Economics (9640) | The demand for labour, marginal productivity theory

The Demand for Labour and Marginal Productivity Theory

Welcome to the fascinating world of the labour market! In this chapter, we move away from consumers buying products and look at firms buying the most important factor of production: labour (workers). Understanding this topic is crucial because it explains how wages are set and why certain jobs or industries hire more people than others.

Don't worry if the terminology seems new. We will break down the key idea—the Marginal Productivity Theory—into simple steps, focusing on what motivates a profit-maximising firm.

1. Derived Demand: The Foundation of Labour Demand

Before we discuss marginal productivity, we must understand the fundamental concept governing all factor markets:

Derived Demand

The demand for any factor of production (like labour, capital, or land) is derived from the demand for the final product or service that factor helps produce.

• If consumers suddenly stop buying expensive organic coffee, the demand for coffee bean pickers, roasters, and baristas will fall. The demand for labour is derived from the demand for coffee.
• If demand for electric cars surges, the demand for battery engineers and assembly line workers (labour) will increase dramatically.

Memory Aid: The demand for the worker is derived from the demand for the output.

Key Takeaway: A firm doesn't hire a worker just for the sake of it; they hire a worker because the output that worker creates can be sold for revenue.

2. Marginal Productivity Theory of the Demand for Labour

The Marginal Productivity Theory explains how a profit-maximising firm decides exactly how many workers to hire. The simple rule for any input (like labour) is to hire until the extra revenue generated by that input equals the extra cost of hiring it.

2.1 Key Concepts: Measuring Worker Value

To apply the rule, we need to calculate the value of the 'extra' worker.

1. Marginal Physical Product (MPP)

The MPP is the additional quantity of output produced by employing one more unit of labour (one more worker), assuming all other inputs remain constant.

\(MPP = \frac{\Delta \text{Total Product}}{\Delta \text{Quantity of Labour}}\)

2. Marginal Revenue (MR)

This is the extra revenue the firm earns from selling one additional unit of output.

3. Marginal Revenue Product (MRP)

The MRP is the additional revenue generated by employing one more unit of labour. This measures the *money value* the extra worker brings into the firm.

\(MRP = MPP \times MR\)

Example: If a new chef (labour) makes 5 extra pizzas (MPP) and the firm sells each pizza for \$10 (MR), the MRP is \$50.

2.2 The Hiring Rule (Profit Maximisation)

The cost side of the equation is the Marginal Cost of Labour (MCL), which, in a simple competitive labour market, is simply the wage rate (W).

A firm will continue to hire workers as long as the extra revenue they bring in (MRP) is greater than or equal to the cost of hiring them (W).

The Rule for Optimal Employment:
Hire workers up to the point where \(MRP = W\) (or \(MRP = MCL\))

• If MRP > W, the firm should hire the worker, as they add more to revenue than to cost, increasing profit.
• If MRP < W, the firm should not hire the worker (or should fire the last one hired), as they cost more than they earn for the firm, decreasing profit.

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3. The Demand Curve for Labour (D\(_L\))

The demand curve for labour shows the relationship between the wage rate (W) and the number of workers firms wish to employ (\(Q_L\)).

3.1 Shape of the Curve

The D\(_L\) curve is downward sloping. This means that as the wage rate falls, the quantity of labour demanded increases (and vice versa).

The reason the curve slopes downward is rooted in the Law of Diminishing Marginal Returns (a concept studied earlier in production theory):

1. As a firm hires more and more workers (while capital/land remains fixed in the short run), the Marginal Physical Product (MPP) of each extra worker will eventually start to fall.
2. Since \(MRP = MPP \times MR\), if MPP falls, the Marginal Revenue Product (MRP) must also fall.
3. Therefore, if a firm wants to hire a larger number of workers (who are now less productive), the firm is only willing to do so at a lower wage rate (W).

Important Note: In the short run, the firm's demand curve for labour (D\(_L\)) is essentially the portion of its Marginal Revenue Product (MRP) curve that is downward sloping.

4. Causes of Shifts in the Demand Curve for Labour

A shift in the demand curve for labour (a change in D\(_L\)) occurs when a factor *other than the wage rate* changes the quantity of labour demanded at every possible wage.

A shift to the right means firms want to hire more workers (D\(_L\) increases); a shift to the left means they want to hire fewer (D\(_L\) decreases).

4.1 Factors Causing Shifts in D\(_L\)

1. Change in Demand for the Final Product (Crucial Link to Derived Demand):
   • If consumer demand for the product increases (e.g., higher price or quantity sold), the MR for the firm increases. Since \(MRP = MPP \times MR\), the MRP increases, shifting D\(_L\) right.
2. Change in Labour Productivity (MPP):
   • If workers become more productive (e.g., through better training, technology, or motivation), their MPP increases. This raises the MRP, shifting D\(_L\) right.
3. Changes in the Price of Other Factors (Substitutes and Complements):
   • Labour is often a substitute for capital (machines). If the price of capital falls (e.g., interest rates fall or machines become cheaper), firms may substitute capital for labour, shifting D\(_L\) left.
   • If labour is a complement to capital (e.g., highly skilled technicians needed to operate new complex machines), a fall in the price of capital could lead to more hiring of labour, shifting D\(_L\) right.
4. Non-Wage Employment Costs:
   • These are costs to the employer beyond the basic wage, such as national insurance contributions, pension contributions, or mandatory healthcare payments. If these costs rise, the total cost of labour increases (MCL rises), leading firms to demand less labour, shifting D\(_L\) left.

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5. Determinants of the Elasticity of Demand for Labour

The Elasticity of Demand for Labour (\(PED_L\)) measures how responsive the quantity demanded of labour is to a change in the wage rate.

If demand is elastic, a small rise in wages leads to a large fall in the number of workers hired. If demand is inelastic, even a large wage rise causes only a small reduction in the number of workers hired.

The key determinants are often summarised using Marshall's Rules:

1. Price Elasticity of Demand for the Final Product (PED):

• This is the most crucial link to derived demand.
• If the product the labour makes has elastic demand (consumers easily switch away if the price rises), then a wage increase (which raises production costs and thus the price of the product) will cause a large drop in product sales. This large drop in sales causes a large fall in the need for labour.
• Result: If PED for the product is elastic, \(PED_L\) is likely to be elastic.

2. Ease of Factor Substitution:

• Can firms easily replace labour with capital (machines or automation)?
• If substitution is easy (e.g., a simple packing job can be automated), demand for labour is elastic, as firms will switch away quickly if wages rise.
• If substitution is difficult (e.g., complex heart surgery), demand for labour is inelastic.

3. Proportion of Labour Cost in Total Cost:

• How big is the wage bill relative to the total cost of production?
• If labour costs are a large proportion of total costs (e.g., a cleaning company), a rise in wages will significantly affect overall costs and prices. The firm is very sensitive to wage changes, so demand is elastic.
• If labour costs are a small proportion (e.g., a highly automated microchip factory), a wage rise won't hurt much, and demand is inelastic.

4. Time Period:

• In the short run, firms might be locked into contracts or unable to quickly buy and install new machinery, making demand relatively inelastic.
• In the long run, firms have time to research and implement new, cheaper automated processes if wages remain high, making demand more elastic.

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