Question

The demand for labor by an industry is given by the curve L = 1200 - 10w, where L is the labor demanded per day and w is the wage rate. The supply curve is given by L = 20w. What is the equilibrium wage rate and quantity of labor hired? What is the economic rent earned by workers?

Short answer

The equilibrium wage rate will be $40, and the quantity of labor hired will be 800 laborers. The economic rent will be $16,000.

Step-by-step solution

Explanation

The equilibrium wage and quantity of labor hired are calculated below:

$$\begin{gathered} {\text{Given,L}}_{\text{D}}\text{= 1,200 - 10w} \\ {\text{L}}_{\text{S}}\text{= 20w} \\ \text{Equilibrium :} \\ {\text{L}}_{\text{D}}{\text{=L}}_{\text{S}} \\ \text{1,200 - 10w = 20w} \\ \text{30w = 1,200} \\ \text{w = \$ 40} \\ \text{Thus, L = 1,200 - 10}\left(\text{40}\right) \\ \text{= 1,200 - 400} \\ \text{= 800} \end{gathered}$$

The wage rate will be $40, and 800 laborers will be hired.

The economic rent is calculated below:

The economic rent is the labor surplus, the area above the minimum level needed by the laborers to work.

$$\begin{gathered} EconomicRent=0.5\times \left(\$40\right)\times \left(800\right) \\ =\$16000 \end{gathered}$$

The economic rent will be $16,000.