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Difficulty: MediumShort-Run Cost Concepts and Calculations

A poultry farm operating in the short run incurs a Total Fixed Cost (TFC\text{TFC}) of ₦5,000\text{₦}5,000. When output increases from 4040 crates to 5050 crates of eggs, the farm's Average Variable Cost (AVC\text{AVC}) rises from ₦150\text{₦}150 per crate to ��180\text{��}180 per crate. What is the Marginal Cost (MC\text{MC}) per crate for these additional 1010 crates?

  1. A
    ₦30\text{₦}30 per crate
  2. ₦300\text{₦}300 per crateAnswer
  3. C
    ₦800\text{₦}800 per crate
  4. D
    ₦1,400\text{₦}1,400 per crate

Answer

The Marginal Cost (MC\text{MC}) per crate for the additional 1010 crates is ₦300\text{₦}300.
To find Marginal Cost (MC\text{MC}), calculate the change in total cost resulting from producing the additional 1010 crates. At 4040 crates, TVC=40×₦150=₦6,000\text{TVC} = 40 \times \text{₦}150 = \text{₦}6,000. At 5050 crates, TVC=50×₦180=₦9,000\text{TVC} = 50 \times \text{₦}180 = \text{₦}9,000. The change in total variable cost is ₦9,000−₦6,000=₦3,000\text{₦}9,000 - \text{₦}6,000 = \text{₦}3,000. Dividing this by the output increase of 1010 crates gives MC=₦300\text{MC} = \text{₦}300 per crate.

Step-by-Step Solution

1
Calculate Total Variable Cost (TVC\text{TVC}) at output level Q1=40Q_1 = 40 and Q2=50Q_2 = 50.
TVC1=40×₦150=₦6,000\text{TVC}_1 = 40 \times \text{₦}150 = \text{₦}6,000; TVC2=50×₦180=₦9,000\text{TVC}_2 = 50 \times \text{₦}180 = \text{₦}9,000.
Total Variable Cost is derived by multiplying total output quantity (QQ) by Average Variable Cost (AVC\text{AVC}).
2
Determine the change in Total Variable Cost (ΔTVC\Delta \text{TVC}).
ΔTVC=₦9,000−₦6,000=₦3,000\Delta \text{TVC} = \text{₦}9,000 - \text{₦}6,000 = \text{₦}3,000.
Because Total Fixed Cost (TFC\text{TFC}) is constant in the short run (ΔTFC=0\Delta \text{TFC} = 0), the change in Total Cost (ΔTC\Delta \text{TC}) equals the change in Total Variable Cost (ΔTVC\Delta \text{TVC}).
3
Compute Marginal Cost (MC\text{MC}) by dividing ΔTC\Delta \text{TC} by the change in output (ΔQ\Delta Q).
MC=₦3,00050−40=₦3,00010=₦300\text{MC} = \frac{\text{₦}3,000}{50 - 40} = \frac{\text{₦}3,000}{10} = \text{₦}300 per crate.
Marginal cost is defined as the additional cost incurred from producing one extra unit of output: MC=ΔTCΔQ\text{MC} = \frac{\Delta \text{TC}}{\Delta Q}.

Key Concept

Short-Run Marginal Cost and Average Variable Cost Calculations
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Topics

Short-Run Cost Concepts and Calculations

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