Labour Markets – Chapter 14 Detailed Notes

Motivating Examples: Scarcity of Unique Skills

• Contrasting labour markets illustrate how scarcity and number of potential employers shape wages.
  • Romelu Lukaku (professional striker)
  • Annual salary ≈ € 7,500,000.
  • Many football clubs compete → high bargaining power for worker.
  • Ursula von der Leyen (President, EU-Commission)
  • Annual salary ≈ € 330,000.
  • Effectively single employer (EU) → monopsonistic element keeps wage relatively low.
• Highlights
  • Competition on the demand side raises the price of scarce labour.
  • Monopsony / limited buyers depress wages even for highly skilled labour.

Chapter Road-Map

• Short-run labour demand of a perfectly competitive firm.
• Long-run labour demand of a perfectly competitive firm.
• Aggregation to market demand for labour.
• Adjustments under imperfect competition (monopoly/monopolistic competition).
• Individual labour-supply decisions.
• Applications: taxes, transfers, minimum wages, sectoral shifts.

1. Perfectly Competitive Firm – Short-Run Demand for Labour

• Assumptions
  • Product market: perfect competition ⇒ price-taker; output price $p$ fixed.
  • Capital $K$ and technology fixed in SR; labour $L$ variable.
  • Input markets perfectly competitive ⇒ constant wage $w$ and rental rate $r$.
• Technology & profit
  • Production function $Q=f(L,K)$ (with \partial Q/\partial L>0, \partial^2 Q/\partial L^2<0).
  • Profit: $\Pi=pQ-wL-rK$.
  • First-order condition (FOC):
    $\frac{\partial\Pi}{\partial L}=p\frac{\partial Q}{\partial L}-w=0 \Rightarrow p\,\text{MP}_L=w.$
• Key concepts
  • Marginal Product of Labour: $\text{MP}_L=\partial Q/\partial L$.
  • Value of Marginal Product: $\text{VMP}<em>L=p\,\text{MP}</em>L$.
  • Profit maximisation rule: $\text{VMP}_L=w$ (i.e. MR=MC for labour).
• Graphical illustration (Fig. 14.1)
  • Panel (a): $\text{MP}_L$ curve slopes downward (diminishing marginal returns).
  • Panel (b): $\text{VMP}_L$ downward; intersects horizontal wage line at optimal $L$.
  • Wage fall shifts equilibrium rightward (higher employment).
• Numerical example (price $p=10$, $w=10$, fixed $K=10{,}000$, $r=1$)
  • Technology: $Q=K\cdot L=10{,}000 L$.
  • $\text{MP}_L=10{,}000$ (constant).
  • \text{VMP}_L=10\times10{,}000=100{,}000> w ⇒ corner solution: hire until capacity or other constraint; illustrates limitations of simplistic linear technology.

2. Perfectly Competitive Firm – Long-Run Demand for Labour

• All inputs variable; firm chooses $L$ and $K$ to maximise profit subject to cost.
• Cost (isocost) line: $C=wL+rK$; slope $= -w/r$.
• Isoquant: combinations producing given $q_0$.
• At optimum (point P) :
  $\frac{\partial Q/\partial L}{\partial Q/\partial K}=\frac{w}{r}$ (tangency ⇒ MRTS equals input-price ratio).
• Wage change decomposes:
  1. Substitution effect (movement along isoquant).
  2. Scale effect (parallel outward shift of isoquant if total cost changes).

Special Cases

1. Perfect Complements (fixed proportions)
   • Short-run: wage fall no substitution (capital fixed), employment unchanged.
   • Long-run: both inputs and output expand; LR labour demand increases.
2. Perfect Substitutes
   • Initial situation: if w>r \times (\text{MP}K/\text{MP}L) firm uses only capital.
   • Wage falls sufficiently ⇒ abrupt switch to labour-intensive technique; LR labour demand extremely elastic.

• General elasticities
  • LR demand more elastic than SR because substitution possible only in LR.
  • Demand more elastic the more elastic product-demand and the easier input substitutability.

3. Market Demand for Labour under Perfect Competition

• Horizontal sum of firms’ $\text{VMP}_L$ curves at given output price.
• Wage reduction sequence (Fig. 14.4):
  • Each firm moves down its $\text{VMP}_L$ → higher $L$.
  • Aggregate output rises ⇒ market price $p$ falls ⇒ each $\text{VMP}_L$ curve shifts down.
  • Combined effect → market demand curve D is steeper than simple horizontal aggregation.
• Implicit simplifying assumptions
  • Homogeneous labour & industry; perfect competition.
  • Reality: multiple types of labour employed across diverse sectors; when wage share in total cost small, simplified aggregation still reasonable (e.g. electricians example, 0.01 % of total labour cost).

4. Market Demand for Labour under Imperfect Competition

• With market power, marginal revenue \text{MR}<p ⇒ define Marginal Revenue Product:
  $\text{MRP}<em>L = \text{MR}\times \text{MP}</em>L.$
• Hiring rule: $\text{MRP}_L = w$.
• Since $\text{MRP}<em>L<\text{VMP}</em>L$ for downward-sloping demand, labour demand is lower than in perfect competition.
• Diminishing returns still apply ⇒ SR curve downward sloping; LR more elastic.
• Monopolist’s labour demand coincides with industry demand so no additional price-feedback adjustment when aggregating.

5. The Individual Supply of Labour

Preferences & Utility

• Goods: Consumption income $C$ vs Leisure hours $h$ (with total time $T$, labour hours $H=T-h$).
• Utility function $U(C,h)$ with \partial U/\partial C>0, \partial^2U/\partial C^2<0; likewise for $h$.
  • Example: Cobb–Douglas U=C^{\alpha}h^{\beta},\ 0<\alpha,\beta<1.
• Indifference curves downward-sloping; slope = Marginal Rate of Substitution:
  $\text{MRS}_{h,C}=\frac{\partial U/\partial h}{\partial U/\partial C}= -\frac{\Delta C}{\Delta h}.$

Budget Constraint

• Monetary income: $C = wH + V = w(T-h)+V = wT + V - wh.$
• Optimal choice solves
  $\max_{h} U(C,h) \quad \text{s.t.} \; C=w(T-h)+V.$
• FOC ⇒ $\text{MRS}_{h,C}=w$: marginal value of leisure equals wage (opportunity cost of leisure).

Graphical Example (Fig. 14.5)

• Parameters: $w_0=10€$, $T=24$, $V=0$.
• Extreme bundles:
  • Full leisure $h=24$ ⇒ $C=0$.
  • Zero leisure $h=0$ ⇒ $C=240€$.
• Optimum A: $h^<em>=15$ ⇒ labour $H^</em>=9$; income $C^*=90€$; indifference curve tangent to budget.

Comparative Statics

• Wage rise rotates budget around $C=V$ intercept.
• Substitution effect: higher $w$ → leisure more expensive → $h$ falls.
• Income effect: higher $w$ raises real income → if leisure normal, $h$ increases.
• Combined result can create backward-bending supply: labour supplied increases at low wages, decreases at high wages (Fig. 14.7).
• Perfect complements case (10 € income ↔ 1 h leisure)
  • Only income effect; at $w=20€$ optimum occurs where $C=10h$ intersects budget: $h=16$, $H=8$.
• Perfect substitutes case, same trade-off 10 € per 1 h leisure
  • Linear indifference curves: if w>10€ choose zero leisure ($h=0$), supply all time to work; if w<10€ supply none.

Target-Income Behaviour

• Some workers aim for daily income target (e.g., taxi drivers).
  • Supply curve vertical at income objective: $w\uparrow$ ⇒ hours $H$ fall (Camerer et al., 1997).

6. Aggregate Labour Supply

• Market supply is horizontal summation of individual supply curves (Fig. 2-12).
  • Entry margin: as wages rise, new workers enter labour force or switch sectors.
• Even if some individuals reduce hours at high wages, aggregate curve typically upward sloping because:
  • Participation rises.
  • Cross-sector mobility (e.g., AI-engineer wages > $350{,}000$ attract students into CS).

7. Policy Applications

7.1 Taxes & Transfers (David & Sarah examples)

• Piece-wise linear budget constraints create kinks and low effective net wages.
• David (low-skill)
  • Unemployment benefit €110, wage $w=5€$.
  • 0–€150 earnings zone: benefit withdrawn gradually ⇒ effective net wage €1.33/h.
  • Above €150: benefit lost; after 30 h, additional earnings taxed 20 % ⇒ net wage €4/h.
  • Optimal choice on given indifference curve: 0 hours (corner solution) ⇒ work disincentive.
• Sarah (high-skill, $w=30€$)
  • First €150 untaxed; €150–€600 taxed 20 % ⇒ net $24€/h$; above €600 taxed 60 % ⇒ net $12€/h$.
  • Optimal hours ≈ 20 h where marginal utility of income equals flatter post-tax wage.
• Trade-off for policy makers: provide safety net vs maintain work incentives.

7.2 Minimum Wage Legislation

• Theory (competitive market)
  • If $w<em>{min}>\text{VMP}</em>L$ ⇒ employment falls, unemployment emerges (Fig. 79: D–S diagram).
  • Adjustments: offshoring, capital-labour substitution, reduction of non-wage benefits.
• Empirical evidence (meta-analysis of ~1,400 studies)
  • Mixed results; overall small negative employment effects, larger for youth, students, low-skill minorities.
  • Methodological issues: non-random policy, short-run vs long-run, other margins (quality, hours, benefits).
• Recent research
  • Putty-clay model: entry/exit dynamics in restaurant industry (Aaronson et al., 2018).
  • Job growth more affected than immediate employment (Meer & West, 2016).
  • Automation risk: jobs with automatable tasks more likely to decline after hikes (Lordan & Neumark, 2018).

8. Key Equations & Definitions (Quick Reference)

• Marginal Product of Labour: $\text{MP}_L=\partial Q/\partial L$.
• Value Marginal Product: $\text{VMP}<em>L=p \times \text{MP}</em>L$.
• Marginal Revenue Product (imperfect comp.): $\text{MRP}<em>L=\text{MR} \times \text{MP}</em>L$.
• Hiring rule (competitive): $\text{VMP}_L=w$.
• Hiring rule (imperfect): $\text{MRP}_L=w$.
• Isocost: $C=wL+rK$; slope $= -w/r$.
• Budget constraint individual: $C=w(T-h)+V$.
• Labour supply elasticity (qualitative):
  • SR demand < LR demand (elasticity);
  • Market demand steeper than aggregate $\text{VMP}_L$ due to price feedback.

9. Ethical & Practical Considerations

• Minimum wage as living-wage policy vs potential unemployment.
• Tax/transfer design must balance equity (safety net) with efficiency (incentives).
• Monopsony power or imperfect competition justify deviations from competitive wage outcomes (e.g., living wage, minimum wage can raise both wage and employment in classical monopsony).
• Sectoral shifts (e.g., AI boom) illustrate dynamic nature of labour allocation and importance of education policy.

10. Suggested Reading

• Frank, R. H. & Cartwright, E. (2013). "Microeconomics and Behavior", Chapter 14.
• Empirical studies: Camerer et al. 1997 (taxi drivers), Sorkin 2015, Aaronson et al. 2018, Meer & West 2016, Lordan & Neumark 2018.