The nature of demand for labour as a derived demand

Demand for labour arises because businesses need workers to produce goods and services that customers want. It is known as a derived demand, meaning it depends on the demand for the products those workers create.

Sources of demand and supply for labour

• Demand side - Businesses require workers to manufacture goods or provide services. If customer demand for these goods rises, firms will need more workers to increase output. Conversely, if product demand falls, firms may reduce their workforce, leading to higher unemployment.
• Supply side - Workers come from the economically active population, which includes all individuals in an economy who are of working age and able to work, whether they are currently employed or seeking jobs.

Firms will only hire additional workers if doing so generates more revenue than the cost of employing them, ensuring the decision contributes to overall profitability.

Marginal productivity theory and marginal revenue product

Marginal productivity theory explains how the demand for labour (or any factor of production) is linked to the extra value it creates for a firm. This value is measured through marginal revenue product, which helps firms decide the optimal number of workers to employ.

Key concepts in marginal productivity theory

• Marginal revenue product of labour (MRP_L) - The additional revenue a firm earns by hiring one more worker.
• Marginal physical product of labour (MPP_L) - The extra output produced by employing one additional worker.
• Marginal revenue (MR) - The price per unit of the good sold.
• Marginal cost of labour (MC_L) - The expense of hiring one more worker, which in a perfectly competitive labour market equals the wage rate for that worker.

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)

Determining the optimal number of workers

• In a perfectly competitive labour market, the equilibrium wage is set where the supply of labour equals the demand.
• Firms maximise profits by hiring workers up to the point where MRP_L equals the wage rate.
• If MRP_L exceeds the wage, the firm can boost profits by adding more workers.
• If MRP_L is below the wage, the firm has too many workers and should reduce its workforce.

The MRP_L curve slopes downwards due to the law of diminishing returns, where each extra worker adds less additional output. This curve also represents the demand curve for labour.

How productivity affects the demand for labour

Productivity measures how efficiently workers produce output, and it directly influences a firm's demand for labour by affecting costs and competitiveness.

Impact of productivity on unit labour costs

• Unit labour costs refer to the labour expense per unit of output.
• Higher productivity can lower these costs, making firms more competitive, especially in international markets.
• If productivity rises without a matching increase in wages, unit labour costs fall, potentially increasing demand for labour as firms expand.
• If wages rise but productivity increases by the same proportion, unit labour costs remain unchanged, leaving demand for labour unaffected.
• High unit labour costs often indicate low productivity, which can harm a firm's ability to compete globally by making its products more expensive.

Formula for unit labour cost

$\text{Unit labour cost}=\frac{\text{wage rate per hour}}{\text{output per hour}}$

Where:

• Unit labour cost = Cost per unit of output (£)
• Wage rate per hour = Hourly pay (£)
• Output per hour = Units produced per hour

Worked example - Calculating unit labour costs with changes in wages and productivity

A worker earns £18 per hour and produces 6 units per hour. After a 15% wage increase (to £20.70 per hour) and a 15% productivity rise (to 6.9 units per hour), calculate the initial and new unit labour costs.

Step 1: Identify the values

• Initial wage = £18 per hour
• Initial output = 6 units per hour
• New wage = £20.70 per hour
• New output = 6.9 units per hour

Step 2: Calculate initial unit labour cost

$\text{Unit labour cost}=\frac{\pounds 18}{6}=\pounds 3.00\text{ per unit}$

Step 3: Calculate new unit labour cost

$\text{Unit labour cost}=\frac{\pounds 20.70}{6.9}=\pounds 3.00\text{ per unit}$

Step 4: Interpretation

The unit labour cost stays at £3.00 per unit, showing that equal rises in wages and productivity keep costs stable.

Factors that shift the demand curve for labour

The demand curve for labour, represented by the MRP_L curve, can shift due to various influences that alter the revenue generated by workers or the costs of employing them.

Causes of shifts in the MRP_L curve

• Changes in product price (MR) - A rise in the selling price of goods increases MRP_L, shifting the demand curve rightwards and raising demand for labour.
• Improvements in labour productivity - Factors like new technology or better training boost MPP_L, shifting the demand curve rightwards.
• Rises in labour-related costs - Increases in expenses such as training, equipment, insurance, or uniforms can reduce MRP_L, shifting the demand curve leftwards.

These shifts reflect how external changes affect a firm's willingness to hire at different wage levels.

Elasticity of demand for labour

Elasticity of demand for labour shows how sensitive the quantity of labour demanded is to changes in wage rates. It helps explain why some labour markets adjust quickly to wage fluctuations while others do not.

Formula for elasticity of demand for labour

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

Interpreting the elasticity of demand for labour:

• If the value is greater than 1 (elastic), small wage increases lead to large drops in labour demand.
• If the value is less than 1 (inelastic), even big wage changes cause only small adjustments in labour demand.

Factors influencing elasticity of demand for labour

• Time period - Demand is more elastic over the long run, as firms can adapt (e.g., by investing in machinery), but inelastic in the short run due to limited options.
• Ease of substitution - If workers can be easily replaced by capital (e.g., machines), demand is more elastic.
• Share of total costs - When wages form a small part of overall costs, demand is more inelastic, as firms are less sensitive to wage changes.
• Price elasticity of demand for the product - If the final product has elastic demand, labour demand is also more elastic, as firms pass on wage costs through higher prices without losing many sales.