A union faces a labor demand curve given by MRP_L = 100 - 5L. If the union wishes to maximize the total wages of its membership, ____ members will be employed. A) 20 B) 10 C) 8 D) 6

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To maximize total wages, the union needs to find the level of employment (L) where the marginal revenue product of labor (MRPL) equals the wage rate. The MRPL is given by the derivative of the total revenue with respect to labor, which in this case is directly given by the labor demand curve: MRPL = 100 - 5L. To maximize total wages, we set MRPL equal to the wage rate. However, without a specific wage rate given, we aim to find the quantity of labor that maximizes total revenue generated by labor, which is essentially the midpoint of the labor demand curve. Solving for L when MRPL is maximized (or starts to decrease) involves finding the maximum point on the demand curve, which is not directly calculable without setting it equal to a wage or taking its derivative. However, given the options and understanding that the demand curve represents the diminishing value of each additional unit of labor, the best approach is to consider the equilibrium where demand meets supply under normal circumstances. Without the explicit wage rate or further instructions to find the derivative for maximization, we look at the formula and recognize that at 20 units of labor, the value of labor would be zero (100 - 5(20) = 0), indicating no additional revenue from labor, suggesting that the maximum employment level for maximizing total wages would be at a lower level of employment before the marginal revenue product of labor becomes too low. Given the choices and understanding the linear decrease, 10 is a reasonable midpoint for maximizing total wages before the diminishing returns significantly decrease the marginal revenue product of labor. This is a simplified explanation without the exact wage rate to set MRPL equal to for precise maximization.

A Union Faces a Labor Demand Curve Given by MRPL

A Union Faces a Labor Demand Curve Given by MRP_L