The concept of derived demand for labour

The demand for labour originates from firms that need workers to produce goods and services, while the supply comes from individuals who are able and willing to work. This demand is not direct but stems from the need for the output that labour helps create.

Sources of demand and supply in the labour market

Demand for labour:

• This is a derived demand, meaning it depends on the demand for the goods or services that workers produce.
• Firms hire labour to generate revenue from sales.

Supply of labour:

• This comes from the economically active population.
• This includes all people in an economy who are of working age and capable of employment, whether they are currently working or unemployed.

How changes in product demand affect labour demand

• An increase in demand for goods leads to higher derived demand for labour, as firms need more workers to boost production.
• A decrease in demand for goods results in lower derived demand for labour, which can cause unemployment as firms reduce their workforce.

Marginal revenue product and its role in hiring decisions

The marginal productivity theory explains that the demand for labour, like other factors of production, is based on the additional value it brings to a firm. Firms hire workers only if the revenue they generate exceeds the cost of employing them.

Calculating marginal revenue product of labour

Marginal revenue product of labour (MRP_L) measures the extra revenue a firm gains from hiring one additional worker.

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

Where:

• MPP_L = Marginal physical product of labour (extra units produced by one more worker)
• MR = Marginal revenue (price per unit sold, in £)

Hiring decisions based on MRP_L

• Firms hire additional workers if MRP_L exceeds the cost of employment, as this increases profits.
• The MRP_L curve slopes downwards, mirroring the MPP_L curve, due to the law of diminishing returns: each new worker adds less additional output as resources become stretched.

Worked example - Calculating marginal revenue product of labour

A firm produces gadgets, and hiring one more worker adds 10 units to output per hour. Each gadget sells for £20. Calculate the MRP_L and determine if hiring is profitable if the worker costs £180 per hour.

Step 1: Identify the values

• MPP_L = 10 units per hour
• MR = £20 per unit

Step 2: Apply the MRP_L formula

${\text{MRP}}_{\text{L}}=10\times \pounds 20=\pounds 200\text{ per hour}$

Step 3: Compare with cost

The MRP_L of £200 exceeds the cost of £180, so hiring the worker would increase profits.

Equilibrium wage and optimum employment levels

In a perfectly competitive labour market, wages and employment levels are determined by the interaction of supply and demand. The MRP_L curve represents the demand curve for labour.

Marginal cost of labour and market equilibrium

Marginal cost of labour (MC_L) is the additional cost of hiring one more worker, which equals the wage rate in a competitive market. The equilibrium wage occurs where the supply of labour equals demand, setting the market wage rate.

Determining the optimum number of workers

• At the point where MRP_L equals the equilibrium wage, the firm employs the ideal number of workers.
• If MRP_L > wage, the firm can boost profits by hiring more workers.
• If MRP_L < wage, the firm is over-employing and should reduce its workforce to cut costs.

Factors affecting the demand for labour

Several elements influence how much labour a firm demands, often shifting the demand curve (MRP_L curve) left or right. Productivity plays a key role, as it affects efficiency and costs.

Influences that shift the demand curve for labour

• Changes in product price (MR) - Higher prices increase MRP_L, shifting demand rightwards; lower prices do the opposite.
• Labour productivity changes - Improvements from technology or training raise MPP_L, increasing demand.
• Labour cost changes - Increases in non-wage costs (e.g., training, insurance, equipment) reduce demand by raising MC_L.

The impact of productivity on unit labour costs

Unit labour costs represent the labour expense per unit of output. Higher productivity lowers these costs, enhancing demand for labour.

$\text{Unit labour costs}=\frac{\text{labour costs}}{\text{units of output}}$

Effects of productivity changes:

• If wages rise but productivity increases proportionally, unit labour costs stay the same, leaving labour demand unchanged.
• High unit labour costs signal low productivity, harming a country's international competitiveness.
• Decreases in unit labour costs from productivity gains improve competitiveness by making exports cheaper.

Worked example - Calculating unit labour costs with productivity changes

A worker earns £20 per hour and produces 4 units per hour. After a 15% wage increase to £23 per hour, productivity rises by 15% to 4.6 units per hour. Calculate the unit labour costs before and after.

Step 1: Identify the values

• Initial wage = £20 per hour
• Initial output = 4 units per hour
• New wage = £23 per hour
• New output = 4.6 units per hour

Step 2: Calculate initial unit labour cost

$\text{Unit labour cost}=\frac{\pounds 20}{4}=\pounds 5\text{ per unit}$

Step 3: Calculate new unit labour cost

$\text{Unit labour cost}=\frac{\pounds 23}{4.6}=\pounds 5\text{ per unit}$

Step 4: Interpretation

Unit labour costs remain unchanged at £5 per unit, so demand for labour is unaffected despite the wage rise.

Elasticity of demand for labour

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

Formula for elasticity of demand for labour

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

• Elastic demand means small wage changes cause large shifts in quantity demanded.
• Inelastic demand means large wage changes cause small shifts in quantity demanded.

Factors influencing elasticity of demand for labour

• Time period - Demand is more elastic in the long run (firms can adjust) and more inelastic in the short run.
• Substitutability - If labour can be replaced easily (e.g., by machines), demand is more elastic.
• Proportion of total costs - When wages form a small part of costs, demand is inelastic; when large, it is more elastic.
• Price elasticity of demand (PED) for the product - If the product's PED is high, labour demand is more elastic, as wage changes affect product prices and sales.