BEO6600 · Business Economics
Taxation and Welfare
This is the densest, highest-yield session in the closed-book exam. A per-unit tax drives a wedge between the price buyers pay (PB) and the price sellers receive (PS): PB rises, PS falls, and quantity falls — and the outcome is identical whether the tax is levied on buyers or sellers. Government collects tax revenue = t × Q (a rectangle, merely transferred), but consumer and producer surplus fall by more; the difference is the deadweight-loss triangle. The burden lands on whichever side is less elastic. As a tax grows, deadweight loss rises roughly with its square while revenue rises then falls — the Laffer curve. A subsidy is the mirror image (over-production, a deadweight loss too), and an externality makes the market trade the wrong quantity, fixed by a corrective (Pigovian) tax or subsidy, or by tradable permits.
What this chapter covers
- 015.1 Tax incidence: the less-elastic side bears more
- 02Statutory vs economic incidence (independent of who pays)
- 035.2 The wedge, the revenue rectangle and the deadweight-loss triangle
- 045.3 The size of the tax and the Laffer curve
- 055.4 Subsidies: the mirror wedge and over-production deadweight loss
- 065.5 Negative and positive externalities
- 075.6 Correcting externalities: Pigovian tax/subsidy, permits, a note on Coase
Worked example: a $0.60 per-unit tax — revenue and deadweight loss
- +1(a) The wedge: PB − PS = $3.40 − $2.80 = $0.60 = the tax, exactly as required.
- +1(b) Tax revenue = t × Qafter = $0.60 × 90 = $54 — the rectangle, transferred from buyers and sellers to government.
- +1(c) Deadweight loss = ½ × t × ΔQ = ½ × $0.60 × (100 − 90) = ½ × 0.60 × 10 = $3 — the triangle, lost to everyone.
- +1(d) More inelastic demand → smaller deadweight loss. Quantity shrinks less when demand (or supply) is less elastic, so the DWL triangle is smaller. This is why efficient taxes fall on inelastic goods.
- +1Read it: revenue is merely transferred; only the $3 triangle is destroyed. Do not shade the rectangle as 'the loss' — that is a classic dropped mark.
Key terms
- Tax wedge
- The gap a per-unit tax opens between the price buyers pay (PB) and the price sellers receive (PS): PB − PS = t. The result — PB up, PS down, quantity down — is the same whether the tax is levied on buyers or sellers.
- Tax incidence
- Who actually bears the burden of a tax, as opposed to who legally pays it (statutory incidence). The burden falls more heavily on the side that is less elastic (steeper) — the side that cannot easily change behaviour to escape the tax — regardless of who writes the cheque.
- Deadweight loss
- The triangle of surplus destroyed when a tax (or subsidy, or market power) pushes quantity away from the efficient Q*: ½ × t × ΔQ for a tax. It is surplus from mutually beneficial trades that no longer happen, captured by no one — distinct from the revenue rectangle, which is merely transferred.
- Laffer curve
- The inverted-U relationship between the tax rate and tax revenue. As the rate rises, deadweight loss grows roughly with its square, while revenue rises then falls; at a 0% rate and a prohibitive 100% rate revenue is zero, so a revenue-maximising rate t* sits in between.
- Corrective (Pigovian) tax/subsidy
- A policy that makes a decision-maker internalise an externality by setting the corrective tax equal to the external cost (for a negative externality) or the corrective subsidy equal to the external benefit (for a positive one), moving the market to the social optimum Q*. Tradable pollution permits achieve the same outcome via the quantity route.
Taxation and Welfare FAQ
Does it matter whether a tax is levied on buyers or sellers?
No — the outcome is identical either way. A tax on sellers shifts supply up by the tax; a tax on buyers shifts demand down by the tax; both leave buyers paying more, sellers receiving less, and quantity lower by the same amounts. Statutory incidence (who pays the tax office) and economic incidence (who really bears the burden) are different things; the burden is split by relative elasticity, not by who hands over the money.
Who bears more of a tax?
The less-elastic (steeper) side — the side that cannot easily change its behaviour to escape the tax. Elastic supply plus inelastic demand puts the burden on consumers; inelastic supply plus elastic demand puts it on producers. A payroll tax 'on employers' can land squarely on workers if labour supply is inelastic.
What is the difference between the tax revenue and the deadweight loss?
Tax revenue is the rectangle t × Q — surplus merely transferred from buyers and sellers to government, not lost to society. The deadweight loss is the triangle beyond the new quantity: surplus from mutually beneficial trades that no longer happen, destroyed and captured by no one. Shading the rectangle as 'the loss' is a classic dropped mark.
Do subsidies and externalities also create deadweight loss?
Yes. A subsidy pushes quantity above the efficient Q* (over-production); both surpluses rise, but the taxpayer-funded cost is larger still, so the gap is a deadweight loss. An externality makes the market trade the wrong quantity — over-producing under a negative externality, under-producing under a positive one — and the fix is a corrective tax equal to the external cost, a subsidy equal to the external benefit, or tradable permits (the quantity route, with Coase-theorem logic).
Exam move
This session is the highest-yield drawing in the exam, so practise it until it is automatic. For a tax: open the wedge at the new quantity, mark PB on demand and PS on supply, shade the revenue rectangle (t × Q) and the deadweight-loss triangle (½ × t × ΔQ), and label every axis, curve and area. Then reason: the less-elastic side bears more, and more elastic curves mean a bigger deadweight loss. For the Laffer curve, remember deadweight loss rises with the square of the tax while revenue rises then falls. For a subsidy, draw the mirror wedge and the over-production deadweight loss. For externalities, draw the social curve on whichever side the spillover lands — negative → over-produce → tax = external cost; positive → under-produce → subsidy = external benefit.
