Marginal Product of Labor - MP_L and MC

MP_L and MC

The marginal product of labor is directly related to costs of production. Costs are divided between fixed and variable costs. Fixed costs are costs that relate to the fixed input, capital, or rK where r is the rate of return and K is the quantity of capital. Variable costs are the costs of the variable input, labor, or wL where w is the wage rate and L is the amount of labor employed. Thus VC = wL . MC is the change in total cost per unit change in output or ∆C/∆Q. In the short run, production can be varied only by changing the variable input. Thus only variable costs change as output increases ∆C = ∆VC = ∆Lw. Marginal costs is ∆Lw/∆Q. Now, ∆L/∆Q is the reciprocal of the marginal product of labor (∆Q/∆L). Therefore, marginal cost is simply the wage rate w divided by the marginal product of labor

MC = ∆VC∕∆q;

∆VC = w∆L;

∆L∕∆q the change in quantity of labor to affect a one unit change in output = 1∕MPL.

Therefore MC = w ∕ MP_L

Thus if the marginal product of labor is rising then marginal costs will be falling and if the marginal product of labor is falling marginal costs will be rising.(assuming a constant wage rate).