**4.2 Short-run labor demand curve**

Imagine a firm in the short run. The capital inputs are fixed. The firm needs to decide how many workers to hire. Hiring an additional worker increases the firm's output and therefore revenue. The output the additional worker contributes is the **marginal product of labor**, *MPL*. <sup>3</sup> The revenue by selling the output contributed by the additional worker is the **marginal revenue product of labor**, *MRPL*. We assume that the final goods and services markets are perfectly competitive, and the market price of the firm's product is *P*. Thus,

$$\mathbf{M} \mathbf{R} \mathbf{P}\_L = \mathbf{M} \mathbf{P}\_L \times \mathbf{P} \tag{5}$$

While hiring the additional worker raises the revenue, the firm has to pay the wage to the worker. The cost of hiring one additional worker is the **marginal wage cost**, *MWC*. We assume that the labor market is perfectly competitive, and the wage rate is *w*. Thus,

$$\text{MWC} = w \tag{6}$$

If *MRPL* > *MWC*, the firm wants to hire more workers because the benefit from hiring an additional worker is greater than the cost. On the other hand, if *MRPL* < *MWC*, the firm does not want to hire because the cost from hiring an additional worker is greater than the benefit the firm can receive. The firm has the optimal amount of labor when

$$\text{MRP}\_L = \text{MWC} \tag{7}$$

<sup>2</sup> Derived demand is the demand for intermediate goods that is derived from the demand for the final goods [3].

<sup>3</sup> A firm's production exhibits diminishing marginal product of labor.

or

$$\mathbf{MP\_L} \times \mathbf{P} = \mathbf{w} \tag{8}$$

**Table 3** assumes that the firm can sell its output at \$50 in a competitive market. When the firm hires the first worker, the worker produces 10 units of output, resulting in a marginal product of labor of 10 units. The marginal revenue product of labor is, therefore, *MPL* � *P* ¼ \$500. If the market-determined wage rate is *w* ¼ \$500, the firm will hire one worker.

Assume that the market-determined wage rate is *w* ¼ \$300. The gain from hiring the second worker is \$450, while the cost is \$300. Therefore, the firm will hire a second worker. Similarly, the gain from hiring the third worker is \$400, while the cost is \$300. Therefore, the firm will hire a third worker. In fact, the firm will continue hiring until the gain equals the cost. It results in hiring five workers at *w* ¼ \$300.

By plotting the number of labor (column (1)) on the horizontal axis and wage (column (5)) on the vertical axis, we have a downward sloping short-run labor demand curve (**Figure 7**).

#### **4.3 Long-run labor demand curve**

In long run, both labor and capital are variable. Suppose wage increases. How would a firm respond to the increase in wage?



**Table 3.** *Firm's short-run hiring decision*.

*Labor Markets DOI: http://dx.doi.org/10.5772/intechopen.101687*

**Figure 7.** *Short-run labor demand curve.*

**Figure 8.** *Long-run labor demand curve*.

When wage increases, both the substitution effect and scale effect cause the demand for labor to decrease. Thus, wage and demand for labor are negatively related in the long run, which means the long-run labor demand curve is also downward sloping (**Figure 8**).
