If the average total cost of a firm is Rs 54, the total fixed cost is Rs 45000, and the firm produces 2500 units of output, what is the average variable cost per unit?

Introduction / Context:
Cost concepts such as total fixed cost, total variable cost, average total cost and average variable cost are basic tools in microeconomic analysis of firms. Exam questions often provide some of these values and ask you to calculate the missing ones using algebraic relationships. This question gives average total cost, total fixed cost and quantity produced, and asks for the average variable cost, which helps reinforce the understanding of the cost structure of a firm.

Given Data / Assumptions:
• Average total cost (ATC) is Rs 54 per unit. • Total fixed cost (TFC) is Rs 45000. • Quantity of output (Q) is 2500 units. • We must find average variable cost (AVC) per unit.

Concept / Approach:
The key relationships between the cost concepts are as follows. Total cost (TC) equals total fixed cost plus total variable cost. Average total cost equals total cost divided by quantity. Average variable cost equals total variable cost divided by quantity. Another useful identity is that average total cost equals average fixed cost plus average variable cost. Average fixed cost equals total fixed cost divided by quantity. Using these relationships, we can first find total cost from average total cost and quantity, then deduce total variable cost by subtracting total fixed cost, and finally divide by quantity to find average variable cost.

Step-by-Step Solution:
Step 1: Use the definition of average total cost. ATC equals TC divided by Q, so TC equals ATC multiplied by Q. Step 2: Substitute the given values. ATC is 54 and Q is 2500, so TC equals 54 * 2500. Step 3: Compute 54 * 2500. Multiply 54 by 1000 to get 54000, then by 1500 to get 81000, but more simply 54 * 2500 equals 135000. So total cost is Rs 135000. Step 4: Total cost is the sum of total fixed cost and total variable cost. Therefore, TVC equals TC minus TFC. Step 5: Substitute the numbers. TVC equals 135000 minus 45000, which equals 90000. Step 6: Average variable cost equals total variable cost divided by quantity, so AVC equals 90000 divided by 2500. Step 7: Compute 90000 divided by 2500. Dividing numerator and denominator by 100, we get 900 divided by 25, which equals 36. So AVC is Rs 36 per unit.

Verification / Alternative check:
As an alternative check, we can use the identity ATC equals AFC plus AVC. First calculate average fixed cost. AFC equals TFC divided by Q, so equals 45000 divided by 2500. This equals 18. Since ATC is 54, AVC equals ATC minus AFC, that is 54 minus 18, which again gives 36. This cross check confirms that the calculated average variable cost is correct.

Why Other Options Are Wrong:
Rs 24 would imply that average fixed cost equals 30, because 54 minus 24 is 30, which would give total fixed cost of 30 multiplied by 2500, or 75000, not the given 45000.
Rs 18 is actually the average fixed cost, not average variable cost, so marking it as AVC would mix up the roles of fixed and variable components.

Rs 60 would be greater than the average total cost of 54, which is impossible because average total cost includes both fixed and variable components, and the variable part cannot by itself exceed the sum.

Common Pitfalls:
A common mistake is to confuse total and average magnitudes or to forget that average total cost is the sum of average fixed cost and average variable cost. Some learners directly subtract total fixed cost from average total cost without multiplying by quantity, which leads to incorrect results. Another pitfall is careless arithmetic, especially when multiplying or dividing by large numbers like 2500. Writing down each step clearly helps avoid such errors.

Final Answer:
The average variable cost of the firm, given the data, is Rs 36 per unit.