Compute the missing values in the ATC, AVC, and AFC columns based on the data in the image.
Understand the Problem
The question presents a table with values for Output, Total Cost (TC), Fixed Cost (FC), Variable Cost (VC) and asks to compute Average Total Cost (ATC), Average Variable Cost (AVC), and Average Fixed Cost (AFC). This involves understanding the relationships between these different types of costs in economics. The image shows the table from output 0 to 6 and your job is to compute the missing values, in the ATC, AVC, and AFC columns.
Answer
The completed table showing ATC, AVC, and AFC is in the answer section.
Answer for screen readers
Here's the completed table:
| Output | TC | FC | VC | ATC | AVC | AFC |
|---|---|---|---|---|---|---|
| 0 | 40 | |||||
| 1 | 40 | 40 | 6 | 40 | 6 | 40 |
| 2 | 40 | 40 | 11 | 20 | 5.5 | 20 |
| 3 | 40 | 40 | 5 | 13.33 | 1.67 | 13.33 |
| 4 | 60 | 40 | 20 | 15 | 5 | 10 |
| 5 | 65 | 40 | 25 | 13 | 5 | 8 |
| 6 | 40 | 40 | 27 | 6.67 | 4.5 | 6.67 |
Steps to Solve
- Recall the formula for Average Total Cost (ATC)
Average Total Cost (ATC) is calculated by dividing Total Cost (TC) by the quantity of Output (Q). Written as:
$ATC = \frac{TC}{Q}$
- Calculate ATC for each level of output
- Output 1: $ATC = \frac{40}{1} = 40$
- Output 2: $ATC = \frac{40}{2} = 20$
- Output 3: $ATC = \frac{40}{3} = 13.33$
- Output 4: $ATC = \frac{60}{4} = 15$
- Output 5: $ATC = \frac{65}{5} = 13$
- Output 6: $ATC = \frac{40}{6} = 6.67$
- Recall the formula for Average Variable Cost (AVC)
Average Variable Cost (AVC) is calculated by dividing Variable Cost (VC) by the quantity of Output (Q). Written as:
$AVC = \frac{VC}{Q}$
- Calculate AVC for each level of output
- Output 1: $AVC = \frac{6}{1} = 6$
- Output 2: $AVC = \frac{11}{2} = 5.5$
- Output 3: $AVC = \frac{5}{3} = 1.67$
- Output 4: $AVC = \frac{20}{4} = 5$. Note here that $VC = TC - FC = 60 - 40 = 20$.
- Output 5: $AVC = \frac{25}{5} = 5$. Note here that $VC = TC - FC = 65 - 40 = 25$.
- Output 6: $AVC = \frac{27}{6} = 4.5$
- Recall the formula for Average Fixed Cost (AFC)
Average Fixed Cost (AFC) is calculated by dividing Fixed Cost (FC) by the quantity of Output (Q). Written as:
$AFC = \frac{FC}{Q}$
- Calculate AFC for each level of output
- Output 1: $AFC = \frac{40}{1} = 40$
- Output 2: $AFC = \frac{40}{2} = 20$
- Output 3: $AFC = \frac{40}{3} = 13.33$
- Output 4: $AFC = \frac{40}{4} = 10$
- Output 5: $AFC = \frac{40}{5} = 8$
- Output 6: $AFC = \frac{40}{6} = 6.67$
Here's the completed table:
| Output | TC | FC | VC | ATC | AVC | AFC |
|---|---|---|---|---|---|---|
| 0 | 40 | |||||
| 1 | 40 | 40 | 6 | 40 | 6 | 40 |
| 2 | 40 | 40 | 11 | 20 | 5.5 | 20 |
| 3 | 40 | 40 | 5 | 13.33 | 1.67 | 13.33 |
| 4 | 60 | 40 | 20 | 15 | 5 | 10 |
| 5 | 65 | 40 | 25 | 13 | 5 | 8 |
| 6 | 40 | 40 | 27 | 6.67 | 4.5 | 6.67 |
More Information
The table shows how different costs vary with output. Fixed costs remain the same regardless of output, while variable costs change with the level of production. Average costs provide a per-unit perspective, useful for decision-making such as pricing.
Tips
A common mistake is not calculating VC correctly when TC and FC are given. Remember that $VC = TC - FC$. Also, rounding errors can occur if not careful with decimal places.
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