Labour Market Forces and Government Intervention – Monopsony
Learning objectives (Syllabus 8.3)
- Explain why the demand for labour is a derived demand.
- Identify the factors that shift the demand and the supply of labour and distinguish them from movements along the curves.
- Derive the Marginal Revenue Product of Labour (MRPL) and the Marginal Factor Cost (MFC) for a monopsonist.
- Analyse how a monopsony employer determines the wage rate and the level of employment and compare the outcome with a perfectly competitive labour market.
- Assess the welfare loss created by monopsony power and evaluate two government policies that can correct it.
1. Derived demand for labour (Syllabus 8.3.1)
Firms hire labour only to produce a good or service that will be sold in a product market.
Because the quantity of labour required depends on the level of output, the demand for labour is derived from the demand for the firm’s output.
The link is the Marginal Revenue Product of Labour (MRPL):
\[
\text{MRPL}= \frac{\partial (\text{Revenue})}{\partial L}
= \frac{\partial (P\cdot Q)}{\partial L}
= P \times \frac{\partial Q}{\partial L}
= P \times \text{MPL}
\]
where \(P\) = price of the product and \(\text{MPL}\) = marginal product of labour.
2. Factors that shift the demand for labour (Syllabus 8.3.2)
- Output price (\(P\)) – a rise raises MRPL → labour‑demand curve shifts right.
- Technology / productivity – improvements raise MPL (and therefore MRPL) → shift right.
- Input price of other factors (e.g., capital) – a fall makes capital cheaper, allowing more labour‑capital combinations → MPL rises → shift right.
- Expectations about future demand – optimistic expectations increase current hiring → shift right.
- Number of firms in the product market – entry of new firms raises total product‑market demand → shift right.
3. Shifts versus movements along the labour‑demand curve (Syllabus 8.3.3)
- Movement along MRPL – caused by a change in the wage rate while \(P\), technology and other determinants are unchanged.
- Shift of MRPL – caused by any factor listed in section 2 (e.g., a higher product price moves the whole MRPL curve outward).
4. Deriving the MRPL (Syllabus 8.3.4)
Assume a Cobb‑Douglas production function with capital fixed:
\[
Q = A L^{\alpha} K^{\beta}\qquad (K\text{ constant})
\]
Marginal product of labour:
\[
\text{MPL}= \frac{\partial Q}{\partial L}= \alpha A L^{\alpha-1} K^{\beta}
\]
Multiplying by the product price gives MRPL:
\[
\boxed{\text{MRPL}= P \times \alpha A L^{\alpha-1} K^{\beta}}
\]
This expression shows the explicit dependence of MRPL on product price, technology (\(A,\alpha\)) and the amount of capital used.
5. Factors that shift the supply of labour (Syllabus 8.3.5)
- Wage rate – higher wages attract more workers (upward‑sloping supply curve).
- Population & demographics – growth of the working‑age population shifts supply right.
- Education & training – a more skilled workforce increases the effective supply of qualified labour.
- Migration & geographic mobility – easier movement of workers into the region shifts supply right.
- Non‑wage preferences – changes in attitudes to leisure, family responsibilities, etc., shift supply left or right.
- Alternative employment opportunities – better pay or conditions elsewhere shift the supply curve left for the sector under consideration.
6. Shifts versus movements along the labour‑supply curve (Syllabus 8.3.6)
- Movement along the supply curve – caused by a change in the wage rate while other determinants remain constant.
- Shift of the supply curve – caused by any factor listed in section 5 (e.g., a new immigration policy shifts the curve right).
7. The monopsony model
A monopsony exists when a single large employer (or a group acting as one buyer) faces the entire labour market. The firm confronts an upward‑sloping labour‑supply curve \(S(w)\) and chooses employment \(L\) to maximise profit:
\[
\max_{L}\; \Pi = P\,Q(L) - w(L)\,L
\]
where \(w(L)\) is the wage paid to each worker at the chosen level of employment.
7.1 Deriving the Marginal Factor Cost (MFC) (Syllabus 8.3.4)
Total wage bill: \(w(L)L\). Differentiating with respect to \(L\) gives:
\[
\boxed{\text{MFC}= \frac{d[w(L)L]}{dL}= w(L) + \frac{dw}{dL}\,L}
\]
Because the labour‑supply curve is upward‑sloping, \(\frac{dw}{dL}>0\); therefore the MFC curve lies **above** the labour‑supply curve at every level of employment.
7.2 Profit‑maximising condition
The monopsonist hires labour where
\[
\text{MFC}= \text{MRPL}
\]
The corresponding wage is read off the labour‑supply curve at that quantity of labour.
8. Comparison with a perfectly competitive labour market
| Feature | Competitive market | Monopsony |
|---|
| Number of buyers of labour | Many (price‑takers) | One dominant buyer |
| Labour‑supply curve faced by the firm | Perfectly elastic at the market wage | Upward‑sloping \(S(w)\) |
| Equilibrium condition | \(w = \text{MRPL}\) | \(\text{MFC} = \text{MRPL}\) |
| Resulting wage | Higher (equals MRPL) | Lower (below MRPL) |
| Employment level | Efficient \(L^{*}\) | Reduced \(L_{m} |
9. Graphical illustration
In a standard labour‑market diagram (wage on the vertical axis, employment on the horizontal axis):
- The upward‑sloping labour‑supply curve is labelled S.
- The MFC curve, which lies above S, is drawn as a steeper line starting from the origin.
- The downward‑sloping MRPL curve represents the derived demand for labour.
- Competitive equilibrium – intersection of S and MRPL at \((L^{*},w^{*})\).
- Monopsony equilibrium – intersection of MFC and MRPL at \((L_{m},w_{m})\); the wage is read vertically from \((L_{m})\) up to the supply curve S.
- The dead‑weight loss is the triangular area bounded by MRPL, the supply curve, and the vertical line at \(L_{m}\).
10. Welfare implications of monopsony (Syllabus 8.3.5‑8.3.6)
- Dead‑weight loss (DWL) – the triangle between MRPL and the labour‑supply curve from \(L_{m}\) to the competitive level \(L^{*}\). It represents the loss of total surplus (worker + employer).
- Worker surplus – workers receive a wage \(w_{m}\) that is below their marginal product, so they are worse off than in competition.
- Employer surplus – the monopsonist captures the difference between MRPL and the wage paid, increasing its profit relative to a competitive market.
11. Government policies to correct monopsony power (Syllabus 8.3.6)
| Policy | Mechanism | Expected effect on wage, employment and DWL |
|---|
| Minimum‑wage legislation |
Sets a legal floor \(w_{\min}\) above the monopsony wage. |
If \(w_{m}
|
| Collective bargaining (unions) |
Negotiates a higher wage, effectively shifting the labour‑supply curve faced by the firm leftward. |
Higher wage and, depending on the shift, employment can increase (if the new wage is still below MRPL) or fall (if the wage exceeds MRPL). Typically reduces DWL. |
| Employment subsidy |
The government pays a per‑worker amount \(s\) to the employer, lowering the employer’s effective marginal factor cost to \(\text{MFC}-s\). |
Moves the effective MFC curve toward the supply curve, increasing employment toward the competitive level and reducing DWL. |
| Promoting competition in the product market |
Reduces the monopsonist’s market power (e.g., by removing barriers to entry). |
Higher product‑market competition raises MRPL, which can raise both wage and employment, narrowing the monopsony gap. |
11.1 Example: Binding minimum wage
Suppose a minimum wage satisfies \(w_{m}< w_{\min}< w^{*}\). The new equilibrium is where the horizontal line at \(w_{\min}\) meets the MRPL curve.
\[
\text{New employment } L_{mw}\text{ such that } \text{MRPL}(L_{mw}) = w_{\min}
\]
Result:
- Wage rises from \(w_{m}\) to \(w_{\min}\).
- Employment rises from \(L_{m}\) to \(L_{mw}\) (but remains below the competitive level \(L^{*}\) unless the minimum wage equals \(w^{*}\)).
- Dead‑weight loss shrinks – the triangular area between MRPL and the supply curve becomes smaller.
12. Summary checklist (AO1)
- Explain why labour demand is derived from product‑market demand (MRPL).
- List the determinants that shift labour demand and supply; distinguish them from movements along the curves.
- Derive the MFC formula and explain why it lies above the labour‑supply curve.
- State the monopsonist’s profit‑maximising condition \(\text{MFC}= \text{MRPL}\) and compare the resulting wage and employment with the competitive outcome.
- Identify and illustrate the dead‑weight loss created by monopsony.
- Describe at least two government policies (e.g., minimum wage, employment subsidy) that can reduce monopsony inefficiency and explain their impact on wages, employment and total surplus.
13. Practice questions (AO2/AO3)
- Given the labour‑supply function \(w = 10 + 0.5L\), product price \(P = \$20\) and production function \(Q = L^{0.5}\):
- Derive MRPL as a function of \(L\).
- Derive MFC as a function of \(L\).
- Find the monopsonist’s optimal employment \(L_{m}\) and the corresponding wage \(w_{m}\).
- Determine the competitive‑market equilibrium employment \(L^{*}\) and wage \(w^{*}\).
Solution outline:
- Production function: \(Q = L^{0.5}\) ⇒ \(\text{MPL}= \frac{dQ}{dL}= \frac{1}{2}L^{-0.5}\).
- MRPL \(= P \times \text{MPL}= 20 \times \frac{1}{2}L^{-0.5}=10L^{-0.5}\).
- Supply: \(w(L)=10+0.5L\) ⇒ \(\frac{dw}{dL}=0.5\).
MFC \(= w + L\frac{dw}{dL}= (10+0.5L)+0.5L = 10+L\).
- Monopsony: set MFC = MRPL → \(10+L = 10L^{-0.5}\). Solve for \(L\): multiply by \(L^{0.5}\) → \((10+L)L^{0.5}=10\). Numerical solution gives \(L_{m}\approx 2.0\) (students may use trial‑and‑error or a calculator).
Wage \(w_{m}=10+0.5L_{m}\approx \$11\).
- Competitive market: set \(w = \text{MRPL}\) → \(10+0.5L = 10L^{-0.5}\). Solving yields \(L^{*}\approx 4.0\) and \(w^{*}=10+0.5(4)=\$12\).
- Assume a minimum wage of \(\$15\) is introduced in the scenario above. Explain how this affects employment, wages and total surplus. Illustrate the change on a diagram.
- Discuss the likely long‑run response of a monopsonist if higher labour costs (e.g., due to a minimum wage) encourage investment in automation. What are the implications for the labour market and for government policy?
14. Further reading (no links)
Students should consult the Cambridge A‑Level Economics (9708) textbook, especially the chapters on labour‑market structures and government intervention. Specification documents from AQA, Edexcel and OCR provide additional examples, examiner tips and past‑paper questions on monopsony.