MGEA02H3 Chap.4 Elasticity and Excise Taxes
Elasticity and Excise Taxes
Point elasticity the course way
Elasticity is measured with the calculus point formula, ED = |(dQ/dP)(P/Q)|, inverting the slope when the curve is written in price form.
Along a straight demand curve elasticity falls from elastic to inelastic, passing through one at the midpoint, and revenue responds to price according to dTR/dP = Q(1 − ED).
Who bears an excise tax
A per-unit tax is modelled by shifting supply up or demand down by the tax. The split between buyers and sellers follows ES/ED, not the legal payer.
Revenue is the tax times the new quantity, and the excess burden is the triangle of lost trades, which grows with the elasticities. Past tests also ask for the revenue-maximising tax.
What the answer keys reward
Tax questions in the keys shift the curve by the tax, solve the new quantity, read the buyers’ price from demand and the sellers’ price from supply, and only then compute revenue and excess burden.
Incidence items reach the split through the elasticity ratio, and keys accept either route if both are shown.
In true-or-false items on taxes, the explanation earns nearly all the marks, so a correct verdict without a mechanism scores little.
How this topic connects to later chapters
Elasticity returns in chapter 8, where the monopolist’s marginal revenue equals P(1 − 1/ED) and output is always chosen on the elastic part of demand.
The tax wedge reappears in chapter 7, where entry and exit make buyers bear the whole tax in the long run, and in chapter 10, where a corrective tax is designed to change quantity on purpose and so carries no excess burden.
What this chapter covers
- 01
Point elasticity of demand and supply
- 02
Elasticity along a linear demand curve
- 03
Total revenue and elasticity
- 04
Tax incidence and the ES/ED ratio
- 05
Tax revenue and excess burden
- 06
The revenue-maximising tax
Worked example · free
A $10 tax and how the burden is shared
- 2Before the tax, Q = 2,000 at $40; ED = 0.5 and ES = 2.
- 2Shift supply to P = 30 + 0.01Q, so Q = 1,800.
- 2Buyers pay $48 and sellers keep $38, a 4 to 1 split matching ES/ED.
- 2Revenue is $18,000 and the excess burden is ½ × 200 × 10 = $1,000.
Key terms
- Price Elasticity of Demand
- Price elasticity of demand is the percentage change in quantity demanded per percentage change in price, reported here as a positive number.
- Tax Incidence
- Tax incidence is the division of a tax’s burden between buyers and sellers, set by the elasticities.
- Excess Burden
- Excess burden is the surplus lost because a tax prevents trades, beyond the revenue collected.
- Unit Elastic Demand
- Unit elastic demand has an elasticity of exactly one, where a small price change leaves spending unchanged.
- Tax Wedge
- A tax wedge is the gap between the price buyers pay and the price sellers receive.
Elasticity and Excise Taxes FAQ
Does it matter whether buyers or sellers pay the tax to the government?
No. Shifting supply up or demand down by the same tax produces the same quantity, the same two prices and the same revenue. Only the elasticities of demand and supply decide who bears the burden.
How can a revenue change be found without knowing the price?
Use ΔTR ≈ Q(1 − ED)ΔP. Multiply current quantity by one minus the elasticity and by the price change; the price itself is not needed, which is why some past questions leave it out.
Why does more elastic demand increase the excess burden?
With more elastic demand, quantity falls further when the tax raises the price. The excess burden is half the fall in quantity times the tax, so a bigger fall in quantity means a bigger triangle of lost trades.
Why do inelastic goods make cheaper taxes?
When demand is inelastic, a tax barely reduces the quantity bought, so few trades are lost and the excess burden is small relative to the revenue raised. The cost to society of each dollar collected, revenue plus burden over revenue, is therefore lower.
Exam move
For one pair of linear curves, compute both elasticities at equilibrium, predict the split of a tax from their ratio, then solve the taxed equilibrium and confirm the prediction. Finish with the revenue-maximising tax. Finish each session by stating the five limiting cases from memory, perfectly elastic and inelastic demand and supply, and who bears the tax in each.
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