Marginal revenue productivity theory of wages

The marginal revenue productivity theory of wages is a theory in neoclassical economics stating that wages are paid at a level equal to the marginal revenue product of labor, MRP (the value of the marginal product of labor), which is the increment to revenues caused by the increment to output produced by the last laborer employed. This is because no firm would employ additional labor whose cost would exceed the revenue generated for the firm.^[1]

The marginal revenue product (MRP) of a worker is equal to the product of the marginal product of labour (MP) (the increment to output from an increment to labor used) and the marginal revenue (MR) (the increment to sales revenue from an increment to output): 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 there is no need to employ.

The idea that payments to factors of production equilibrate to their marginal productivity had been laid out early on by such as John Bates Clark and Knut Wicksell, who presented a far simpler and more robust demonstration of the principle. Much of the present conception of that theory stems from Wicksell's model.

Mathematical Relation

The marginal revenue product of labour MRP_L is the increase in revenue per unit increase in the variable input = ∆TR/∆L

MR = ∆TR/∆Q

MP_L = ∆Q/∆L

MR x MP_L = (∆TR/∆Q) x (∆Q/∆L) = ∆TR/∆L

Note that 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 (and every other worker affects the marginal productivity of the additional worker).

As above noted the firm will continue to add units of labor until the MRP equals the wage rate w—mathematically until

MRP_L = w

MR(MP_L) = w

MR = w/MP_L

MR = MC which is the profit maximizing rule.

Marginal Revenue Product in a perfectly competitive market

Under perfect competition, marginal revenue product is equal to marginal physical product (extra unit produced as a result of a new employment) multiplied by price.

$MRP = MPP \times \text{AR}\,\!$

$MRP = MPP \times \text{Price}\,\!$

This is because the firm in perfect competition is a price taker. It does not have to lower the price in order to sell additional units of the good.

MRP in monopoly or imperfect competition

Firms operating under conditions of monopoly or imperfect competition are faced with downward sloping demand curves. If they want to sell extra units of output, they must lower 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 imperfect competition will slope downwards, when plotted against labor usage, at a faster rate than in perfect competition.

References

1. Daniel S. Hamermesh, "The demand for labor in the long run"; published in Handbook of Labor Economics (Orley Ashenfelter and Richard Layard, ed.), 1986, p. 429.