HL Paper 3 — working a tax problem step by step
Quantitative methods · indirect tax · market equilibrium · HL
Paper 3 rewards method shown clearly. Here's a worked indirect-tax problem the way it should be set out — every step, every unit.
The setup
Demand: Qd = 200 − 2P. Supply: Qs = −40 + 3P. (P in $, Q in units.) A specific tax of $10 per unit is then imposed on producers.
Step 1 — Equilibrium before the tax
Set Qd = Qs: 200 − 2P = −40 + 3P → 240 = 5P → P = $48
Quantity: Q = 200 − 2(48) = 104 units
(Check: −40 + 3(48) = 104 ✓)
Step 2 — The tax shifts supply
A $10 specific tax on producers means they need $10 more for every quantity.
New supply: Qs = −40 + 3(P − 10) = −70 + 3P
Step 3 — New equilibrium
200 − 2P = −70 + 3P → 270 = 5P → P = $54 (the price consumers pay)
Quantity: Q = 200 − 2(54) = 92 units
Producers receive 54 − 10 = $44
Step 4 — Who bears the tax
Consumer price rose $48 → $54: consumers bear $6 of the $10. Producer receipt fell $48 → $44: producers bear $4. Because demand is less elastic than supply here, consumers carry the larger share — 60% vs 40%.
Step 5 — Revenue and welfare
Government revenue = $10 × 92 = $920
Consumer burden = $6 × 92 = $552; producer burden = $4 × 92 = $368 (sum = $920)
Deadweight loss = ½ × $10 × (104 − 92) = ½ × 10 × 12 = $60
The exam takeaway
Paper 3 marks reward the method, not just the final number. Show the equilibrium, show the shifted equation, label every value with its unit, and state who bears more and why. That last step — linking the burden split back to relative elasticity — is where the top marks sit.
This is a taste of the full bank
These four are part of a larger set of carefully chosen real-world examples — each picked to stretch across several syllabus areas, with built-in evaluation and the deployment phrases that turn a fact into marks. I share the complete bank with my students. Book a free class and let's talk about how it fits your exam.