The concept of derived demand for labour

Labour represents one of the key factors of production, essential for businesses to create goods and services. Without it, firms would be unable to operate effectively.

Sources of labour demand and supply

• Demand side - Businesses generate the need for workers to produce items that customers want.
• Supply side - Individuals who are able and of working age provide the workforce, forming the economically active population. This group includes both those with jobs and those seeking employment.

Derived demand explained

The need for workers stems directly from the demand for the products they help create. If consumer interest in a product rises, firms will require more staff to boost output. Conversely, a drop in product demand leads to reduced staffing needs. This connection means labour demand is not independent but derived from market conditions for goods and services.

Marginal revenue product and profit-maximising employment

Firms aim to hire workers only if they contribute positively to profits. This decision hinges on balancing the extra income generated by an additional employee against the associated costs.

Key concepts in marginal productivity theory

• Marginal revenue product of labour (MRP_L) - The additional income a firm earns by employing one more worker.
• Marginal physical product of labour (MPP_L) - The extra output produced by that additional worker.
• Marginal revenue (MR) - The price received per unit of output sold.

Formula for marginal revenue product of labour

${\text{MRP}}_{\text{L}}={\text{MPP}}_{\text{L}}\times \text{MR}$

Where:

• MRP_L = Marginal revenue product of labour (£)
• MPP_L = Marginal physical product of labour (units)
• MR = Marginal revenue (£ per unit)

Marginal cost of labour

The marginal cost of labour (MC_L) refers to the expense of hiring one extra worker. In markets where firms cannot set wages (perfect competition), this cost equals the going wage rate, determined by overall supply and demand equilibrium.

Achieving profit-maximising employment

• Firms reach the ideal staffing level when MRP_L matches MC_L.
• At this point, the revenue from the last worker hired equals their cost.
• If MRP_L exceeds the wage, hiring more staff would boost profits as they add greater value than their cost.
• If MRP_L falls below the wage, the firm has too many employees, as they increase expenses more than income, reducing overall profits.

Shape of the MRP_L and MPP_L curves

The MRP_L curve mirrors the shape of the MPP_L curve, both sloping downwards. This pattern arises from the law of diminishing returns: each new worker contributes less additional output than the previous one, leading to falling MRP_L as employment grows.

Factors influencing labour demand and its curve

Several elements affect how many workers a firm seeks, including productivity levels and external changes. The MRP_L curve serves as the labour demand curve, shifting in response to these factors.

Impact of productivity on labour demand

• Productivity measures output per worker.
• Higher productivity lowers unit labour costs (total labour expenses divided by output quantity), making a firm more competitive internationally.
• If wages rise but productivity increases proportionally, unit labour costs stay constant, leaving labour demand unchanged.
• Lower unit labour costs from better productivity enhance competitiveness, potentially increasing labour demand.

Factors shifting the labour demand (MRP_L) curve

• Product price changes - Higher prices for goods (increasing MR) shift the curve rightwards, raising demand.
• Productivity improvements - Advances like new machinery or staff training boost MPP_L, shifting the curve rightwards.
• Labour cost increases - Additional expenses (e.g., training or equipment) can shift the curve leftwards, reducing demand.

Overall, rising wages typically decrease labour demand, though this depends on productivity adjustments.

Elasticity of labour demand and influencing factors

Elasticity assesses how sensitive labour demand is to wage changes, helping predict employment shifts in response to economic pressures.

Calculating elasticity of labour demand

$\text{Elasticity of labour demand}=\frac{\text{percentage change in quantity of labour demanded}}{\text{percentage change in wage rate}}$

Where:

• Percentage change in quantity of labour demanded = (New quantity - old quantity) / old quantity × 100
• Percentage change in wage rate = (New wage - old wage) / old wage × 100

Elastic demand means small wage rises cause large drops in hiring, while inelastic demand shows limited response even to big wage shifts.

Factors affecting elasticity of labour demand

• Time period - More elastic in the long run, as firms can adjust staffing over time.
• Substitution with capital - Elastic if machines can easily replace workers (e.g., automation).
• Wage proportion of total costs - Inelastic if wages form a small part of expenses; elastic if they are a large share.
• Price elasticity of product demand - More elastic labour demand if the product's demand is price elastic.

Worked example - Calculating elasticity of labour demand

A firm initially employs 300 workers at a wage of £10 per hour. After wages rise to £12.50 per hour, employment falls to 240 workers. Calculate the elasticity of labour demand.

Step 1: Identify the values

• Old quantity = 300 workers
• New quantity = 240 workers
• Old wage = £10 per hour
• New wage = £12.50 per hour

Step 2: Calculate percentage changes

Percentage change in quantity demanded = (240 - 300) / 300 × 100 = -20%

Percentage change in wage rate = (12.50 - 10) / 10 × 100 = 25%

Step 3: Apply the elasticity formula

$\text{Elasticity of labour demand}=\frac{-20\%}{25\%}=-0.8$

Step 4: Interpretation

The value of -0.8 indicates inelastic demand, as the percentage fall in quantity demanded is smaller than the percentage rise in wages.