuel in Sri Lanka fall mostly on consumers, because demand for these goods is inelastic. A firm in a market with many substitutes, such as a biscuit maker, cannot pass on a new tax so easily and must absorb more of it in its margins.

Exam angle

Short answer: “Define consumer surplus.” The difference between what consumers are willing to pay and what they actually pay; the area under the demand curve above the price.

Structured question: “With Qd = 6,000 − 20P and Qs = 30P − 1,500, a Rs. 25 tax is placed on sellers. Show how the burden is shared.” New supply 30P − 2,250, so buyers pay Rs. 165, sellers keep Rs. 140, Q = 2,700. Consumers bear Rs. 15 (60%), producers Rs. 10 (40%).

Essay: “Explain how the burden of an indirect tax is distributed between consumers and producers, and its effect on consumer and producer surplus.” Define impact and incidence, draw the tax diagram, explain the elasticity rule with cases, work a numerical example, and show the fall in CS and PS and the deadweight loss.

Remember it

The tax sticks to the stubborn side: whoever is less elastic pays more. Surplus = triangles: CS above price, PS below price.