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Difficulty: MediumShort-Run Cost Concepts and Calculations

A shoe manufacturing firm operates in the short run. When producing 1010 pairs of shoes, its Average Fixed Cost (AFC\text{AFC}) is ₦800\text{₦}800 per pair and its Total Variable Cost (TVC\text{TVC}) is ₦15,000\text{₦}15,000. If increasing output to 1111 pairs raises the firm's Total Cost (TC\text{TC}) to ₦25,500\text{₦}25,500, what is the Marginal Cost (MC\text{MC}) of the 11th11\text{th} pair of shoes?

Answer: 2500 ₦

Answer

The Marginal Cost of producing the 11th pair of shoes is ₦2,500.
To find the Marginal Cost of the 11th unit, we first determine the Total Cost at 10 units. Total Fixed Cost (TFC) is constant and equal to AFC × Q = ₦800 × 10 = ₦8,000. Adding the Total Variable Cost (TVC) of ₦15,000 gives an initial Total Cost (TC₁) of ₦23,000. When output increases to 11 units, Total Cost (TC₂) becomes ₦25,500. The Marginal Cost is the change in Total Cost per unit change in output: ₦25,500 - ₦23,000 = ₦2,500.

Step-by-Step Solution

1
Calculate Total Fixed Cost (TFC) at 10 units
TFC = ₦800 × 10 = ₦8,000
Average Fixed Cost is Total Fixed Cost divided by quantity (AFC = TFC / Q), so TFC = AFC × Q.
2
Calculate Total Cost (TC₁) for 10 units
TC₁ = ₦8,000 + ₦15,000 = ₦23,000
Total Cost is the sum of Total Fixed Cost and Total Variable Cost (TC = TFC + TVC).
3
Calculate Marginal Cost (MC) for the 11th unit
MC = ₦25,500 - ₦23,000 = ₦2,500
Marginal Cost measures the change in total cost resulting from producing one additional unit of output (MC = ΔTC / ΔQ).

Key Concept

Short-Run Cost Identities and Marginal Cost Calculation
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Topics

Short-Run Cost Concepts and Calculations

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