Cindy’s Car Wash has average variable costs of $2 and average total costs of $3 when it produces 100 units of output (car washes). The firm’s total variable cost is
a. $100.
b. $200.
c. $300.
d. $500.
The correct answer and explanation is :
To determine the total variable cost (TVC), we use the formula:
[
TVC = \text{Average Variable Cost (AVC)} \times \text{Quantity (Q)}
]
From the problem:
- AVC = $2
- Q = 100 (car washes)
Now, applying the values:
[
TVC = 2 \times 100 = 200
]
Thus, the correct answer is:
b. $200.
Explanation:
Understanding Variable Costs
Variable costs are costs that change with the level of output. In this case, Cindy’s Car Wash incurs a cost of $2 per car wash for expenses that vary with production, such as water, soap, electricity, and labor.
Average Variable Cost and Total Variable Cost
Average Variable Cost (AVC) is the cost per unit of output. The total variable cost (TVC) is calculated by multiplying AVC by the number of units produced. Since AVC is $2 and Cindy’s Car Wash produces 100 car washes, multiplying these values gives us a total variable cost of $200.
Role of Total Cost in Production Decisions
We are also given that Average Total Cost (ATC) is $3 at 100 units. ATC includes both fixed and variable costs:
[
ATC = \frac{TC}{Q}
]
[
3 = \frac{TC}{100}
]
[
TC = 3 \times 100 = 300
]
Since Total Cost (TC) = Total Fixed Cost (TFC) + Total Variable Cost (TVC), we can solve for TFC:
[
TFC = TC – TVC = 300 – 200 = 100
]
Thus, Cindy’s Car Wash has $100 in fixed costs (costs that do not change with output).
Conclusion
Understanding AVC and TVC helps businesses manage costs and set prices. Cindy’s Car Wash must ensure its pricing covers at least $3 per wash to break even.