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9708 · 2.5

Consumer and producer surplus — practice questions

Practice and worked examples for 9708 Consumer and producer surplus. Short previews only — attempt the full question in MarkScheme against the official scheme.

Worked example 1

In a competitive market, demand is P = 20 − Q and supply is P = 4 + Q (P in £, Q in units).

(a) Find equilibrium price and quantity. (b) Calculate consumer surplus and producer surplus at equilibrium.

Show solution outline

(a) Equilibrium: 20 − Q = 4 + Q → 2Q = 16 → Q = 8, P = £12.

(b) Consumer surplus Maximum willingness to pay at Q = 0 is £20. CS = ½ × base × height = ½ × 8 × (20 − 12) = ½ × 8 × 8 = £32.

Producer surplus Minimum supply price at Q = 0 is £4. PS = ½ × 8 × (12 − 4) = ½ × 8 × 8 = £32.

Total surplus = £64 — this is maximised at free-market equilibrium.

On a diagram: shade CS as triangle below demand above P = 12; PS as triangle above supply below P = 12.

Worked example 2

Following on from the previous example (Demand: P = 20 − Q, Supply: P = 4 + Q), the government imposes a specific tax of £4 per unit on producers.

(a) Find the new price paid by consumers and the new quantity traded. (b) Calculate the new consumer surplus, producer surplus, government revenue, and the deadweight loss.

Show solution outline

(a) New Equilibrium with Tax: The tax shifts the supply curve vertically upwards by £4. New supply equation: P = (4 + Q) + 4 → P = 8 + Q. To find the new equilibrium, set new supply equal to demand: 8 + Q = 20 − Q 2Q = 12 Q_tax = 6 units

Substitute Q=6 into the demand curve to find the price consumers pay (Pc): Pc = 20 - 6 = £14

The price producers receive (Pp) is Pc minus the tax: Pp = £14 - £4 = £10.

(b) Welfare Analysis: New Consumer Surplus (CS): Area of the triangle below demand, above the new price Pc = £14. CS = ½ × base × height = ½ × Q_tax × (Max Price - Pc) CS = ½ × 6 × (20 - 14) = ½ × 6 × 6 = £18.

New Producer Surplus (PS): Area of the triangle above original supply, below the new price Pp = £10. PS = ½ × base × height = ½ × Q_tax × (Pp - Min Price) PS = ½ × 6 × (10 - 4) = ½ × 6 × 6 = £18.

Government Revenue: Area of the rectangle representing the tax. Revenue = Tax per unit × Quantity = £4 × 6 = £24.

Deadweight Loss (DWL): The loss in total surplus. Original total surplus was £32 + £32 = £64. New total surplus = New CS + New PS + Gov Revenue = £18 + £18 + £24 = £60. DWL = Original Surplus - New Surplus = £64 - £60 = £4. Alternatively, calculate the area of the DWL triangle: DWL = ½ × (Change in Q) × (Tax) = ½ × (8 - 6) × £4 = ½ × 2 × 4 = £4.

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