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Question
Microeconomics
Posted 2 months ago

The table below shows the total output that Bart's Beans produces with differing amounts of labor.
\begin{tabular}{ll} 
Units of Labor & Total Product of Labor (TPL)\left(T P_{L}\right) \\
\hline 0 & 0 \\
1 & 2 \\
2 & 6 \\
3 & 12 \\
4 & 17 \\
5 & 21 \\
6 & 24 \\
7 & 26 \\
8 & 25 \\
9 & 23
\end{tabular}

At what quantity of labor does diminishing returns to labor set in?

Choose 1 answer:
(A) at the 5th 5^{\text {th }} unit of labor
(B) At the 1st 1^{\text {st }} unit of labor
(C) at the 8th 8^{\text {th }} unit of labor
(D) at the 4th 4^{\text {th }} unit of labor
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Answer from Sia
Posted 2 months ago
Solution
a
Definition of Diminishing Returns: Diminishing returns to labor occur when the marginal product of labor (MPL) starts to decrease as more units of labor are added
b
Calculation of MPL: The marginal product of labor is calculated as the change in total product of labor (TPL) divided by the change in units of labor. For each unit of labor, MPL can be calculated as follows: MPL1=TPL1TPL0=20=2MPL2=TPL2TPL1=62=4MPL3=TPL3TPL2=126=6MPL4=TPL4TPL3=1712=5MPL5=TPL5TPL4=2117=4MPL6=TPL6TPL5=2421=3MPL7=TPL7TPL6=2624=2MPL8=TPL8TPL7=2526=1MPL9=TPL9TPL8=2325=2 \begin{align*} MPL_1 &= TPL_1 - TPL_0 = 2 - 0 = 2 \\ MPL_2 &= TPL_2 - TPL_1 = 6 - 2 = 4 \\ MPL_3 &= TPL_3 - TPL_2 = 12 - 6 = 6 \\ MPL_4 &= TPL_4 - TPL_3 = 17 - 12 = 5 \\ MPL_5 &= TPL_5 - TPL_4 = 21 - 17 = 4 \\ MPL_6 &= TPL_6 - TPL_5 = 24 - 21 = 3 \\ MPL_7 &= TPL_7 - TPL_6 = 26 - 24 = 2 \\ MPL_8 &= TPL_8 - TPL_7 = 25 - 26 = -1 \\ MPL_9 &= TPL_9 - TPL_8 = 23 - 25 = -2 \\ \end{align*}
c
Identification of Diminishing Returns: Diminishing returns set in when the MPL starts to decrease. From the calculations, MPL starts to decrease after the 3rd unit of labor (from 6 to 5). Therefore, diminishing returns to labor set in at the 4th unit of labor
Answer
(D) at the 4th unit of labor
Key Concept
Diminishing Returns to Labor
Explanation
Diminishing returns to labor occur when the marginal product of labor starts to decrease as more units of labor are added. In this case, the marginal product of labor starts to decrease after the 3rd unit of labor, indicating that diminishing returns set in at the 4th unit of labor.

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