A firm operating in the short run employs labor as a variable input while keeping capital … — JAMB UTME

A firm operating in the short run employs labor as a variable input while keeping capital fixed. When the firm employs $4$ workers, total output is $120$ units. When a $5$ th worker is added, total output increases to $145$ units. What is the marginal product of the $5$ th worker in units?

Answer: 25 units

Answer

The marginal product of the 5th worker is 25 units.

The marginal product of the 5th worker is calculated as the difference between the total output with 5 workers (145 units) and the total output with 4 workers (120 units), which equals 25 units.

Step-by-Step Solution

Identify the Total Product (

TP

) corresponding to

4

and

5

workers.

TP_4 = 120

units and

TP_5 = 145

units.

Marginal product measures the addition to total product resulting from employing one extra unit of the variable factor.

Calculate the change in total product (

\Delta TP

) and change in labor (

\Delta L

\Delta TP = 145 - 120 = 25

units,

\Delta L = 5 - 4 = 1

unit.

Evaluating the incremental changes provides the variables required for the marginal product formula.

Compute the Marginal Product (

MP_5

MP_5 = \frac{\Delta TP}{\Delta L} = \frac{25}{1} = 25

units.

Dividing the increase in output by the increase in labor yields the marginal output of the 5th worker.

Key Concept

Marginal Product of Labor

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