Cambridge A‑Level Economics (9708) – Unit 5/7: Derived Demand in Factor Markets
Syllabus codes: 5.3 (AS) / 7.6 (A‑Level)
1. Definition of Derived Demand (Syllabus 5.3 (i))
- Derived demand is the **demand for a factor of production** (labour, capital, land, entrepreneurship) that exists **because** there is demand for the final goods or services that the factor helps to produce.
- It is called “derived” because the factor’s demand is **derived from the demand for the product**.
- In the margin‑decision framework, a firm will employ an additional unit of a factor only if the value of its marginal product (VMP) exceeds or equals the factor’s price (W). This links derived demand directly to profit‑maximising behaviour (AO2).
2. Linking Product and Factor Markets (Syllabus 5.3 (i) & (ii))
- Consumers create demand for final goods in the product market.
- Firms respond by purchasing the required factors in the factor market.
- The quantity of a factor demanded depends on:
- the quantity of the product the firm intends to produce, and
- the technology (input‑output coefficients) used to produce that product.
Diagram suggestion: A two‑panel diagram – left panel shows the product‑market demand & supply for the final good; an arrow labelled “derived demand” points to the right panel showing the derived‑demand curve for a factor.
3. Deriving the Factor‑Demand Curve (Syllabus 5.3 (iii)–(iv))
The derived demand for a factor (F) can be expressed as a function of the price of the final product (PY) and the technology employed:
\( Q_{D}^{F}=g\big(P_{Y},\;\text{technology}\big) \)
- QDF – quantity of the factor demanded.
- PY – price of the final product.
- Technology – determines the marginal product of the factor (MPF) and the input‑output coefficient (aF = 1/MPF).
When technology improves, MPF rises, aF falls and the derived‑demand curve shifts left (less of the factor is needed for any given output level).
4. Determinants of Derived Demand (Syllabus 5.3 (i)–(vii))
| Determinant (Syllabus code) |
Effect on Factor Demand |
Explanation (linked to syllabus) |
| Price of the final product, PY (5.3 (iii)) |
↑ PY → ↑ derived demand |
Higher product price raises revenue, encouraging firms to expand output and hire more of the factor (VMP rises). |
| Technology / productivity of the factor (5.3 (iv)) |
↑ productivity → ↓ derived demand |
Improved technology raises MPF, reducing the amount of the factor required per unit of output (input‑output coefficient falls). |
| Price of substitute factors (5.3 (v)) |
↑ price of substitute → ↑ demand for the considered factor |
Firms substitute away from the more expensive factor towards the cheaper one, increasing derived demand for the cheaper factor. |
| Price of complementary factors (5.3 (vi)) |
↑ price of complement → ↓ derived demand |
Higher cost of a complementary factor raises total production cost, reducing the quantity of all associated factors demanded. |
| Number of firms in the industry (5.3 (vii)) |
↑ number of firms → ↑ derived demand |
More firms mean higher aggregate output, shifting the factor‑demand curve to the right. |
| Changes in consumer tastes / income (affecting product demand) (5.3 (i)) |
↑ product‑market demand → ↑ derived demand |
Any factor that shifts the product‑market demand curve also shifts the derived‑demand curve for the factor. |
| Price of the factor itself (W) – causes movement **along** the curve (5.3 (ii)) |
↑ W → movement up the derived‑demand curve (lower QDF) |
When the factor price changes, the derived‑demand curve is unchanged; the firm moves to a new point on the curve where VMP = W. |
5. Movements Along vs. Shifts of the Derived‑Demand Curve
- Movement along the curve: Caused by a change in the factor’s own price (W) while product‑market conditions and technology remain unchanged.
- Shift of the curve: Caused by any of the determinants listed above (e.g., change in PY, technology, prices of related factors, entry/exit of firms, consumer preferences).
6. Elasticity of Derived Demand (Syllabus 5.3 (viii))
Elasticity measures the responsiveness of the quantity demanded of a factor to a change in the price of the final product:
\( \varepsilon_{D}^{F}= \dfrac{\% \Delta Q_{D}^{F}}{\% \Delta P_{Y}} \)
Four key determinants (required by the syllabus):
| Determinant |
Effect on Elasticity |
Illustrative example |
| Availability of close substitutes for the factor |
More substitutes → more elastic derived demand |
Labour can be replaced by robots; a rise in robot price makes labour demand more responsive. |
| Share of total cost accounted for by the factor |
Higher cost‑share → more elastic derived demand |
Energy costs form a large share of a steel plant’s total cost, so a change in steel price greatly affects energy demand. |
| Elasticity of demand for the final product |
If product demand is elastic, derived demand tends to be elastic |
Smart‑phone demand is price‑elastic; a fall in phone price reduces the derived demand for assembly‑line workers noticeably. |
| Time horizon |
Long‑run elasticity > short‑run elasticity |
In the short run firms cannot change plant size, but in the long run they can adopt new technology, making labour demand more responsive to product‑price changes. |
7. Core Factor‑Market Concepts Required for the Same Unit
- Marginal Product of a Factor (MPF) – additional output from one more unit of the factor.
- Value of the Marginal Product (VMP) – VMP = MPF × PY.
- Factor‑price determination (competitive market) – firms hire up to the point where VMP = W (factor price). This is the marginal‑product rule (AO2).
- Short‑run vs. long‑run derived demand:
- Short‑run: technology is fixed; derived‑demand curve is relatively steep.
- Long‑run: firms can adjust technology and factor ratios; the curve is flatter (more elastic) and can shift as technology changes.
- Factor‑price elasticity of supply – measures how responsive the quantity supplied of a factor is to a change in its price.
\( \varepsilon_{S}^{F}= \dfrac{\% \Delta Q_{S}^{F}}{\% \Delta W} \)
High elasticity (e.g., skilled engineers) means supply adjusts quickly, which can moderate price changes when derived demand shifts.
Diagram suggestion: Supply curve for the factor with a steep (inelastic) and a flat (elastic) version to show the interaction with the derived‑demand curve.
8. Illustrative Examples
Example 1 – Labour in the automobile industry
- Market price of cars rises → firms expect higher revenue.
- They increase output, hiring more assembly‑line workers → right‑ward shift of the labour‑derived‑demand curve.
- Short‑run: increase limited by existing factory capacity.
- Long‑run: firms may invest in more automated lines, reducing the labour share (left‑ward shift of labour demand, right‑ward shift of capital demand).
Example 2 – Capital in the textile sector
- Introduction of automated looms raises the marginal product of capital.
- Fewer workers are needed per metre of cloth → labour‑derived‑demand shifts left.
- At the same time, the derived demand for capital (machines) shifts right because firms want more capital to exploit the new technology.
Example 3 – Skilled engineers and CAD software
- New, more efficient CAD package increases engineers’ productivity.
- Each engineer can now handle more projects → input‑output coefficient for engineering falls → derived demand for engineers shifts left.
- Derived demand for the CAD software (a complementary capital good) shifts right.
- In the long run, the industry may retrain some engineers as CAD specialists, altering the factor mix.
9. Summary Points (AO1)
- Derived demand links product and factor markets; factor demand is a function of product price (PY) and technology.
- Any change that shifts product‑market demand, improves technology, or alters the price of related factors shifts the derived‑demand curve.
- Movement along the curve is caused solely by a change in the factor’s own price (W).
- Elasticity of derived demand depends on:
- availability of substitutes,
- cost‑share of the factor,
- elasticity of demand for the final product,
- time horizon.
- Understanding derived demand is essential for analysing factor‑price movements, employment levels, and the impact of technological change.
10. Examination‑Style Questions (Marks indicated)
- (4 marks) Define “derived demand” and explain why it is called “derived”.
- (8 marks) Using diagrams, illustrate how an increase in the price of a final good affects the derived demand for the labour used to produce that good. Explain the underlying mechanism.
- (10 marks) Discuss the four main determinants of the elasticity of derived demand for a factor of production, giving a relevant example for each.
- (12 marks) Evaluate the likely impact on the derived demand for skilled engineers if a new, more efficient computer‑aided design (CAD) software is introduced. In your answer, consider short‑run and long‑run effects, and discuss any relevant factor‑market concepts (e.g., MP, VMP, factor‑price elasticity of supply).