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Question

Difficulty: MediumShort-Run Production and Law of Diminishing Returns

At a commercial maize farm operating with fixed land and equipment, employing 44 farm workers yields an average product of 30 crates30\text{ crates} of maize. When a 5th5\text{th} worker is hired, the marginal product contributed by this worker is 20 crates20\text{ crates}. What is the average product of labor when 55 workers are employed?

Answer: 28 crates

Answer

The average product of labor when 5 workers are employed is 28 crates.
To determine the average product (APAP) when 55 workers are employed, first calculate the total product (TPTP) for 44 workers: 4×30=120 crates4 \times 30 = 120\text{ crates}. Next, add the marginal product (MPMP) of the 5th5\text{th} worker to find total output for 55 workers: 120+20=140 crates120 + 20 = 140\text{ crates}. Finally, divide total output by the total number of workers (55): 140/5=28 crates140 / 5 = 28\text{ crates}.

Step-by-Step Solution

1
Calculate total product (TPTP) for 4 workers
TP4=120 cratesTP_4 = 120\text{ crates}
Total product equals average product multiplied by total units of labor (TP=AP×LTP = AP \times L).
2
Calculate total product (TPTP) for 5 workers
TP5=140 cratesTP_5 = 140\text{ crates}
Total product with 5 workers is the sum of previous total product and the marginal product of the 5th worker (TP5=TP4+MP5TP_5 = TP_4 + MP_5).
3
Compute average product (APAP) for 5 workers
AP5=28 cratesAP_5 = 28\text{ crates}
Average product is calculated by dividing total product by total units of variable input (AP=TP/LAP = TP / L).

Key Concept

Relationship between Total Product, Average Product, and Marginal Product in Short-Run Production
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Topics

Short-Run Production and Law of Diminishing Returns

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