A firm operating in the short run incurs a total cost of \text{₦}400 when output is zero u… — JAMB UTME

A firm operating in the short run incurs a total cost of $\text{₦}400$ when output is zero units. At an output level of $8$ units, its average total cost ( $ATC$ ) is $\text{₦}100$ . If the marginal cost ( $MC$ ) of producing the $9^{\text{th}}$ unit is $\text{₦}110$ and the marginal cost of producing the $10^{\text{th}}$ unit is $\text{₦}130$ , what is the average variable cost ( $AVC$ ) in Naira at an output level of $10$ units?

Answer: 64 Naira

Answer

The average variable cost (AVC) of producing 10 units is 64 Naira.

By applying short-run cost identities, TFC is determined as 400 Naira from TC at Q = 0. TC at Q = 8 is 8 × 100 = 800 Naira. Adding the MC for the 9th (110) and 10th (130) units gives TC at Q = 10 as 1040 Naira. Subtracting TFC (400) gives TVC = 640 Naira. Dividing TVC by Q = 10 gives AVC = 64 Naira.

Step-by-Step Solution

Determine Total Fixed Cost (TFC)

TFC = 400 Naira

At an output level of zero (Q = 0), variable costs are zero, so Total Cost equals Total Fixed Cost.

Calculate Total Cost at 8 units (TC(8))

TC(8) = 800 Naira

Total Cost is equal to Quantity multiplied by Average Total Cost: TC = Q × ATC = 8 × 100 = 800.

Calculate Total Cost at 10 units (TC(10))

TC(10) = 1040 Naira

Add the Marginal Cost of the 9th unit (110) and 10th unit (130) to TC(8): TC(10) = 800 + 110 + 130 = 1040.

Calculate Total Variable Cost at 10 units (TVC(10))

TVC(10) = 640 Naira

Total Variable Cost is derived by subtracting Total Fixed Cost from Total Cost: TVC = TC - TFC = 1040 - 400 = 640.

Compute Average Variable Cost at 10 units (AVC(10))

AVC(10) = 64 Naira

Average Variable Cost is Total Variable Cost divided by quantity: AVC = TVC / Q = 640 / 10 = 64.

Key Concept

Short-Run Cost Relationships and Calculations

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