The assumption of diminishing marginal product of labour means that, in order to work more, workers must be offered a higher real wage. We can use this assumption to derive the labour demand curve.
This concept, the amount that output increases for a unit increase in labour input, is called the marginal product of labour (MPN). The MPN is given by the slope of the production function. This means that as labour use increases the amount of extra output that is gained from an increase in labour input becomes smaller. This is known as the diminishing marginal product of labour.
Given the diminishing marginal product of labour, if we graph the marginal product of labour against labour use, we would have a downward sloping curve. THis is illustrated in the figure below.
We assume that the goal of any firm is to maximize profit, which equals total revenue minus total cost. When a firm hires an additional unit of labour, it incurs a marginal cost and receives a marginal benefit. The marginal cost is measured by W, the nominal wage that must be paid to the extra unit of labour that is hired. The marginal benefit to the firm is the value of the additional unit of output that is produced by that additional unit of labour. This marginal benefit is called the value of the marginal product, and is measured as the marginal product of labour, MPN, multiplied by the price, P. A profit maximizing firm will hire labour until marginal benefit equals marginal cost.
W = MPN * P
The profit maximizing condition in the equation above can be rearranged in terms of the real wage w = W/P .
w = MPN
This equation states that a profit maximizing firm will hire labour until the real wage equals the marginal product of labour. We can put this equation together with the figure above to derive the demand for labour curve. The demand for labour curve is just the MPN curve, drawn with the real wage on the vertical axis. The demand for labour curve is shown in the figure below.