The correct option is
B. AC = (TC) / Q; TC = VC + FC.
Detailed Explanation:
- Understanding the Terms:
- Average Cost (AC): This is the cost per unit of output produced. It is calculated by dividing the total cost (TC) by the quantity of goods produced (Q).
- Total Cost (TC): This is the total expense incurred in the production of goods. It includes both fixed costs (FC) and variable costs (VC).
- Variable Cost (VC): These are costs that change with the level of output. For example, raw materials and labor directly involved in production.
-
Fixed Cost (FC): These are costs that do not change with the level of output. For example, rent, salaries of permanent staff, and equipment costs.
-
Formulas:
- The formula for Average Cost (AC) is:
[
AC = \frac{TC}{Q}
]
-
The formula for Total Cost (TC) is:
[
TC = VC + FC
]
-
Why Option B is Correct:
- Option B states that AC = (TC) / Q and TC = VC + FC. This is correct because it accurately reflects the definitions and relationships between average cost, total cost, variable cost, and fixed cost.
-
To derive AC, you take the total cost (which is the sum of variable and fixed costs) and divide it by the quantity produced. This gives you the average cost per unit.
-
Why Other Options are Incorrect:
- Option A: AC = TC; TC = VC + FC: This is incorrect because it states that Average Cost (AC) is equal to Total Cost (TC), which is not true. AC is the total cost divided by the quantity produced, not equal to TC itself.
- Option C: AC = TC; TC = (VC)(FC) Q: This is incorrect for two reasons. First, it incorrectly states that AC equals TC, and second, it suggests that TC is the product of variable cost and fixed cost multiplied by quantity, which is not how total cost is calculated.
- Option D: AC = TC - FC; VC = TC - AC: This is also incorrect. It misrepresents the relationship between average cost and total cost. AC cannot be derived by subtracting fixed costs from total costs, and the equation for VC is also incorrect.
Example Calculation:
Let’s say a company has the following costs:
- Fixed Costs (FC) = $1000
- Variable Costs (VC) = $2000
- Quantity produced (Q) = 100 units
-
Calculate Total Cost (TC):
[
TC = VC + FC = 2000 + 1000 = 3000
]
-
Calculate Average Cost (AC):
[
AC = \frac{TC}{Q} = \frac{3000}{100} = 30
]
This means the average cost per unit produced is $30.
Common Pitfalls:
- Confusing total cost with average cost. Remember, average cost is always per unit, while total cost is the overall expense.
- Forgetting to include both fixed and variable costs when calculating total cost.
- Misapplying the formulas, especially in the context of different production levels.
Revision Summary:
- Average Cost (AC) is calculated as Total Cost (TC) divided by Quantity (Q).
- Total Cost (TC) is the sum of Variable Cost (VC) and Fixed Cost (FC).
- Correct relationships are crucial for understanding cost structures in production.
- Always ensure to differentiate between total and average costs in calculations.