A palm oil processing mill operates in the short run with fixed processing machinery and v… — JAMB UTME

A palm oil processing mill operates in the short run with fixed processing machinery and variable labor ( $L$ ). When $3$ workers are employed, the average product ( $AP$ ) of labor is $16$ barrels per day. When a $4\text{th}$ worker is added, the total product ( $TP$ ) increases to $64$ barrels per day. What is the marginal product ( $MP$ ) of the $4\text{th}$ worker in barrels per day?

Answer: 16 barrels

Answer

The marginal product of the 4th worker is 16 barrels per day.

To find the marginal product of the 4th worker, first determine total output with 3 workers:

TP_3 = AP_3 \times 3 = 16 \times 3 = 48

barrels. The marginal product of the 4th worker is the change in total product when moving from 3 to 4 workers:

MP_4 = TP_4 - TP_3 = 64 - 48 = 16

barrels.

Step-by-Step Solution

Calculate the Total Product for 3 workers (

TP_3

)

TP_3 = 48 barrels

Total Product is calculated by multiplying Average Product by the number of workers (

TP = AP \times L = 16 \times 3 = 48

Calculate the Marginal Product of the 4th worker (

MP_4

)

MP_4 = 16 barrels

Marginal Product is the addition to Total Product resulting from employing one additional unit of labor (

MP_4 = TP_4 - TP_3 = 64 - 48 = 16

Key Concept

Short-Run Production: Deriving Marginal Product from Average Product and Total Product

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