Question

Using the same information as in Exercise 8, suppose now that the only labor available is controlled by a monopolistic labor union that wishes to maximize the rent earned by union members. What will be the quantity of labor employed and the wage rate? How does your answer compare with your answer to Exercise 8? Discuss. (Hint: The union’s marginal revenue curve is given by MR = 120 - 0.2L.)

Short answer

The quantity of labor employed will be 480 laborers, and the wage rate will be $72. The monopolistic wage rate is higher, and the labor employed will be less than the competitive market.

Step-by-step solution

Step 1. Explanation

The labor demand curve is L = 1200 -10w; thus, the inverse labor demand curve will be w = 120 – 0.1L. The labor supply curve is L = 20w, i.e., w = 0.05L. The labor marginal revenue curve will be

MR = 12 – 0.2L. At equilibrium, the marginal revenue curve is equal to the labor supply curve.

$$\begin{gathered} \text{MR = S} \\ \text{120 - 0.2L = 0.05L} \\ \text{0.25L = 120} \\ \text{L = 480} \\ \text{w = 120 - 0.1L} \\ \text{= 120 - 0.1}\left(\text{480}\right) \\ \text{= 120 - 48} \\ \text{= \$ 72} \end{gathered}$$

The monopolistic labor demand will be 480 laborers at the wage rate of $72.

The monopolistic wage rate is higher than the competitive market (Example 8), and the labor employed will be lesser than the competitive market (Example 8). The monopolistic labor employed is lower than the competitive market because the competitive market operates at the socially efficient level.​​​​