# Average Fixed Cost

In economics, average fixed cost (AFC) is the fixed cost per unit of output. Fixed costs are such costs which do not vary with change in output. AFC is calculated by dividing total fixed cost by the output level.

Whether a cost is fixed or variable depends on whether we are considering a cost in short-run or long-run. Average fixed cost is relevant only in the short-run. Short-run is defined as a time period in which at least one of the inputs, typically capital, is fixed. Since all inputs are variable in the long-run, no costs are fixed in the long-run.

Typical examples of fixed costs include salaries of permanent employees, rent paid on non-cancellable lease, mortgage payments on plant and machinery, etc.

## Formula

Average fixed cost (AFC) equals total fixed cost (FC) divided by output (Q):

$$ AFC\ =\ \frac{FC}{Q} $$

Total cost (TC) of a firm are either fixed (FC) or variable (VC). This can be written mathematically as follows:

$$ TC\ =\ FC\ +\ VC $$

If we divide both sides of the equation by output Q, we get:

$$ \frac{TC}{Q}\ =\ \frac{FC}{Q}\ +\ \frac{VC}{Q} $$

It shows that average fixed cost can also be defined as the difference between average total cost and average variable cost:

$$ AFC\ =\ ATC\ -\ AVC $$

## Example and Graph

Sucrose Farms is engaged in cultivation of sugar cane. They have hired 3 workers on a one-year contract which is non-cancelable. They pay a salary of $25,000 per annum to each worker. They have also obtained some farming equipment for which they pay a $60,000 rent per annum. The depreciation they charge on the farm building and the farm fencing is $20,000 per annum. They have to apply insecticides and pesticides which costs $1,000 per square kilometer. The business' total output is 1200 tons of sugar cane. Find the firm’s average fixed cost.

Sucrose Farms total fixed cost in the short-run is $155,000 (i.e. ($25,000 × 3) for labor, $60,000 on account of farming equipment rent and $20,000 on account of depreciation).

Since its total production is 1,200 tons, average fixed cost of $129.2 per ton ($155,000/1,200).

Please note that the cost of pesticides is not a fixed cost because it varies with change in production level.

If we plot the total fixed cost and average fixed cost for Sucrose Farms, we will get the following graph:

As output increases, total fixed cost remains the same but the average fixed cost falls indefinitely. This is why we have a flat total fixed cost curve and constantly declining average fixed cost curve.

Since all inputs can change in the long-run, there is no long-run average fixed cost curve.

Written by Obaidullah Jan, ACA, CFA and last modified on