<p>This relation can be obtained if we realize that Total Cost can be written as a function of output (which in turn is a function of input factors), but also, that Total Cost equals total payments to factors of production. In real terms,</p>

<p>$$TC=TC(Q) = (w/p)N + (r/p)K$$
with the payment rates exogenous. But $Q = Q(N,K)$. Differentiate both sides by $N$:</p>

<p>$$\frac {\partial TC(Q(N,K))}{\partial N} = w/p $$</p>

<p>$$\Rightarrow \frac {\partial TC(Q(N,K))}{\partial Q}\cdot \frac {\partial Q(N,K)}{\partial N} = w/p$$</p>

<p>$$\Rightarrow MC \cdot MPN = w/p \Rightarrow MC = \frac {w/p}{MPN}$$ </p>

<p>One can perform the same exercise to obtain the analogous relation with respect to capital:</p>

<p>$$MC = \frac {r/p}{MPK}$$</p>

CC BY-SA 3.0
2014-12-20T00:56:56.843Z
2014-12-22T16:27:15.667Z
2014-12-22T16:27:15.667Z
Alecos Papadopoulos
<p>As said in the title, why is real wage divided by marginal product of labor often called real marginal cost?</p>

<p>In mathematical formula, $mc_t = (W_t/P_t)/MPN_t$ where $MPN_t$ refers to marginal product of labor, $\partial Y_t/\partial N_t$ and $N_t$ is amount of labor. $W_t$ refers to nominal wage, and $P_t$ refers to price level. </p>

<macroeconomics><microeconomics><wages>
why is real wage divided by marginal product of labor often called real marginal cost?
Kama
# why is real wage divided by marginal product of labor often called real marginal cost?

(Asked by: username_0 on 2014-12-19)

As said in the title, why is real wage divided by marginal product of labor often called real marginal cost?

In mathematical formula, $mc\_t = (W\_t/P\_t)/MPN\_t$ where $MPN\_t$ refers to marginal product of labor, $\partial Y\_t/\partial N\_t$ and $N\_t$ is amount of labor. $W\_t$ refers to nominal wage, and $P\_t$ refers to price level.

**Tags:** macroeconomics, microeconomics, wages

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## 1 answers

### Answer by username_1 on 2014-12-20. Score: 1

This relation can be obtained if we realize that Total Cost can be written as a function of output (which in turn is a function of input factors), but also, that Total Cost equals total payments to factors of production. In real terms,

$$TC=TC(Q) = (w/p)N + (r/p)K$$
with the payment rates exogenous. But $Q = Q(N,K)$. Differentiate both sides by $N$:

$$\frac {\partial TC(Q(N,K))}{\partial N} = w/p $$

$$\Rightarrow \frac {\partial TC(Q(N,K))}{\partial Q}\cdot \frac {\partial Q(N,K)}{\partial N} = w/p$$

$$\Rightarrow MC \cdot MPN = w/p \Rightarrow MC = \frac {w/p}{MPN}$$

One can perform the same exercise to obtain the analogous relation with respect to capital:

$$MC = \frac {r/p}{MPK}$$


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