The marginal revenue productivity theory of wages is a model of wage levels in which they set to match to the marginal revenue product of labor, MRP, which is the increment to revenues caused by the increment to output produced by the last laborer employed. In a model, this is justified by an assumption that the firm is profit-maximizing and thus would employ labor only up to the point that marginal labor costs equal the marginal revenue generated for the firm. This is a model of the neoclassical economics type. The marginal revenue product of a worker is equal to the product of the marginal product of labour and the marginal revenue : MRP = MP × MR. The theory states that workers will be hired up to the point when the marginal revenue product is equal to the wage rate. If the marginal revenue brought by the worker is less than the wage rate, then employing that laborer would cause a decrease in profit. The idea that payments to factors of production equal their marginal productivity had been laid out by John Bates Clark and Knut Wicksell in simpler models. Much of the MRP theory stems from Wicksell's model.
Mathematical relation
The marginal revenue product of labour MRPL is the increase in revenue per unit increase in the variable input = ∆TR/∆L Here TR is the Total Revenue, MP is the marginal product, Q is the amount of goods, MR is marginal revenue and L is Labour The change in output is not limited to that directly attributable to the additional worker. Assuming that the firm is operating with diminishing marginal returns then the addition of an extra worker reduces the average productivity of every other worker. The firm is modeled as choosing to add units of labor until the MRP equals the wage rate w—mathematically until
Firms operating as monopolies or in imperfect competition face downward-sloping demand curves. To sell extra units of output, they would have to lower their output's price. Under such market conditions, marginal revenue product will not equal MPP×Price. This is because the firm is not able to sell output at a fixed price per unit. Thus the MRP curve of a firm in monopoly or in imperfect competition will slope downwards, when plotted against labor usage, at a faster rate than in perfect specific competition.
