$ W\equiv MRP_L $

$ W\equiv MP_L * P $

$ \frac{W}{P} \equiv MP_L $

In the labor market Wages will have a direct relationship to the productivity of labor empoloyed. Employers (Demand side) will hire workers to maximize profit.


MPL derivation: The profit maximizing firm will bid marginal rates wage rates to clear market

In deriving the demand for labor it is important to remember that the basic productivity of labor is subject to change with the price of capital (a complement) and with the level of technology in the economy.


Labor Demand derivation: Changes in the economy will effect the productivity of labor and therefore change the wage which maximizes profit.

If the wage falls, the investment of capital may change (for example) and then the productivity of a unit of labor decreases (capital per effective worker decreases see Solow Growth Model). So the shift along the old MRP curve will not reflect the full adjustment in labor demand, it will in fact be less elastic because of the decreased incentive to invest in complimentary capital.

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