significance of price elasticity of demand and of supply in determining the extent of these changes

1. Foundations – the building blocks of micro‑economics

1.1 Scarcity and choice

• Scarcity: limited resources versus unlimited wants.
• Opportunity cost: the value of the next best alternative foregone when a choice is made.
• Illustrated by a Production Possibility Curve (PPC):
  • Points on the curve = efficient production.
  • Points inside = inefficiency (unused resources).
  • Points outside = unattainable with current resources.
  • Shift outward = economic growth (more resources or better technology); shift inward = recession or disaster.

1.2 Factors of production & classification of goods

Factor	Definition
Land	All natural resources (soil, minerals, climate).
Labour	Human effort – physical and mental.
Capital	Man‑made inputs (machinery, buildings, tools).
Enterprise	Risk‑taking, organisation and coordination of the other factors.

Goods are classified as:

• Private goods: rival & excludable (e.g., a sandwich).
• Public goods: non‑rival & non‑excludable (e.g., street lighting).
• Merit goods: socially desirable, often under‑consumed (e.g., education).
• Demerit goods: socially undesirable, often over‑consumed (e.g., cigarettes).

2. Market equilibrium – a quick refresher

2.1 Demand and supply curves

• Demand (D): quantity consumers are willing to buy at each price, ceteris paribus.
• Supply (S): quantity producers are willing to sell at each price, ceteris paribus.
• Both curves are typically downward‑ and upward‑sloping respectively because of diminishing marginal utility (demand) and rising marginal cost (supply).

2.2 Determinants of demand

Determinant	Effect on D
Income (normal vs. inferior)	↑ income → right shift for normal goods; left shift for inferior goods.
Prices of related goods	↑ price of substitute → right shift; ↑ price of complement → left shift.
Tastes & preferences	Favourable change → right shift.
Expectations of future price or income	Expect higher future price → current demand rises.
Number of buyers	More buyers → right shift.

2.3 Determinants of supply

Determinant	Effect on S
Input prices (wages, raw materials)	Higher input costs → left shift.
Technology	Improvement → right shift.
Expectations of future price	Expect higher future price → current supply falls (left shift).
Number of sellers	More sellers → right shift.
Taxes, subsidies, regulation	Tax → left shift; subsidy → right shift.

2.4 Equilibrium and movement

• Equilibrium (E): intersection of D and S; price P*, quantity Q*.
• A shift in either curve creates a new equilibrium (P₁, Q₁).
• Movement **along** a curve (price change) reflects a change in quantity supplied/demanded, not a shift.

3. Elasticity – measuring responsiveness

3.1 Price elasticity of demand (PED)

Formula (percentage change):

\[ E_d=\frac{\% \Delta Q_d}{\% \Delta P} \]

Mid‑point (arc) formula – preferred for exam questions:

\[ E_d=\frac{(Q_2-Q_1)}{(Q_2+Q_1)/2}\;\bigg/\;\frac{(P_2-P_1)}{(P_2+P_1)/2} \]

Interpretation:

• Elastic (|E_d|>1): quantity changes proportionally more than price.
• Inelastic (|E_d|<1): quantity changes proportionally less.
• Unit‑elastic (|E_d|=1): proportional change.

3.2 Other demand elasticities

Elasticity	Formula	Sign
Income elasticity of demand (YED)	\(E_y=\dfrac{\% \Delta Q_d}{\% \Delta Y}\)	Positive for normal goods, negative for inferior goods.
Cross‑price elasticity of demand (XED)	\(E_{xy}=\dfrac{\% \Delta Q_x}{\% \Delta P_y}\)	Positive for substitutes, negative for complements.

3.3 Price elasticity of supply (PES)

\[ E_s=\frac{\% \Delta Q_s}{\% \Delta P} \qquad E_s=\frac{(Q_2-Q_1)}{(Q_2+Q_1)/2}\;\bigg/\;\frac{(P_2-P_1)}{(P_2+P_1)/2} \]

Interpretation mirrors demand. Supply tends to be:

• More elastic in the long run (firms can adjust plant size).
• Less elastic in the short run (fixed capacity).

3.4 Elasticity and total revenue (TR)

• If demand is elastic, a price **decrease** raises TR (ΔQ outweighs ΔP).
• If demand is inelastic, a price **increase** raises TR.
• At unit‑elasticity, TR is maximised.

4. Consumer and producer surplus – graphical measurement

4.1 Definitions

• Consumer surplus (CS): area between the demand curve and the market price, up to the quantity bought.
• Producer surplus (PS): area between the market price and the supply curve, up to the quantity sold.

4.2 Calculating surplus for linear curves

Demand: \(P = a - bQ\) ; Supply: \(P = c + dQ\)

\[ CS = \tfrac12 Q_0\,(a-P_0) \qquad PS = \tfrac12 Q_0\,(P_0-c) \]

Where \(P_0\) and \(Q_0\) are the equilibrium price and quantity.

4.3 How elasticity influences changes in surplus

Price change	Demand elasticity	Effect on CS	Supply elasticity	Effect on PS
Price rise	Elastic	Large loss (big fall in Q)	Elastic	Moderate gain (Q rises a fair amount)
Price rise	Inelastic	Small loss (Q falls little)	Inelastic	Large gain (price effect dominates)
Price fall	Elastic	Large gain (Q rises sharply)	Elastic	Moderate loss (Q falls a fair amount)
Price fall	Inelastic	Small gain (Q rises little)	Inelastic	Large loss (price effect dominates)

5. Government intervention – welfare analysis

5.1 Taxes

• Specific (per‑unit) tax shifts the supply curve **upwards** by the amount of the tax.
• Incidence depends on relative elasticities:
  • If demand is more elastic than supply → producers bear a larger share.
  • If supply is more elastic than demand → consumers bear a larger share.
• Welfare effects:
  • Consumer surplus ↓
  • Producer surplus ↓
  • Government revenue = tax × Q₁ (new quantity)
  • Dead‑weight loss (DWL) = triangle between the old and new curves, reflecting the reduction in Q.

5.2 Subsidies

• A specific subsidy shifts the supply curve **downwards** (or the demand curve **upwards**) by the subsidy amount.
• Incidence again follows relative elasticities – the side that is more inelastic enjoys a larger share of the benefit.
• Welfare effects:
  • CS ↑, PS ↑
  • Government outlay = subsidy × Q₁
  • DWL arises if the subsidy induces production beyond the efficient quantity (over‑production).

5.3 Price controls

• Price ceiling (set below P*):
  • Creates a shortage: Q_d > Q_s.
  • CS may rise for those who obtain the good, but the **potential** CS lost is shown by the DWL triangle between the demand curve and the ceiling price from Q_s to Q_d.
• Price floor (set above P*):
  • Creates a surplus: Q_s > Q_d.
  • PS may rise for the units sold, but the unsold surplus represents a DWL triangle between the supply curve and the floor price from Q_d to Q_s.

6. Numerical illustrations (exam‑style)

6.1 Specific tax – incidence and DWL

1. Initial equilibrium: P* = £8, Q* = 120.
   Demand: P = 20 – 0.1Q → \(E_d ≈ 1.5\) at P* (elastic).
   Supply: P = 2 + 0.05Q → \(E_s ≈ 0.6\) at P* (inelastic).
2. Specific tax of £2 per unit on producers.
   New supply: P = 2 + 0.05Q + 2 = 4 + 0.05Q.
3. New equilibrium:
   \(20 - 0.1Q = 4 + 0.05Q\) ⇒ \(0.15Q = 16\) ⇒ \(Q_1 ≈ 107\).
   Price paid by consumers: \(P_C = 20 - 0.1(107) ≈ £9.3\).
   Price received by producers: \(P_P = P_C - 2 ≈ £7.3\).
4. Welfare changes (area of triangles):
   • ΔCS = ½ (120 + 107) × (9.3 – 8) ≈ £183.
   • ΔPS = ½ (120 + 107) × (8 – 7.3) ≈ £115.
   • Government revenue = 2 × 107 ≈ £214.
   • DWL = ΔCS + ΔPS – Revenue ≈ £84.
5. Because supply is relatively inelastic, producers bear the larger share of the tax burden (larger fall in PS). The DWL reflects the reduced quantity (107 < 120).

6.2 Specific subsidy – incidence and DWL

1. Same market as above, but a £2 per‑unit subsidy to producers.
2. Supply shifts **down**: \(P = 2 + 0.05Q - 2 = 0.05Q\).
3. New equilibrium:
   \(20 - 0.1Q = 0.05Q\) ⇒ \(0.15Q = 20\) ⇒ \(Q_2 ≈ 133\).
   Consumer price: \(P_C = 20 - 0.1(133) ≈ £6.7\).
   Producer price (including subsidy): \(P_P = P_C + 2 ≈ £8.7\).
4. Welfare changes:
   • ΔCS = ½ (120 + 133) × (8 – 6.7) ≈ £96.
   • ΔPS = ½ (120 + 133) × (8.7 – 8) ≈ £55.
   • Government outlay = 2 × 133 ≈ £266.
   • DWL = Government outlay – (ΔCS + ΔPS) ≈ £115 (over‑production).
5. Supply is inelastic, so producers receive most of the benefit (larger rise in PS). The DWL arises because quantity expands beyond the efficient level.

6.3 Price ceiling (below equilibrium)

1. Ceiling set at £6 (P* = £8).
2. Quantity demanded at £6: \(Q_D = (20‑6)/0.1 = 140\).
3. Quantity supplied at £6: \(Q_S = (6‑2)/0.05 = 80\).
4. Shortage = 60 units.
5. Welfare:
   • CS for the 80 units actually bought = area under D above £6 up to Q=80.
   • Potential CS (if 140 could be supplied) is lost – shown by the DWL triangle between the demand curve and the ceiling price from Q=80 to Q=140.

6.4 Price floor (above equilibrium)

1. Floor set at £10 (P* = £8).
2. Quantity supplied at £10: \(Q_S = (10‑2)/0.05 = 160\).
3. Quantity demanded at £10: \(Q_D = (20‑10)/0.1 = 100\).
4. Surplus = 60 units.
5. Welfare:
   • PS for the 100 units sold = area above S below £10 up to Q=100.
   • The 60 unsold units represent a DWL triangle between the supply curve and the floor price from Q=100 to Q=160.

7. Key take‑aways for the Cambridge syllabus (AO1‑AO3)

• AO1 – Knowledge: Definitions of scarcity, PPC, determinants, elasticity types, CS/PS, DWL, tax/subsidy incidence.
• AO2 – Application: Use diagrams to illustrate shifts, calculate elasticities with the midpoint formula, compute surplus changes and DWL in numerical questions.
• AO3 – Analysis & Evaluation: Explain how relative elasticities determine who bears a tax or subsidy, assess the efficiency of price controls, discuss short‑run vs. long‑run elasticity, and evaluate policy choices (e.g., “Is a tax on cigarettes welfare‑enhancing?”).

8. Sample AS/A‑Level exam question & marking guide

“Explain how the price elasticity of demand and the price elasticity of supply affect the magnitude of the change in consumer and producer surplus when a specific tax is introduced on a good. Use diagrams where appropriate, and comment on the likely size of the dead‑weight loss.”

Suggested answer structure (10‑12 marks)

1. State definitions of PED and PES, include the midpoint formula (2 marks).
2. Draw the initial equilibrium and the new supply curve after the tax; label CS, PS, government revenue and the DWL triangle (3 marks).
3. Explain the incidence rule: the more elastic side bears the smaller share of the tax; link this to the relative sizes of the CS and PS changes (2 marks).
4. Show how a higher PED (or PES) leads to a larger quantity reduction, therefore a larger DWL (2 marks).
5. Evaluation: discuss extreme cases (perfectly elastic/inelastic demand or supply) and the policy implication (1 mark).

Marking criteria (summarised)

Level	What examiners look for
0‑2	Limited knowledge, no relevant diagram.
3‑5	Correct definitions and a basic diagram; some explanation of incidence.
6‑8	Clear link between elasticities and surplus changes; accurate DWL description.
9‑12	Full, accurate analysis, appropriate evaluation, and well‑labelled diagram.

9. Quick revision checklist

• Know the four factors of production and the four types of goods.
• Be able to draw and shift D and S curves; label equilibrium.
• Memorise the midpoint formulas for PED, PES, YED, XED.
• Remember the three elasticity categories and their impact on total revenue.
• Calculate CS and PS for linear curves; recognise the shape of DWL triangles.
• Tax incidence: more elastic side bears less burden; opposite for subsidies.
• Price ceiling → shortage & DWL; price floor → surplus & DWL.
• In evaluation, always consider:
  • short‑run vs. long‑run elasticities,
  • distributional effects,
  • administrative costs,
  • possible unintended consequences.