demand for labour as a derived demand

Labour Market Forces and Government Intervention (Cambridge AS/A Level Economics 9708)

Learning Objectives

• Explain why the demand for labour is a derived demand and how it is derived from the demand for the final product.
• Analyse the determinants that shift the labour‑demand curve and distinguish between short‑run and long‑run effects.
• Identify the determinants of labour‑supply, draw the supply curve and distinguish short‑run from long‑run movements.
• Compare wage‑determination mechanisms in perfectly competitive, trade‑union, minimum‑wage and monopsony labour markets (including the bargaining‑curve and efficiency‑wage concepts).
• Define and calculate transfer earnings and economic rent.
• Evaluate the efficiency and equity implications of government policies that intervene in the labour market.
• Describe the main reasons for wage differentials.

1. Derived Demand for Labour

The demand for any factor of production is called derived demand because it depends on the demand for the goods and services that the factor helps to produce.

Marginal Revenue Product of Labour (MRP_L)

\[ \text{MRP}_L = \text{MP}_L \times \text{MR} \]

• MP_L – marginal product of labour (additional output from one more worker).
• MR – marginal revenue from selling the additional output.

Under perfect competition in the product market, MR = P (the market price of the output). If the firm has market power (monopoly or monopolistic competition), MR < P and the same formula applies.

Profit‑maximising rule

Firms hire workers up to the point where:

\[ \text{MRP}_L = W \] where W is the prevailing wage rate. This condition generates the downward‑sloping labour‑demand curve (the MRP_L curve). The rule assumes profit‑maximising behaviour and that the firm takes the product‑market price (or MR) as given.

2. Determinants that Shift the Labour‑Demand Curve

Any factor that changes the marginal revenue product of labour shifts the labour‑demand curve.

Determinant	Direction of Shift	Why it Affects MRPL
Price of the final product (or MR)	Right if price rises; left if price falls	Higher price raises MR (or P under competition) → higher MRPL
Technological change that raises labour productivity	Right	Increases MPL → higher MRPL
Technological change that makes labour redundant (automation)	Left	Decreases MPL → lower MRPL
Change in the price of other inputs (capital, raw materials)	Left if other input costs rise; right if they fall	Higher input costs reduce profit → lower MR and therefore lower MRPL
Number of firms in the product market	Right with more firms; left with fewer firms	More firms increase total industry demand for labour
Consumer tastes / preferences for the final product	Right if tastes shift towards the product; left if they shift away	Changes the market demand for the product, altering MR/P and hence MRPL
Government policies that affect derived demand (output tax, subsidy, regulation)	Output tax → left; subsidy → right	Taxes lower the effective price received by firms; subsidies raise it, moving MR and MRPL
Expectations of future demand	Right if firms expect higher future sales; left if they expect a downturn	Anticipated higher sales raise expected MR → firms may hire ahead of time
Training and skill‑enhancement of the existing workforce	Right	Improves MPL for each worker, shifting the demand curve outward

Short‑run vs. Long‑run Shifts in Labour Demand

• Short‑run: Only labour is variable; capital and technology are fixed. A change in product price or MR moves the demand curve, but the shape is limited by the existing production technology.
• Long‑run: All factors (capital, technology, organisational structure) are variable. Improvements in technology or capital‑intensive innovation can raise MP_L substantially, causing a larger right‑ward shift than in the short run.

In diagrams, the short‑run demand curve is flatter (less responsive) because MP_L cannot be increased by new capital; the long‑run curve is steeper, reflecting higher productivity possibilities.

3. Labour‑Supply Curve

Labour supply shows the quantity of labour that workers are willing to offer at each wage rate.

Determinants of Labour Supply

Determinant	Effect on Supply Curve
Wage rate (net of tax)	Higher net wages → upward‑sloping supply
Alternative employment opportunities (transfer earnings)	Better alternatives shift supply left (workers can earn more elsewhere)
Population size and demographics (age structure, gender participation)	Growth in working‑age population shifts supply right
Education and training	Higher skill levels increase the number of workers willing to work at any given wage → rightward shift
Immigration policy	More open immigration → rightward shift; restrictions → leftward shift
Tax on labour income / social security contributions	Reduces net wage → leftward shift (lower incentive to work)
Working conditions, job security, non‑wage benefits	Improved conditions shift supply right; poorer conditions shift left
Preferences for leisure vs. work	Strong preference for leisure shifts supply left; a culture of high work ethic shifts right

Short‑run vs. Long‑run Supply

• Short‑run: Some workers cannot instantly change their labour‑force status (e.g., students, retirees). Supply is relatively inelastic.
• Long‑run: Migration, changes in education, retirement decisions and population growth make supply more elastic; the curve becomes flatter.

4. Wage Determination in Different Labour‑Market Structures

4.1 Perfectly Competitive Labour Market

• Firms are wage‑takers; the equilibrium wage (W*) and employment (L*) are where the labour‑demand curve (MRP_L) meets the labour‑supply curve (S_L).
• Any shift in D_L or S_L moves the equilibrium accordingly.

4.2 Trade‑Union (Collective‑Bargaining) Model

Unions negotiate a wage above the competitive level. The relationship between the wage that the union can obtain and the level of employment is shown by a bargaining curve (or wage‑setting curve).

• Negotiated outcome: Intersection of the bargaining curve with the MRP_L curve.
• Result is usually a higher wage and lower employment (under‑employment) compared with the competitive equilibrium.
• Efficiency‑wage argument: Paying a wage above the market‑clearing level can raise productivity (lower turnover, higher morale) and may partially offset the loss of jobs.

4.3 Minimum‑Wage Legislation (Price Floor)

• A legally imposed wage floor (W_min) above the competitive equilibrium creates a surplus of labour (unemployment) in a perfectly competitive market.
• If the labour market is monopsonistic, a modest minimum wage set between the monopsony‑equilibrium wage and the competitive wage can raise both wages and employment.

4.4 Monopsony (Single Large Employer)

The firm faces an upward‑sloping labour‑supply curve, so the marginal factor cost (MFC) of labour exceeds the wage paid.

\[ \text{MFC} = \frac{d(W \times L)}{dL}= W + \frac{dW}{dL}\,L \;>\; W \]

Profit‑maximising condition:

\[ \text{MRP}_L = \text{MFC} \]

• The monopsonist hires fewer workers at a lower wage than would occur under competition.
• A minimum wage set between the competitive wage and the monopsony‑equilibrium wage can increase both wages and employment.

5. Wage Differentials

Wage differentials are the differences in pay between groups of workers.

• Skill‑based differentials: Higher pay for more skilled, educated or experienced workers.
• Geographical differentials: Higher wages in regions with higher living costs or labour shortages.
• Occupational differentials: Certain occupations (e.g., doctors, engineers) command higher pay due to scarcity of qualified workers.
• Gender and ethnic differentials: May arise from discrimination or differing labour‑force participation rates.
• Union‑related differentials: Unionised workers often earn more than non‑unionised peers.

6. Transfer Earnings and Economic Rent

Concept	Definition	Numerical Illustration
Transfer earnings	The minimum payment required to keep a factor in its current use (its opportunity cost).	A worker could earn $70 /week in an alternative job. If the firm pays $80 /week, the transfer earnings are $70.
Economic rent	Any payment to a factor above its transfer earnings.	In the example above, $10 /week ($80 – $70) is economic rent.

7. Efficiency and Equity of Government Intervention

7.1 Policies that Affect Derived Demand

• Output tax: Lowers the price received by firms → MR falls → labour‑demand curve shifts left.
• Subsidy to firms (e.g., production subsidy): Raises effective price received → MR rises → labour‑demand curve shifts right.
• Investment in R&D or training programmes: Improves technology or worker productivity → MP_L rises → long‑run rightward shift of labour demand.

7.2 Policies that Affect Labour Supply

• Education and vocational training: Increases skills → rightward shift of S_L.
• Immigration policy: More open immigration → rightward shift; tighter controls → leftward shift.
• Tax on labour income / National Insurance: Reduces net wage → leftward shift of S_L.
• Social security benefits (e.g., unemployment benefit): May reduce the incentive to work, shifting supply left.

7.3 Direct Wage‑Setting Policies

• Minimum wage: Price floor; can cause unemployment in a competitive market but may improve both wages and employment in a monopsony.
• Statutory wage rates for specific occupations (e.g., nurses, teachers): Similar effects to a minimum wage for that occupational group.

7.4 Evaluation – Efficiency vs. Equity

• Efficiency: Policies that move the market away from the competitive equilibrium generate dead‑weight loss (area between MRP and MFC or between supply and demand).
• Equity: Raising wages for low‑skill workers improves income distribution but may create unemployment if the labour market is perfectly competitive.
• Government failure: Incorrect assessment of the size of the distortion, high administrative costs, or unintended side‑effects (e.g., informal employment) can reduce net welfare gains.

8. Worked Numerical Examples

Example 1 – Competitive Labour Market

Product price = $25 per unit (perfect competition). MP_L for successive workers: 4, 3, 2, 1 units. Labour‑supply curve: W = 10 + 2L.

1. Calculate MRP_L = MP_L × P:
   • Worker 1: 4 × 25 = $100
   • Worker 2: 3 × 25 = $75
   • Worker 3: 2 × 25 = $50
   • Worker 4: 1 × 25 = $25
2. Set MRP = W to find the profit‑maximising point:
   For L = 3, W = 10 + 2(3) = $16; MRP = $50 → MRP > W, so hire.
   
   For L = 4, W = 10 + 2(4) = $18; MRP = $25 → MRP < W, stop hiring.
   Equilibrium: 3 workers employed at a wage of $16.

Example 2 – Trade‑Union Bargaining (with Bargaining Curve)

Same MRP curve as Example 1. Union’s bargaining curve: W = 20 + 0.5L.

1. Find the intersection of MRP and the bargaining curve.
   • L = 2 → MRP = $75; bargaining wage = 20 + 0.5(2) = $21 → MRP > W, employment can rise.
   • L = 3 → MRP = $50; bargaining wage = 20 + 0.5(3) = $21.5 → MRP < W, the firm would not hire the third worker.
2. Negotiated outcome: 2 workers at a wage of $21 (higher than the competitive $16) and 1 fewer worker employed.

Example 3 – Monopsony

Labour‑supply: W = 5 + L → MFC = 5 + 2L.

MRP (as in Example 1): 100, 75, 50, 25.

1. Set MRP = MFC:
   • L = 2 → MFC = 5 + 2·2 = $9; MRP = $75 → hire more.
   • L = 3 → MFC = 5 + 2·3 = $11; MRP = $50 → still hire.
   • L = 4 → MFC = 5 + 2·4 = $13; MRP = $25 → stop hiring.
2. Monopsony equilibrium: 3 workers employed at a wage of W = 5 + 3 = $8.
3. Compare with competitive outcome (3 workers at $16). The monopsonist pays a lower wage and extracts a larger surplus.

Example 4 – Short‑run vs. Long‑run Shift in Labour Demand

Initial situation: product price = $20, MP_L = 3 for each worker, labour‑supply W = 8 + L.

• Short‑run shock: Product price rises to $30. MRP rises from 3 × 20 = $60 to 3 × 30 = $90. The labour‑demand curve shifts right; equilibrium moves to L = 4, W = $12.
• Long‑run adjustment: The higher price encourages firms to invest in new machinery that raises MP_L to 5. New MRP = 5 × 30 = $150. The labour‑demand curve shifts further right; new equilibrium at L = 6, W = $14.

9. Summary Checklist for Exam Answers

• State that labour demand is derived from the demand for the final product and write the MRP formula.
• Identify and explain at least three determinants of labour demand and indicate the direction of shift.
• Distinguish clearly between short‑run and long‑run movements in both demand and supply.
• Draw and label the relevant curves for the four wage‑determination models (competitive, union, minimum wage, monopsony).
• Define transfer earnings and economic rent and give a brief numerical example.
• Evaluate a government policy by discussing both efficiency (dead‑weight loss) and equity (distributional impact). Include possible government‑failure arguments.