wage determination in perfect markets: equilibrium wage rate and employment in a labour market

Labour Market – Determination of Wages and Employment

1. Learning Objectives

• Explain how the equilibrium wage (w*) and employment level (L*) are determined in a perfectly competitive labour market.
• Analyse the factors that shift labour‑demand and labour‑supply curves, including the role of elasticities.
• Describe wage‑determination in imperfect markets (monopsony, trade‑union bargaining, wage differentials, transfer earnings and economic rent).
• Evaluate the likely impact of common government interventions and recognise possible government failure.

2. The Perfectly Competitive Labour Market

• Many firms (employers) and many workers – each is a price‑taker.
• Labour is a homogeneous service; no single firm can influence the wage.
• Perfect information, no transaction costs, and free entry/exit.
• Both the product market and the labour market are competitive.

3. Derived Demand for Labour

Firms do not demand labour for its own sake; they demand it because it helps produce a good or service that is itself demanded – this is derived demand.

For a competitive firm:

• Value of the Marginal Product (VMP) = P × MPL, where P = price of the output and MPL = marginal product of labour.
• Because the firm is a price‑taker in the product market, VMP = Marginal Revenue Product (MRP).
• The profit‑maximising rule is MRP = w. The firm hires workers up to the point where the value of the last worker’s output equals the wage paid.

4. Labour‑Demand: Determinants & Elasticities

Factor	Effect on Labour‑Demand	Direction of Curve Shift	Typical Elasticity (ΔL/ΔFactor)
Higher output price (P)	Raises VMP (VMP = P·MPL)	Rightward	Relatively elastic if product demand is elastic
Technological improvement (higher MPL)	More output per worker → higher VMP	Rightward	Often highly elastic in the short run
Higher price of other inputs (e.g., capital)	Labour becomes relatively cheaper → substitution toward labour	Rightward (if substitution possible)	Depends on substitutability; measured by cross‑price elasticity
Expectations of higher future product demand	Firms expand production now, hiring more workers	Rightward	Forward‑looking elasticity – often modest
Labour tax or statutory employer costs	Effective cost of hiring rises	Leftward	Elasticity equals the inverse of the wage‑elasticity of demand

5. Labour‑Supply: Determinants & Elasticities

Factor	Effect on Labour‑Supply	Direction of Curve Shift	Typical Elasticity (ΔL/Δw)
Higher real wage rate	Incentivises more people to work or to work more hours	Movement up the existing curve; a very steep supply curve implies low wage‑elasticity.	Varies – low for low‑skill workers, higher for highly mobile labour
Non‑wage benefits (childcare, health care)	Reduces the opportunity cost of work	Rightward	Positive elasticity – the greater the benefit, the more elastic the supply
Population growth / larger working‑age cohort	More potential workers	Rightward	Elasticity close to 1 in the long run
Higher education and training levels	Increases the number of qualified workers willing to supply labour	Rightward	Elasticity depends on the skill‑specificity of jobs
Immigration	Adds to the pool of workers	Rightward	Often highly elastic for low‑skill sectors
Income tax or reduction in non‑wage benefits	Raises the effective cost of working (lower net wage)	Leftward	Elasticity mirrors the wage‑elasticity of labour supply
Cultural or social attitudes (e.g., female labour‑force participation)	Alters willingness to work at a given wage	Rightward or leftward depending on direction of change	Often reflected in a shift rather than a change in elasticity

6. Competitive Equilibrium

The equilibrium wage (w*) and employment (L*) are found where the labour‑demand curve (D) intersects the labour‑supply curve (S).

• At the intersection: MRP = w* for each firm.
• Any deviation from this point creates a surplus or shortage of labour, prompting price (wage) adjustments.

7. Shifts in the Curves – Impact on w* and L*

• Technological improvement → D shifts right → both w* and L* rise (if supply is not perfectly inelastic).
• Increase in working‑age population → S shifts right → wage falls, employment rises (provided demand is downward sloping).
• Labour tax on firms → D shifts left → lower equilibrium wage and lower employment.
• Increase in income tax on workers → S shifts left → wage to workers may rise (if firms pass the tax onto workers) but employment falls.

8. Imperfect‑Market Wage Determination

8.1 Monopsony (single buyer of labour)

• Labour supply curve is upward sloping; the firm faces the whole supply curve, not a horizontal wage line.
• Profit‑maximising condition: MRP = w + (dw/dL)·L (i.e., marginal factor cost exceeds the wage).
• Result: lower employment and lower wage than in perfect competition.
• Policy implication: a minimum wage set between the monopsony wage and the competitive wage can increase both wages and employment.

8.2 Trade‑Union Bargaining

• Unions negotiate a wage above the competitive level (often modelled as a wage floor).
• Two common structures:
  1. Collective bargaining – a negotiated wage for a sector or firm.
  2. Industrial action – strikes create a temporary labour shortage, pushing wages up.
• Typical outcome: higher wage, lower employment (dead‑weight loss) unless the union also improves productivity.

8.3 Wage Differentials

Differences in wages across occupations, regions or firms arise from:

• Variations in marginal product (skill, experience, education).
• Differences in working conditions, risk, or location.
• Segmentation of the labour market (e.g., gender or ethnic wage gaps).

8.4 Transfer Earnings and Economic Rent

• Transfer earnings – the minimum amount a worker must receive to stay in their current job; equal to the value of their next best alternative (including leisure).
• Economic rent – any earnings above transfer earnings; arises when a worker’s marginal product exceeds the next best alternative.
• In competitive markets, workers receive transfer earnings; rents are competed away unless barriers (e.g., monopsony) exist.

9. Government Intervention in the Labour Market

9.1 Minimum Wage

• Legal floor w_min set above the competitive wage (w*).
• Creates a surplus of labour: L_S > L_D → unemployment equal to the excess supply.
• Diagram: horizontal line at w_min intersecting S at L_S and D at L_D. The triangular area between D and S represents the dead‑weight loss.
• Evaluation depends on the wage‑elasticity of demand – if demand is inelastic, unemployment is small; if elastic, job loss is large.

9.2 Labour Tax (tax on employers)

• Tax t per worker raises the firm’s marginal cost to w + t.
• Effective labour‑demand curve shifts left.
• Result: lower equilibrium wage to workers (unless the tax is fully passed on) and lower employment.
• Dead‑weight loss shown by the triangle between the original and new demand curves.

9.3 Wage Subsidy to Employers

• Subsidy s per worker reduces the firm’s marginal cost to w – s.
• Labour‑demand shifts right, raising employment.
• The effect on the wage received by workers depends on the relative elasticities of demand and supply:
  • If supply is relatively inelastic, most of the subsidy is captured by workers (higher wage).
  • If supply is elastic, firms retain a larger share (wage rises little).

9.4 Training and Education Programs (government‑funded)

• Increase workers’ productivity → higher MPL → rightward shift of labour‑demand.
• Long‑run effect: higher equilibrium wage and higher employment.
• Financing requires taxation; net welfare gain depends on the size of the productivity gain relative to fiscal cost.

9.5 Immigration Controls

• Restricting immigration shifts labour‑supply left → higher wages, lower employment for native workers.
• Open immigration shifts supply right → lower wages, higher employment, but may also raise productivity through skill complementarities.

9.6 Unemployment Benefits

• Increase the reservation wage (the minimum wage workers are willing to accept).
• Shift labour‑supply leftward, potentially raising equilibrium wages but reducing employment.
• May also improve labour‑market efficiency if it allows better job matching (search‑friction benefit).

9.7 Government Failure in Labour Markets (8.1.2)

• Information failures – workers may not know which jobs maximise their earnings or career prospects.
• Transaction costs – high costs of job search, training, or relocation can prevent efficient matching.
• Political economy – interest groups (e.g., unions, employer associations) may capture policy, leading to sub‑optimal outcomes.
• Recognition of these failures helps explain why some interventions (e.g., subsidies for job‑search services) may improve efficiency despite the risk of distortion.

10. Evaluating Intervention – Equity, Efficiency and Elasticities

Criterion	Key Questions for Evaluation
Equity (distributional impact)	Who gains (low‑skill workers, families, retirees) and who loses (unemployed, firms, taxpayers)? Does the policy reduce poverty or inequality?
Efficiency (resource allocation)	Does the policy create a dead‑weight loss? How large is the loss given the wage‑elasticity of demand and supply? Are there incentives for productivity improvement?
Elasticities	How responsive are employers (labour demand) and workers (labour supply) to the policy‑induced wage change? High elasticity → larger employment effects; low elasticity → smaller effects.
Administrative & fiscal costs	What are the costs of monitoring, enforcement, and financing (taxes, borrowing)? Are they justified by the benefits?
Dynamic effects	Long‑run impacts on skill formation, technological adoption, labour‑market flexibility, and possible crowding‑out of private training.
Government failure	Could the policy be poorly designed, mis‑targeted, or captured by interest groups, reducing its net welfare gain?

11. Example Calculation (MRP = Wage)

Assume a product price of £12 per unit. The marginal product of labour (MPL) for the first three workers is:

Worker	MPL (units)	VMP = P × MPL (£)
1st	2.0	24
2nd	1.6	19.2
3rd	1.2	14.4

If the market wage is £18, the firm hires workers whose VMP ≥ £18. Thus it employs the 1st and 2nd workers (VMP = 24 and 19.2) but not the 3rd (VMP = 14.4). Equilibrium employment = 2 workers; the equilibrium wage = £18.

12. Summary

• In a perfectly competitive labour market, firms hire up to the point where MRP = wage. The market equilibrium (w*, L*) is where the derived‑demand curve meets the labour‑supply curve.
• Labour‑demand shifts with product price, technology, input prices, expectations and policy; labour‑supply shifts with wages, benefits, demographics, education, immigration and taxes. Elasticities determine the magnitude of wage and employment changes.
• Imperfect markets – monopsony, trade‑union bargaining, wage differentials, transfer earnings and economic rent – generate wages that differ from the competitive level.
• Government interventions (minimum wage, taxes, subsidies, training, immigration control, unemployment benefits) move the market away from the competitive equilibrium. Their desirability is judged on equity, efficiency, elasticities, administrative costs and potential government failure.
• When answering exam questions, always:
  1. State the relevant theory (e.g., MRP = w, monopsony condition).
  2. Identify the curve shift and predict the direction of change in w and L.
  3. Discuss the impact on different groups and on overall welfare using the evaluation criteria above.