A commercial aquaculture catfish farm operates in the short run with fixed pond facilities… — JAMB UTME

A commercial aquaculture catfish farm operates in the short run with fixed pond facilities and variable labor ( $L$ ). When $4$ units of labor are employed, the average product of labor ( $AP_L$ ) is $25\text{ kg}$ . Employing the $5\text{th}$ unit of labor yields a marginal product ( $MP_L$ ) of $40\text{ kg}$ . When the $6\text{th}$ unit of labor is added, the law of diminishing returns sets in, causing the marginal product of the $6\text{th}$ worker to decrease by $30\%$ relative to that of the $5\text{th}$ worker. What is the total product ( $TP$ ) in kg when $6$ units of labor are employed?

Answer: 168 kg

Answer

The total product when 6 units of labor are employed is 168 kg.

The total output when 6 workers are employed is 168 kg. First, output for 4 workers is

4 \times 25\text{ kg} = 100\text{ kg}

. Adding the 5th worker increases total output to

100\text{ kg} + 40\text{ kg} = 140\text{ kg}

. With diminishing marginal returns, the 6th worker contributes

30\%

less than the 5th worker, which equals

40 \times (1 - 0.30) = 28\text{ kg}

. Therefore, total output for 6 workers is

140\text{ kg} + 28\text{ kg} = 168\text{ kg}

Step-by-Step Solution

Calculate Total Product for 4 units of labor

Total Product at L = 4 is 100 kg

Total product is derived by multiplying average product by the total labor employed (

TP = AP \times L

Calculate Total Product for 5 units of labor

Total Product at L = 5 is 140 kg

Adding the marginal product of the 5th worker (

40\text{ kg}

) to

TP_4

(

100\text{ kg}

) yields

TP_5

Calculate Marginal Product of the 6th worker

Marginal product of the 6th worker is 28 kg

Diminishing marginal returns cause

MP_6

to drop by 30% from

MP_5

, giving

MP_6 = 40 \times 0.70 = 28\text{ kg}

Calculate Total Product for 6 units of labor

Total Product at L = 6 is 168 kg

Summing

TP_5

(

140\text{ kg}

) and

MP_6

(

28\text{ kg}

) gives the total output for 6 workers.

Key Concept

Short-Run Production, Marginal Product, and Law of Diminishing Returns

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