The gap between average total cost and the average variable cost is always the average fixed cost.

Question

Quizplus · Accepted Answer

This is a basic relationship in cost theory known as the "cost decomposition identity." It follows from the fact that total cost = fixed cost + variable cost, and the average of a sum is equal to the sum of the averages. Therefore, average variable cost = (variable cost / quantity produced) and average total cost = (total cost / quantity produced), so:

average variable cost + average fixed cost = (variable cost / quantity produced) + (fixed cost / quantity produced)
average total cost = (total cost / quantity produced) = (variable cost + fixed cost) / quantity produced

Substituting the first equation into the second, we get:

average total cost = average variable cost + average fixed cost

Therefore, the difference between average total cost and average variable cost must be equal to the average fixed cost.

The Gap Between Average Total Cost and the Average Variable