A commercial printing enterprise operating in the short run produces 5 thousand brochures … — JAMB UTME

A commercial printing enterprise operating in the short run produces $5$ thousand brochures at an Average Fixed Cost ( $\text{AFC}$ ) of $\text{₦}160$ per thousand and an Average Variable Cost ( $\text{AVC}$ ) of $\text{₦}120$ per thousand. When the firm expands output to $10$ thousand brochures, its Total Cost ( $\text{TC}$ ) rises to $\text{₦}2,650$ . What is the Marginal Cost ( $\text{MC}$ ) per thousand brochures over this range of output?

Answer: 250 ₦

Answer

The Marginal Cost (

\text{MC}

) per thousand brochures over this output range is

\text{₦}250

To find the Marginal Cost (

\text{MC}

), first compute initial Total Cost at

5

units:

\text{TC}_1 = (\text{AFC} + \text{AVC}) \times Q = (160 + 120) \times 5 = \text{₦}1,400

. Next, determine the change in total cost when expanding to

10

units:

\Delta \text{TC} = \text{₦}2,650 - \text{₦}1,400 = \text{₦}1,250

. Dividing this by the change in output (

\Delta Q = 10 - 5 = 5

) gives

\text{MC} = \frac{1,250}{5} = \text{₦}250

Step-by-Step Solution

Calculate Total Cost at initial output level (

Q_1 = 5

)

\text{ATC}_1 = \text{AFC}_1 + \text{AVC}_1 = 160 + 120 = \text{₦}280

per thousand. Therefore,

\text{TC}_1 = \text{ATC}_1 \times Q_1 = 280 \times 5 = \text{₦}1,400

Total cost at an output level is equal to Average Total Cost multiplied by the output quantity.

Determine the change in Total Cost (

\Delta \text{TC}

) and change in Quantity (

\Delta Q

)

\Delta \text{TC} = \text{TC}_2 - \text{TC}_1 = 2,650 - 1,400 = \text{₦}1,250

;

\Delta Q = Q_2 - Q_1 = 10 - 5 = 5

thousand brochures.

Marginal cost measures the change in total cost resulting from a change in the total output quantity.

Calculate Marginal Cost (

\text{MC}

)

\text{MC} = \frac{\Delta \text{TC}}{\Delta Q} = \frac{1,250}{5} = \text{₦}250

per thousand brochures.

Dividing the change in total cost by the change in output yields the unit marginal cost over the interval.

Key Concept

Short-Run Marginal Cost and Total Cost derivation from Average Cost components

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