A firm operating in the short run faces a total cost function given by TC = 240 + 15Q + 3Q… — JAMB UTME

A firm operating in the short run faces a total cost function given by $TC = 240 + 15Q + 3Q^2$ , where $TC$ represents total cost in Naira ( $\text{₦}$ ) and $Q$ represents the quantity of output produced in units. What is the firm's Average Total Cost ( $\text{ATC}$ ) at the output level where its Average Variable Cost ( $\text{AVC}$ ) is equal to $\text{₦}33$ ?

$\text{₦}73$ Answer
B
$\text{₦}33$
C
$\text{₦}273$
D
$\text{₦}238$

Answer

The firm's Average Total Cost at the specified output level is

\text{₦}73

The correct answer is derived by first expressing Average Variable Cost as

AVC = 15 + 3Q

. Setting

AVC = 33

reveals that the firm produces

6

units of output. At this production level, Average Fixed Cost is

AFC = \text{₦}240 / 6 = \text{₦}40

. Adding

AFC

(

\text{₦}40

) to

AVC

(

\text{₦}33

) yields an Average Total Cost (

ATC

) of

\text{₦}73

Step-by-Step Solution

Extract Total Fixed Cost (

TFC

) and Total Variable Cost (

TVC

) from the given total cost function

TC = 240 + 15Q + 3Q^2

TFC = 240

and

TVC = 15Q + 3Q^2

In short-run cost functions, fixed costs do not vary with output (constant term), while variable costs depend on quantity

Q

Derive the Average Variable Cost (

AVC

) equation by dividing

TVC

by output

Q

AVC = \frac{15Q + 3Q^2}{Q} = 15 + 3Q

Average Variable Cost measures variable cost per unit of output produced.

Determine the output level

Q

when

AVC = \text{₦}33

15 + 3Q = 33 \implies 3Q = 18 \implies Q = 6\text{ units}

Solving the equation identifies the target output level.

Calculate Average Fixed Cost (

AFC

) at

Q = 6\text{ units}

AFC = \frac{TFC}{Q} = \frac{240}{6} = \text{₦}40

Average Fixed Cost is total fixed cost divided by quantity.

Compute Average Total Cost (

ATC

) at

Q = 6\text{ units}

ATC = AFC + AVC = 40 + 33 = \text{₦}73

Average Total Cost is the sum of Average Fixed Cost and Average Variable Cost.

Key Concept

Short-Run Cost Function Derivation and Average Cost Relationships

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