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Zorluk: ZorShort-Run Production and Law of Diminishing Returns

A shoe manufacturing workshop operates in the short run with a fixed building and machinery. When employing 55 workers, the average product of labor is 2828 pairs of shoes per day. Adding a 6th6\text{th} worker brings total output to 168168 pairs per day. Upon hiring a 7th7\text{th} worker, the law of diminishing returns causes the marginal product of the 7th7\text{th} worker to be 50%50\% lower than the marginal product of the 6th6\text{th} worker. What is the average product of labor (in pairs of shoes per day) when 77 workers are employed?

Cevap: 26 pairs

Cevap

The average product of labor when 7 workers are employed is 26 pairs of shoes per day.
To find the average product for 7 workers, first determine total product for 5 workers (5×28=1405 \times 28 = 140). The 6th worker adds 168−140=28168 - 140 = 28 pairs. With diminishing returns reducing the 7th worker's marginal product by 50%, the 7th worker adds 1414 pairs, bringing total output to 182182 pairs. Dividing 182 by 7 yields an average product of 26 pairs per day.

Adım Adım Çözüm

1
Calculate Total Product for 5 workers (TP5TP_5)
TP5=5×28=140TP_5 = 5 \times 28 = 140 pairs
Total Product is the product of Average Product and the number of variable input units (TP=AP×LTP = AP \times L).
2
Determine Marginal Product of the 6th worker (MP6MP_6)
MP6=168−140=28MP_6 = 168 - 140 = 28 pairs
Marginal Product is the additional output produced by hiring one more worker (MPn=TPn−TPn−1MP_n = TP_n - TP_{n-1}).
3
Calculate Marginal Product of the 7th worker (MP7MP_7)
MP7=28×(1−0.50)=14MP_7 = 28 \times (1 - 0.50) = 14 pairs
Due to diminishing marginal returns, MP7MP_7 is 50% less than MP6MP_6.
4
Calculate Total Product for 7 workers (TP7TP_7)
TP7=168+14=182TP_7 = 168 + 14 = 182 pairs
Total Product with 7 workers is the sum of TP6TP_6 and MP7MP_7.
5
Calculate Average Product for 7 workers (AP7AP_7)
AP7=1827=26AP_7 = \frac{182}{7} = 26 pairs per day
Average Product is total output divided by total units of labor (AP=TPLAP = \frac{TP}{L}).

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Short-Run Production and Law of Diminishing Returns
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Short-Run Production and Law of Diminishing Returns

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