causes of changes in consumer and producer surplus

Consumer and Producer Surplus – Causes of Change (Cambridge AS & A‑Level 9708)

1. Core Definitions & Formulae

• Consumer Surplus (CS): The monetary benefit to consumers because they pay less than the maximum they are willing to pay.
  Formula (linear demand):  CS = ½ × Qₑ × (Pmax – Pₑ)
  where P_max is the price where the demand curve meets the vertical axis (the choke price) and Pₑ is the market price.
• Producer Surplus (PS): The monetary benefit to producers because they receive more than the minimum they are willing to accept.
  Formula (linear supply):  PS = ½ × Qₑ × (Pₑ – Pmin)
  where P_min is the price where the supply curve meets the vertical axis.
• Total Surplus (TS): TS = CS + PS. At a competitive equilibrium without externalities, TS is maximised – the market is allocatively efficient.

Worked Numerical Example (Linear Curves)

Demand: P = 100 – 2Q Supply: P = 20 + Q

1. Set demand = supply: 100 – 2Q = 20 + Q → 3Q = 80 → Qₑ = 26.7 (≈ 27 units).
2. Find equilibrium price: Pₑ = 20 + Qₑ = 46.7 (≈ £47).
3. Choke price (demand intercept) = 100; supply intercept = 20.
4. CS = ½ × 27 × (100 – 47) = ½ × 27 × 53 = 715.5.
5. PS = ½ × 27 × (47 – 20) = ½ × 27 × 27 = 364.5.
6. TS = 715.5 + 364.5 = 1 080.

2. Why CS and PS Matter (Key Syllabus Concepts)

• Efficiency & Welfare: CS + PS measures the total net benefit to society. Maximising TS = allocative efficiency.
• Distribution of Income & Welfare: The split of TS between consumers, producers, and the government (via taxes/subsidies) shows who gains and who loses.
• Equilibrium & Disequilibrium: Any movement of price or quantity away from the competitive equilibrium changes CS and PS.

3. Diagram Requirements (A‑Level)

• Vertical axis = Price (P); Horizontal axis = Quantity (Q).
• Draw linear (or clearly shaped) Demand (D) and Supply (S) curves.
• Mark the initial equilibrium (Pₑ, Qₑ) and shade:
  • CS – area above Pₑ and below D.
  • PS – area below Pₑ and above S.
• When a tax, subsidy, price ceiling or floor is introduced, also show:
  • New price(s) faced by consumers (P_c) and producers (P_p).
  • Government‑revenue rectangle (tax) or government‑cost rectangle (subsidy) – label clearly.
  • Dead‑weight‑loss (DWL) triangle.
• If elasticity is discussed, sketch a relatively flat (elastic) and a steep (inelastic) curve as a side note.

4. Main Drivers of Change in CS and PS

4.1. Shifts in Demand

• Increase in demand (right‑ward shift)
  • New equilibrium: higher price, higher quantity.
  • CS: Ambiguous.
    • If demand is **elastic** (flat), the large quantity increase outweighs the price rise → CS rises.
    • If demand is **inelastic** (steep), the price effect dominates → CS falls.
  • PS: Generally **increases** – producers receive a higher price and sell more.
• Decrease in demand (left‑ward shift)
  • New equilibrium: lower price, lower quantity.
  • CS: Usually **decreases**; the magnitude again depends on elasticity (more elastic → larger fall).
  • PS: **Decreases** because of the lower price and reduced output.

4.2. Shifts in Supply

• Increase in supply (right‑ward shift)
  • New equilibrium: lower price, higher quantity.
  • CS: **Increases** – consumers pay less and buy more.
  • PS: Ambiguous.
    • If supply is **elastic** (flat), the quantity gain outweighs the price fall → PS rises.
    • If supply is **inelastic** (steep), the price fall dominates → PS falls.
• Decrease in supply (left‑ward shift)
  • New equilibrium: higher price, lower quantity.
  • CS: **Falls** because of the higher price.
  • PS: Ambiguous.
    • Inelastic supply → price effect dominates → PS rises.
    • Elastic supply → quantity loss dominates → PS falls.

4.3. Role of Price Elasticity (Demand & Supply)

• Elasticity determines the *size* of the CS/PS change for a given price move.
  • High **price elasticity of demand** → large quantity response → larger CS change.
  • High **price elasticity of supply** → large quantity response → larger PS change.
• Elasticities also decide the *distribution* of tax or subsidy burden (see 4.4.1).

4.4. Government Intervention

4.4.1. Per‑Unit Tax (on producers)

1. Supply curve shifts **upward** by the amount of the tax: S → S_tax.
2. Resulting equilibrium:
   • Consumers pay a higher price P_c.
   • Producers receive a lower net price P_p = P_c – t.
   • Quantity falls from Qₑ to Q_t.
3. CS ↓ (higher price, lower quantity).
4. PS ↓ (lower net price, lower quantity).
5. Government revenue: rectangle with height = tax (t) and width = Q_t. Must be drawn and labelled.
6. Dead‑weight loss (DWL): triangle between the original and new supply curves over the reduction in quantity.
7. Incidence rule (syllabus requirement): The side of the market with the **more elastic** curve bears the **smaller** share of the tax burden. Hence:
   • If demand is more elastic than supply → producers bear a larger share.
   • If supply is more elastic than demand → consumers bear a larger share.

4.4.2. Per‑Unit Subsidy (to producers)

1. Supply curve shifts **downward** by the subsidy amount: S → S_sub.
2. New equilibrium:
   • Consumers pay a lower price P_c.
   • Producers receive a higher effective price P_p = P_c + s.
   • Quantity rises to Q_s.
3. CS ↑ (lower price, higher quantity).
4. PS ↑ (higher effective price, higher quantity).
5. Government cost: rectangle with height = subsidy (s) and width = Q_s. Must be drawn and labelled.
6. DWL: Usually **none** if the subsidy corrects a market failure; however, the fiscal cost is borne by taxpayers.
7. Incidence rule: Same as for a tax – the side with the more elastic curve receives a smaller net benefit from the subsidy.

4.4.3. Price Ceiling (set P_c < Pₑ)

• Creates a **shortage**: quantity demanded > quantity supplied at the ceiling price.
• CS: Mixed – consumers who obtain the good at the lower price gain, but overall CS falls because many are rationed out.
• PS: **Falls sharply** – lower price and reduced sales.
• DWL: Triangle between D and S over the shortage quantity.
• Real‑world example: rent controls in Berlin (2020‑2021).

4.4.4. Price Floor (set P_f > Pₑ)

• Creates a **surplus**: quantity supplied > quantity demanded at the floor price.
• CS: **Falls** – higher price reduces consumer surplus.
• PS: Mixed – producers who can sell at the higher price gain, but the surplus units that remain unsold generate no surplus, so total PS may fall.
• DWL: Triangle between D and S over the unsold quantity.
• Real‑world example: EU Common Agricultural Policy price supports.

4.5. Changes in Market Size or Preferences

• Population growth or income growth shifts demand outward (right‑ward).
• Changes in tastes, expectations, or prices of related goods (substitutes/complements) also shift demand.
• These shifts follow the same CS/PS patterns described in Section 4.1.

5. Summary Table of Effects

6. Exam‑Style Checklist (A‑Level)

1. Identify which curve shifts (demand or supply) and the direction of the shift.
2. State the resulting change in equilibrium price and quantity.
3. On the diagram, shade the new CS and PS areas and describe the change (increase, decrease, or ambiguous).
4. If a tax, subsidy, ceiling or floor is involved:
   • Show the new consumer price (P_c) and producer price (P_p).
   • Label the government‑revenue rectangle (tax) or government‑cost rectangle (subsidy).
   • Draw and label the dead‑weight‑loss triangle.
   • Apply the **incidence rule** – the more elastic side bears the smaller burden.
5. Explain how price elasticity of demand and supply influences the magnitude of the CS/PS changes.
6. Link the outcome to the key concepts of **efficiency**, **equilibrium**, and **distribution**.
7. Provide a concise real‑world example to illustrate the mechanism.

7. Quick Reference – Key Concepts

• Efficiency & Welfare: TS = CS + PS is maximised at competitive equilibrium.
• Equilibrium & Disequilibrium: Shifts in D or S move the market away from (or back to) equilibrium, altering CS and PS.
• Elasticity: Determines both the *size* of CS/PS changes and the *distribution* of tax/subsidy burden.
• Distribution: Taxes/subsidies re‑allocate surplus between consumers, producers, and the government.
• Incidence Rule (mandatory for 2.5.2): The side with the more elastic curve bears the smaller share of a tax (or receives the smaller share of a subsidy).