Final answer:
a. The ranges of the 3 stages of production are determined by the marginal product of labor. b. Firm is operating in Stage 2 for L=5 and L=3. c. The starting point of diminishing marginal returns is L=3.25. d. A graph can be drawn to represent the 3 stages of production.
Step-by-step explanation:
a. The ranges of the 3 stages of production can be found by analyzing the marginal product of labor. The first stage is where the marginal product of labor (MPL) is increasing. The second stage is where MPL is decreasing but still positive. The third stage is where MPL becomes negative. In this case, the ranges of the 3 stages are:
• Stage 1: MPL > 0
• Stage 2: MPL > 0 but decreasing
• Stage 3: MPL < 0
b. To find at which stage the firm is operating, we need to calculate the MPL at the given values of L. If the MPL is > 0, the firm is in Stage 1. If the MPL is > 0 but decreasing, the firm is in Stage 2. If the MPL is < 0, the firm is in Stage 3. For L = 5, MPL = 162. For L = 3, MPL = 162.5. Based on these values, the firm is operating in Stage 2 for both L values.
c. To find the starting point of diminishing marginal returns (DMR), we need to determine the L value where MPL starts decreasing. From the given production function, we can see that MPL starts decreasing at L=3.25. So, the L value at the starting of DMR is 3.25.
d. Unfortunately, I am unable to draw a graph here, but you can plot the stages of production on a graph with MPL on the y-axis and L on the x-axis. The graph would show three distinct stages: Stage 1 with increasing MPL, Stage 2 with decreasing MPL but still positive, and Stage 3 with negative MPL.