Interaction of Demand and Supply – Alternative Demand (Substitutes)
1. Quick‑Recall: Where Substitutes Fit in the Syllabus
Recall (1.6 – Classification of goods)
Substitutes are a type of private good (rival and excludable). Because they are scarce, consumers must choose between them, making the concept central to the study of scarcity, choice and resource allocation (syllabus 1.1‑1.6).
2. Core Definitions
- Substitute good: a product that can be used in place of another. When the price of one good changes, the quantity demanded of its substitute moves in the opposite direction.
- Cross‑price elasticity of demand (Exy):
\[
E_{xy}= \frac{\%\Delta Q_{x}}{\%\Delta P_{y}}
\]
Positive → substitutes; Negative → complements.
- Own‑price elasticity of demand (Ed):
\[
E_{d}= \frac{\%\Delta Q_{d}}{\%\Delta P}
\]
Measures the responsiveness of the quantity demanded of a good to a change in its own price.
- Price elasticity of supply (Es)**:
\[
E_{s}= \frac{\%\Delta Q_{s}}{\%\Delta P}
\]
- Market equilibrium: the point where quantity demanded (QD) equals quantity supplied (QS); i.e. QD=QS. The market “clears”.
- Disequilibrium: any situation where QD≠QS. A surplus (QS>QD) pushes price down; a shortage (QD>QS) pushes price up.
3. Determinants of Demand for a Substitute (2.1.2)
| Determinant | Effect on demand for Good X (the substitute) |
|---|
| Price of the other good (Y) | ↑ PY → right‑ward shift of DX (if X and Y are substitutes) |
| Consumer income | Normal good: ↑ income → right‑ward shift; Inferior good: ↑ income → left‑ward shift. |
| Tastes & preferences | Favourable view of X → right‑ward shift. |
| Expectations of future prices | Expect higher future price of X → current demand ↑. |
| Number of buyers | More buyers → right‑ward shift. |
4. Determinants of Supply (2.2.2)
| Determinant | Effect on supply of Good X |
|---|
| Input (factor) prices | ↑ input cost → left‑ward shift of SX. |
| Technology & productivity | Improvement → right‑ward shift. |
| Number of sellers | More firms → right‑ward shift. |
| Expectations of future prices | Expect higher future price → current supply ↓ (hold back stock). |
| Time‑frame (short‑run vs long‑run) | Long‑run supply is more elastic because firms can adjust capacity. |
5. Elasticities in Detail (2.2 – 2.3)
5.1 Cross‑price elasticity (Exy)
- Sign: + → substitutes; – → complements.
- Magnitude:
- |Exy| > 1 → strong relationship (large shift).
- 0 < |Exy| < 1 → weak relationship (small shift).
5.2 Own‑price elasticity of demand (Ed)
- Elastic (|Ed| > 1): a small price change causes a large change in quantity demanded.
- Inelastic (|Ed| < 1): quantity demanded is relatively insensitive to price.
- Relation to substitutes: when a good has a high own‑price elasticity, a rise in its own price makes consumers switch more readily to its substitutes.
5.3 Price elasticity of supply (Es)
- Elastic supply (|Es| ≫ 1): quantity supplied responds strongly to price changes (e.g., firms can quickly increase output).
- Inelastic supply (|Es| < 1): quantity supplied changes little (e.g., fixed‑capacity industries).
6. Demand Shifts Caused by Substitutes (2.1.5 – movement vs shift)
- Price of Good Y (the other good) rises.
- Consumers re‑allocate spending to Good X if X and Y are substitutes.
- The demand curve for Good X shifts:
- Right‑ward for substitutes → higher QD at every price.
- Left‑ward for complements → lower QD at every price.
- The size of the shift depends on the absolute value of Exy (see section 5).
Diagram tip (5.1 – Efficiency)
When drawing the shift, keep the original and new demand curves on the same axes. Shade the area between them and the supply curve to show the change in consumer surplus. Label the original equilibrium (E0) and the new equilibrium (E1). Explain whether the market moves toward or away from allocative efficiency (i.e., whether total surplus increases).
7. Interaction with Supply – Simultaneous Shifts (2.3 – Market equilibrium)
| Scenario |
Demand shift |
Supply shift |
Effect on equilibrium price (P*) |
Effect on equilibrium quantity (Q*) |
| 1. Demand ↑, Supply ↔ |
Right‑ward |
No change |
↑ |
↑ |
| 2. Demand ↓, Supply ↔ |
Left‑ward |
No change |
↓ |
↓ |
| 3. Demand ↑, Supply ↓ |
Right‑ward |
Left‑ward |
↑ (larger) |
Ambiguous (depends on magnitude) |
| 4. Demand ↓, Supply ↑ |
Left‑ward |
Right‑ward |
↓ (larger) |
Ambiguous |
Supply response to a permanent demand shift: If producers expect the shift to be lasting, they may expand capacity (e.g., build new factories). The speed and extent of this response are governed by the price elasticity of supply (Es).
8. Welfare Implications – Consumer & Producer Surplus (5.1)
- Right‑ward demand shift for a substitute raises consumer surplus (CS) for that good because consumers obtain more utility at the same or a lower price.
- Producer surplus (PS) for the original good (whose price fell) may decline, while PS for the substitute rises.
- If the total surplus (CS + PS) rises, the market moves toward a more efficient allocation; if it falls, there is a dead‑weight loss.
9. Real‑World Illustration
Scenario: A sudden oil supply shock pushes the price of gasoline up by 25 %.
- Gasoline and public transport (buses, trains) are substitutes (Egp ≈ 0.5).
- Higher gasoline price → demand for public transport shifts rightward by roughly 12.5 % (0.5 × 25 %).
- Result: higher equilibrium price and quantity in the public‑transport market; consumer surplus for commuters who switch increases, while producer surplus in the fuel market falls.
- This example links a price shock in one market to a demand shift, equilibrium change, and welfare impact in another market.
10. A‑Level Extension – Joint & Derived Demand (2.4 – 2.5)
Joint demand: Two goods are demanded together (e.g., petrol and cars). A price rise in one leads to a left‑ward shift in the demand for the other; cross‑price elasticity is negative.
Derived demand: The demand for a factor of production (e.g., steel) depends on the demand for the final product (e.g., cars). If a substitute for the final product becomes more popular, the derived‑demand market for its inputs can contract.
11. Exam‑Style Question (IGCSE / A‑Level)
Question: The price of gasoline rises by 15 %. The cross‑price elasticity of demand between gasoline and electric cars is Ege = 0.9. Calculate the expected percentage change in the quantity demanded of electric cars and describe the likely effect on the electric‑car market equilibrium, assuming an upward‑sloping supply curve.
Answer outline:
- Use the cross‑price elasticity formula:
\(0.9 = \dfrac{\%\Delta Q_{\text{electric}}}{15\%}\)
- \(\%\Delta Q_{\text{electric}} = 0.9 \times 15\% = 13.5\%\) increase.
- Demand for electric cars shifts rightward by 13.5 %.
- With an upward‑sloping supply curve, the new equilibrium shows a higher price and a higher quantity of electric cars.
- Consumer surplus for electric‑car buyers rises; producer surplus for manufacturers also rises, while gasoline producers lose surplus.
12. Quick‑Reference Checklist – Syllabus Alignment (9708)
| Syllabus requirement | How the notes meet it | What is still missing / could be improved | Actionable suggestion |
|---|
| 1.1‑1.6 (Basic ideas & resource allocation) |
Recall box places substitutes under private goods and links to scarcity & choice. |
None. |
— |
| 2.1‑2.5 (Demand & supply, interaction, surplus) |
Full coverage of demand‑shift mechanics, equilibrium, CS/PS, and diagram tip. |
Explicit list of demand & supply determinants was missing. |
Added tables of determinants (sections 3 & 4). |
| 2.2‑2.3 (Elasticities) |
Cross‑price, own‑price, and supply elasticities defined with formulas and interpretation. |
Own‑price elasticity previously absent. |
Inserted own‑price elasticity box (section 5.2). |
| 2.4‑2.5 (Market equilibrium, surplus, efficiency) |
Four‑scenario table, welfare discussion, and diagram tip linking to efficiency. |
Diagram description was vague. |
Provided explicit “Diagram tip”. |
13. Summary
- Substitutes have a positive cross‑price elasticity; complements have a negative one.
- A price change in one market causes a demand shift in the other, altering equilibrium price, quantity, and total welfare.
- The magnitude of the shift is governed by |Exy|, while the size of the price change depends on the elasticity of supply.
- Own‑price elasticity of demand determines how strongly consumers react to their own price change and therefore how large the spill‑over effect to substitutes can be.
- Understanding these inter‑market links is essential for analysing policy impacts, external shocks, and firm strategy at both IGCSE and A‑Level depth.