If the average total cost of a firm is Rs 54, the average variable cost is Rs 36, and the firm produces 2500 units of output, what is the total fixed cost of the firm?

Introduction / Context:
Understanding the relationship between total fixed cost, total variable cost, average total cost and average variable cost is essential in cost analysis. Many examination questions present two of these averages along with the quantity produced and ask the candidate to compute either total cost or total fixed cost. This question requires using the identity that average total cost equals average fixed cost plus average variable cost and then working backward to total fixed cost using multiplication by quantity.

Given Data / Assumptions:
• Average total cost (ATC) is Rs 54 per unit. • Average variable cost (AVC) is Rs 36 per unit. • Quantity of output (Q) is 2500 units. • We must find the total fixed cost (TFC) in rupees.

Concept / Approach:
The key cost relationships are as follows. Average total cost equals total cost divided by quantity. Average variable cost equals total variable cost divided by quantity. Average fixed cost equals total fixed cost divided by quantity. Also, average total cost is the sum of average variable cost and average fixed cost. Using this last identity, we can first find average fixed cost by subtracting average variable cost from average total cost. Once we know average fixed cost, we multiply it by the quantity to obtain total fixed cost.

Step-by-Step Solution:
Step 1: Use the identity ATC equals AVC plus AFC, where AFC is average fixed cost. Step 2: Rearrange the identity to obtain AFC equals ATC minus AVC. Step 3: Substitute the given values. ATC is 54 and AVC is 36, so AFC equals 54 minus 36. Step 4: Compute 54 minus 36, which equals 18. Therefore, average fixed cost is Rs 18 per unit. Step 5: Use the formula TFC equals AFC multiplied by Q to find total fixed cost. Step 6: Multiply 18 by 2500. Dividing 2500 into 25 * 100, 18 * 25 equals 450, and 450 * 100 equals 45000. Step 7: Therefore, total fixed cost of the firm is Rs 45000.

Verification / Alternative check:
To verify, we can compute total cost directly from average total cost and quantity and then subtract total variable cost. Total cost equals ATC multiplied by Q, which is 54 * 2500 or 135000. Total variable cost equals AVC multiplied by Q, which is 36 * 2500 or 90000. Subtracting total variable cost from total cost gives TFC equals 135000 minus 90000, which equals 45000. This matches our previous calculation using average fixed cost and confirms that the answer is correct.

Why Other Options Are Wrong:
Rs 30000 would correspond to an average fixed cost of 12, which would make average total cost equal to AVC plus 12, that is 48, not the given 54.

Rs 15000 implies an average fixed cost of 6, again inconsistent with the given average total cost value.

Rs 60000 would imply average fixed cost of 24, which would make average total cost equal to 36 plus 24, that is 60, not the given 54.

Common Pitfalls:
Students sometimes confuse total and average costs and attempt to subtract average variable cost directly from total cost or make arithmetic errors when working with the large quantity figure. Another common mistake is to forget that average fixed cost declines as output increases and therefore misjudge whether the computed average fixed cost looks reasonable. Writing out the formulas clearly and checking each calculation step prevents such errors.

Final Answer:
Given the data, the total fixed cost of the firm is Rs 45000.