Given total product of 9 labour units is 2, 5, 9, 12, 14, 15, 15, 14, and 12 respectively. Which unit of labour will produce zero marginal product?
Understand the Problem
The question is asking which unit of labor, among the given outputs, results in zero marginal product. This can typically be determined by analyzing the changes in total product as labor units increase.
Answer
The 6th unit of labor will produce zero marginal product.
Answer for screen readers
The unit of labor that will produce zero marginal product is the 6th unit.
Steps to Solve
- Understanding Marginal Product
The marginal product (MP) of labor refers to the additional output that is generated by adding one more unit of labor. It can be calculated by finding the difference in total product as the number of labor units increases.
- Calculate Marginal Products
Using the given total product for each labor unit, calculate the marginal product for each labor unit by finding the difference between successive total products:
- For the 1st unit of labor: $MP_1 = TP_1 - TP_0 = 5 - 2 = 3$
- For the 2nd unit of labor: $MP_2 = TP_2 - TP_1 = 9 - 5 = 4$
- For the 3rd unit of labor: $MP_3 = TP_3 - TP_2 = 12 - 9 = 3$
- For the 4th unit of labor: $MP_4 = TP_4 - TP_3 = 14 - 12 = 2$
- For the 5th unit of labor: $MP_5 = TP_5 - TP_4 = 15 - 14 = 1$
- For the 6th unit of labor: $MP_6 = TP_6 - TP_5 = 15 - 15 = 0$
- For the 7th unit of labor: $MP_7 = TP_7 - TP_6 = 14 - 15 = -1$
- For the 8th unit of labor: $MP_8 = TP_8 - TP_7 = 12 - 14 = -2$
- Identify the Unit with Zero Marginal Product
The marginal product calculation reveals that the 6th unit of labor has a marginal product of zero, as $MP_6 = 0$.
The unit of labor that will produce zero marginal product is the 6th unit.
More Information
When the marginal product is zero, it indicates that adding an additional unit of labor does not contribute to any additional output. This often occurs when a production process is at its maximum capacity.
Tips
- Failing to calculate the marginal products correctly by neglecting to find the differences between total output values.
- Misinterpreting which unit corresponds to the zero marginal product, leading to confusion about the correct answer.
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