Labour Market Forces and Government Intervention: Deriving the Firm's Demand for Labour

Objective

This section focuses on understanding the derivation of an individual firm’s demand for labour using the concept of Marginal Revenue Product (MRP). This is a fundamental concept in microeconomics and crucial for analyzing how firms make decisions about their workforce.

Understanding Demand for Labour

The demand for labour faced by a firm is derived from the firm's overall production decisions. A firm will hire labour up to the point where the additional revenue generated by employing one more worker equals the additional cost of employing that worker.

Marginal Revenue Product (MRP)

The Marginal Revenue Product (MRP) represents the additional revenue generated by employing one more unit of labour. It is calculated as:

$$MRP = \frac{\Delta Q}{\Delta L} \times MR$$

Where:

• $\Delta Q$ = Change in output
• $\Delta L$ = Change in labour (number of workers)
• $MR$ = Marginal Revenue (the additional revenue from selling one more unit of output)

Derivation of the Firm's Labour Demand Curve

A firm will maximise profit by employing labour up to the point where the Marginal Revenue Product (MRP) is equal to the Marginal Cost of Labour (MCL). The MCL is the additional cost of employing one more worker. This is typically represented by the wage rate.

Therefore, the firm's labour demand curve is derived from the relationship: $$MRP = MCL$$

In terms of the firm's decision rule, it will hire labour as long as $$MR \times \frac{Q}{L} > w$$

Where:

• $w$ = Wage rate
• $Q$ = Quantity of output
• $L$ = Quantity of labour

The MRP Curve

The MRP curve shows the relationship between the quantity of labour employed and the additional revenue generated by that labour. It typically has a negative slope, reflecting the law of diminishing marginal returns. As more workers are employed, the additional output produced by each additional worker tends to decrease.

Table Illustrating the Concept

Labour (L)	Output (Q)	Marginal Product of Labour (MPL)	Marginal Revenue (MR)	Marginal Revenue Product (MRP)	Wage (w)	Profit Maximising Level of Labour
0	0	-	-	-	0	0
1	10	10	20	200	10	1
2	25	15	30	450	10	2
3	35	10	40	400	10	3
4	40	5	45	225	10	4
5	42	2	48	96	10	4
6	42	0	48	0	10	4

Conclusion

The derivation of the firm's demand for labour using MRP is a powerful tool for understanding how firms make employment decisions. It highlights the importance of the relationship between labour input, output, and revenue. The MRP curve reflects the law of diminishing marginal returns, and the firm will employ labour up to the point where the MRP equals the wage rate.