Cambridge Syllabus Notes

Consumer and Producer Surplus – Cambridge AS & A Level Economics (9708)

1. What is Consumer Surplus (CS)?

Definition (Syllabus 4.5.1): The difference between the maximum amount a consumer is willing to pay for a good (their marginal willingness‑to‑pay) and the amount actually paid.
Interpretation: It measures the extra benefit, or “net gain”, that consumers obtain when the market price is lower than their willingness‑to‑pay.
Graphical area: The region above the market price line and below the demand curve (usually a triangle).
Mathematical expression (single consumer): \[ CS=\int_{0}^{Q}P_{\text{max}}(q)\,dq-P^{*}\,Q \] where \(P_{\text{max}}(q)\) is the demand (marginal willingness‑to‑pay) curve, \(P^{*}\) the market price and \(Q\) the quantity purchased.
From the integral to the triangle formula: If demand is linear, \(P_{\text{max}}=a-bQ\). Substituting and integrating gives \[ CS=\frac{1}{2}(a-P^{*})Q, \] i.e. one‑half base × height – the familiar triangle area.

2. What is Producer Surplus (PS)?

Definition (Syllabus 4.5.1): The difference between the amount a producer actually receives for a good and the minimum amount they would be willing to accept (their marginal cost).
Interpretation: It represents the extra benefit, or “net gain”, to producers when the market price exceeds their marginal cost.
Graphical area: The region below the market price line and above the supply curve (usually a triangle).
Mathematical expression (single producer): \[ PS=P^{*}\,Q-\int_{0}^{Q}P_{\text{min}}(q)\,dq \] where \(P_{\text{min}}(q)\) is the supply (marginal cost) curve.
Linear supply simplification: If supply is \(P_{\text{min}}=c+dQ\), then \[ PS=\frac{1}{2}(P^{*}-c)Q. \]

3. Total Surplus (TS) and Allocative Efficiency

Total Surplus: \(TS = CS + PS\). It is the measure of overall welfare generated by market activity.
Allocative efficiency (Syllabus 4.5.2): In a perfectly competitive market that is at equilibrium, TS is maximised. Any deviation from this point creates a dead‑weight loss (DWL) and the market is inefficient.

4. Graphical Representation of Surpluses

Typical market diagram – demand (D) and supply (S) intersect at equilibrium price \(P^{*}\) and quantity \(Q^{*}\).

Consumer surplus (CS): Area A – above \(P^{*}\) and below the demand curve.
Producer surplus (PS): Area B – below \(P^{*}\) and above the supply curve.
Total surplus (TS): Areas A + B combined.

5. Numerical Example – Calculating Both Surpluses

Market demand: \(P = 100 - 2Q\) | Market supply: \(P = 20 + 2Q\)

Equilibrium: \[ 100-2Q = 20+2Q \;\Rightarrow\; 4Q = 80 \;\Rightarrow\; Q^{*}=20,\; P^{*}=60 \]
Consumer Surplus: \[ CS = \tfrac12 (P_{\text{max}}-P^{*})Q^{*} = \tfrac12 (100-60)\times20 = 400 \]
Producer Surplus: \[ PS = \tfrac12 (P^{*}-P_{\text{min}})Q^{*} = \tfrac12 (60-20)\times20 = 400 \]
Total Surplus: \(TS = CS + PS = 800\)

6. How Price Changes Affect Surpluses (Syllabus 4.5.2)

Change in market condition	Effect on Consumer Surplus	Effect on Producer Surplus	Typical diagrammatic feature
Increase in market price (e.g., specific tax on producers)	CS falls – the area under the demand curve above the new higher price shrinks.	PS falls – producers receive a lower net price after tax.	New price line above the old one; DWL = triangle between old and new quantities.
Decrease in market price (e.g., subsidy to producers)	CS rises – larger area under demand above the lower price.	PS rises – producers receive a higher net price.	New price line below the old one; possible DWL if over‑production occurs.
Price ceiling (set below equilibrium)	CS may rise for buyers who obtain the good, but total CS falls because quantity supplied falls.	PS falls – lower price and reduced output.	Dead‑weight loss = triangle to the right of the ceiling‑quantity.
Price floor (set above equilibrium)	CS falls – higher price reduces the number of units consumers can afford.	PS may rise for sellers who can sell at the floor price, but excess supply creates a DWL.	Dead‑weight loss = triangle to the left of the floor‑quantity.

Role of Elasticity (Syllabus 4.5.2 & 4.5.5)

The magnitude of the change in CS or PS depends on the price‑elasticities of demand and supply.
A flatter (more elastic) demand curve means a larger change in CS for a given price shift; a steeper (more inelastic) demand curve gives a smaller change.
When a tax is imposed, the side of the market with the more elastic curve bears a larger share of the welfare loss. Conversely, if supply is more elastic, producers lose more.

7. Tax, Subsidy and Dead‑Weight Loss (Syllabus 4.5.3‑4.5.4)

Specific tax on producers (amount = t):
- Supply shifts vertically upwards by \(t\).
- New equilibrium: price paid by consumers \(P_c\) rises; price received by producers \(P_p = P_c - t\) falls.
- Welfare effects:
  - CS falls (area A shrinks).
  - PS falls (area B shrinks).
  - Government revenue = rectangle \(t \times Q_{\text{new}}\).
  - Dead‑weight loss = \(\frac12 t (Q_{\text{orig}}-Q_{\text{new}})\) – the triangle between the old and new quantities.
Specific subsidy to producers (amount = s):
- Supply shifts downwards by \(s\).
- New equilibrium: price to consumers falls; price received by producers rises to \(P_p = P_c + s\).
- Welfare effects:
  - CS rises.
  - PS rises.
  - Government cost = rectangle \(s \times Q_{\text{new}}\) (a negative revenue).
  - Possible DWL if the subsidy induces over‑production: \(\frac12 s (Q_{\text{new}}-Q_{\text{orig}})\).

8. Impact of Market Failure on Surplus (Syllabus “Efficiency and Inefficiency”)

Negative externalities: The private PS overstates true social benefit because the external cost is not reflected in the supply curve. Social surplus = CS + (PS – external cost). The gap between private and social surplus is a dead‑weight loss.
Positive externalities: Private PS understates social benefit; the market under‑produces, creating a DWL that could be corrected by a subsidy.
Public goods and imperfect competition: Because markets do not allocate these efficiently, CS and PS calculated from the private market do not represent total social welfare.

9. Real‑World Application (Syllabus 4.5.7)

Example – UK carbon tax on electricity generation (2023‑24):

Government introduced a specific tax of £18 per tonne of CO₂ emitted.
For a typical coal‑fired plant, the tax shifts the supply curve upward, raising the price paid by electricity consumers and lowering the net price received by generators.
Resulting welfare effects:
- CS falls because households pay more for electricity.
- PS falls for coal generators.
- Government revenue = tax × quantity of electricity produced from coal.
- Dead‑weight loss arises from the reduced quantity of electricity generated (some of the reduction reflects the desired environmental benefit).
The diagram is identical to the generic tax diagram, but the “tax revenue” rectangle now represents a policy objective (reducing emissions) as well as a fiscal gain.

10. Quick Reference Table

Concept	Definition (Syllabus code)	Typical graphical area	Key analytical points
Consumer Surplus (CS)	Benefit to consumers above the price paid (4.5.1)	Above price line, below demand curve	Depends on demand elasticity; falls with price rises, rises with price falls.
Producer Surplus (PS)	Benefit to producers above their minimum acceptable price (4.5.1)	Below price line, above supply curve	Depends on supply elasticity; falls with price falls, rises with price rises.
Total Surplus (TS)	Overall welfare – CS + PS (4.5.2)	Combined shaded areas A + B	Maximised at competitive equilibrium; any distortion creates DWL.
Dead‑Weight Loss (DWL)	Loss of TS due to market distortion (4.5.3‑4.5.4)	Triangular area between demand and supply that is not realised	Size = ½ × price change × quantity change; allocation of loss depends on relative elasticities.
Government revenue / cost	Part of welfare accounting for taxes or subsidies (4.5.3‑4.5.4)	Rectangle = tax (or subsidy) × quantity traded	Added to TS when evaluating total social welfare.

11. Summary

Consumer surplus quantifies the extra satisfaction consumers obtain when they pay less than their maximum willingness‑to‑pay. Producer surplus does the same for firms. Together they form total surplus, the benchmark for allocative efficiency. The size of each surplus is shaped by the price‑elasticities of demand and supply, and any deviation from competitive equilibrium – through taxes, subsidies, price controls, or market failures – alters CS and PS, creating dead‑weight loss. Including government revenue (or cost) completes the welfare analysis and allows the framework to be applied to real‑world policies such as carbon taxes, agricultural subsidies, or rent controls.

meaning and significance of consumer surplus