Labor Demand

Production function and MPL

The aggregate production function relation between level of output and factor input. The function can be written as ¹

$$Y=f(\overline{K},L)$$

From this, we infer that output solely varies due to variation in the labor input.

• At point below $N^{”}$ , production is a straight line and hence we have constant returns to scale.
• Incremental output is declining to incremental input between $N$ and $N^{”}$.
• Beyond $N^{”}$, there is no increment to output

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Below $N^{”}$, MPL is constant/flat. Past $N^{”}$, MPL is +ve, but declining.

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$$\begin{array}{rl}\text{MPL}& =\text{slope of production function}\\ & =\Delta Y÷\Delta N\end{array}$$

Labor market

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The firms need to take only once decisions, i.e., either the choice of the level of output or level of labor input. Since any change in output will lead to change in level of labor and vice-versa

Profit Maximization criteria in perfect competition

In a perfectly competitive firm, the output will be increased until the marginal cost of productivity of producing a unit of output is equal to the marginal revenue received from its sale.

$$MC=MP$$

In a perfectly competitive market, $MR=P$ and $MC$ is the marginal labor cost which is equal to the money wage divided by the MPL. Thus,

$$\begin{array}{rl}MC=\frac{W}{\text{MPL}}& \&MR=P\\ & \\ \therefore \frac{W}{P}=\text{MPL}& \text{or}\frac{W}{\text{MPL}}=P\end{array}$$

Consider the cases²

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• If $P=1$ and additional labor increases production by one unit (MPL = 1). Hence, firm will pay not more than $1$. $W\le (P=1)$
• If $P=1$ and additional labor increases production by 2 units (MPL = 2) . Hence, the firm will pay not more than 2. $W\le (P=2)$
• If $W=6$ and $P=2$ then real wage = $3$, which means that MPL should be $>3$ to continue producing.³

Footnotes

1. where $Y$ is real output, $\overline{K}$ is constant capital. $L$ is labor input ↩

2. This is for intuitive idea ↩

3. The amount we pay for labor by price should be compensated by the MPL ↩