# Marginal revenue product and demand for labour

To determine the quantity of labour the firm will employ, we need to know what the marginal cost of labour is. In this case, the marginal cost of employing an additional unit of labour is the wage that is paid to the additional unit of labour and the rule is that a profit maximisation firm will continue to employ labour up to the point where the marginal revenue product of labour equals the marginal cost of labour.

$$\text{Marginal revenue product of labour} = {\text{Marginal cost of labour}} = {\text{wage}}$$

$$\text{MRP} = {\text{MCL}} = {\text{w}}$$

The reasoning behind this rule is that as long as an additional worker contributes more to total revenue than what it cost to employ this worker, it is worthwhile for the firm to employ the worker.

### Study the above marginal revenue curve for labour and answer the following questions:

If the wage rate is R2 500 …

• will the firm employ worker number 3?
• will the firm employ worker number 4?
• will the firm employ worker number 5?
• will the firm employ worker number 6?

At a wage rate of R2 500, which is the marginal cost of labour, the firm will employ the third unit of labour since the marginal revenue product of the third unit of labour exceeds the marginal cost of employing the third unit of labour. The marginal revenue product of the third unit of labour is R7 500 while its marginal cost is R2 500. This is also true for the fourth unit of labour. The marginal revenue product for the fourth unit of labour is R5 000 while its marginal cost is R2 500. This process continues until the fifth unit is employed where the marginal revenue product is equal to the marginal cost of R2 500. The firm will not employ the sixth unit of labour since the marginal revenue product, which is R1 000, is less than the marginal cost of R2 500. In this case, the contribution labour makes to total revenue is less than the cost of labour which will lead to a decrease in profits.

This employment decision is represented graphically by adding the marginal cost of labour curves (MCL), which is the wage (w) that is paid, to our marginal revenue curve (MRP) for labour. ### Demand for labour curve

From the diagram, we can see that at a wage of R7 500, three units of labour will be employed, at a wage of R5 000, four units of labour, at a wage of R2 500, five units of labour, and at a wage of R1 000, six units of labour. The marginal revenue curve of labour therefore represents the demand for labour indicating that there is a negative relationship between the wage and the quantity of labour demanded. An important consequence of this downward-sloping demand for labour curve, which is determined by the law of diminishing returns, is that firms will only be willing to employ more workers if the wage rate falls.