Final answer:
The marginal product of labor (MPL) is the additional output produced by each additional unit of labor. The average product of labor (APL) is the total output produced divided by the total units of labor employed. The total number of labor that maximizes output is the point where the MPL equals zero.
Step-by-step explanation:
The marginal product of labor (MPL) is the additional output produced by each additional unit of labor. It can be calculated by taking the derivative of the production function with respect to labor: MPL = dQ/dL. In this case, the production function is Q = -50 + 10L -0.02L^2. Taking the derivative gives MPL = 10 - 0.04L. The average product of labor (APL) is the total output produced divided by the total units of labor employed. It can be calculated by dividing the total product (Q) by the total labor (L). In this case, APL = Q/L.
The MPL graph shows how the marginal product of labor changes as the amount of labor employed increases. It is a downward sloping curve because as more labor is added, the MPL decreases. The APL graph shows how the average product of labor changes as the amount of labor employed increases. It is a U-shaped curve because initially, adding more labor increases the APL, but eventually, diminishing returns set in and the APL decreases. The total number of labor that maximizes output is the point where the MPL equals zero. In this case, MPL = 10 - 0.04L = 0. Solving for L gives L = 250. Therefore, the total number of labor that maximizes output is 250.