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Marginal revenue productivity theory of wages : ウィキペディア英語版
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.〔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.〕
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.
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 MRPL is the increase in revenue per unit increase in the variable input = ∆TR/∆L
:MR = ∆TR/∆Q
:MPL = ∆Q/∆L
:MR x MPL = (∆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
:MRPL = ''w''
:MR(MPL) = ''w''
:MR = w/MPL
:MR = MC which is the profit maximizing rule.

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