Average Cost

Average Cost Formula

The average cost is important for firms since it shows them how much each unit of output costs them.

\(\hbox{Average total cost}=\frac{\hbox{Total cost}}{\hbox{Quantity of output}}\)

We can calculate the average cost using the following equation, where TC stands for the total cost and Q means the total quantity.

The average cost formula is:

\(ATC=\frac{TC}{Q}\)

How can we calculate the average cost using the average cost formula?

As we see in this example, we should divide the total cost by the quantity of output to find the average cost. For instance, for a total cost of $3500, we can produce 1500 chocolate bars. Therefore, the average cost for the production of 1500 chocolate bars is $2.33. This demonstrates average cost decreasing as the fixed costs are spread between more output.

Components of the Average Cost Equation

The average total cost equation breaks into two components: average fixed cost, and average variable cost.

Average fixed cost formula

Average fixed cost (AFC) shows us the total fixed cost for each unit. To calculate the average fixed cost, we have to divide the total fixed cost by the total quantity:

\(\hbox{Average fixed cost}=\frac{\hbox{Fixed cost}}{\hbox{Quantity of output}}\)

\(AFC=\frac{FC}{Q}\)

Average variable cost formula

Average variable cost (AVC) equals the total variable cost per unit of produced quantity. Similarly, to calculate the average variable cost, we should divide the total variable cost by the total quantity:

\(\hbox{Average variable cost}=\frac{\hbox{Variable cost}}{\hbox{Quantity of output}}\)

\(AVC=\frac{VC}{Q}\)

Variable costs are production costs that differ depending on the total output of production.

The average cost is the sum of the fixed cost and average cost. Thus, if we add the average fixed cost and average variable cost, we should find the average total cost.

\(\hbox{Total average cost}=\hbox{Average variable cost (AVC)}+\hbox{Average fixed cost (AFC)}\)

The Average Fixed Cost and the Spreading Effect

The average fixed cost decreases with increasing produced quantity because the fixed cost is a fixed amount. This means it does not change with the produced amount of units.

Since the total fixed cost is fixed, the more you produce, the average fixed cost per unit will decrease further. This is the reason why we have a falling average fixed cost curve in Figure 1 above.

This effect is called the spreading effect since the fixed cost is spread over the produced quantity. Given a certain amount of fixed cost, the average fixed cost decreases as the output increases.

The Average Variable Cost and the Diminishing Returns Effect

On the other hand, we see a rising average variable cost. Each unit of output that the firm produced additionally adds more to the variable cost since a rising amount of variable input would be necessary to produce the additional unit. This effect is also known as diminishing returns to the variable input

This effect is called the diminishing returns effect. Since a greater amount of variable input would be necessary as the output increases, we have higher average variable costs for higher levels of produced outputs.

The U-shaped Average Total Cost Curve

How do the spreading effect and diminishing returns effect cause the U-shape of the Average Cost Function? The relationship between these two affects the shape of the Average Cost Function.

For lower levels of output, the spreading effect dominates the diminishing returns effect, and for higher levels of output, the contrary holds. At low levels of output, small increases in output cause large changes in average fixed cost.

At high levels of output, the average fixed cost is already spread over the produced quantity and has a very small influence on the average total cost. Therefore, we don't observe a strong spreading effect anymore. On the other hand, diminishing returns generally increase as quantity rises. Therefore, the diminishing returns effect dominates the spreading effect for a large number of quantities.

Average Cost Examples

It is very important to understand how to calculate the Average Cost using the total fixed cost and average variable cost. Let's practice calculating the Average Cost and have a closer look at the example of the Willy Wonka chocolate firm. After all, we all like chocolate, right?

In the below table, we have columns for the produced quantity, the total cost as well as the average variable cost, average fixed cost, and average total cost.

As the Willy Wonka chocolate firm produces more chocolate bars, the total costs are increasing as expected. Similarly, we can see that the variable cost of 1 unit is $6, and the average variable cost increases with each additional unit of chocolate bar. The fixed cost equals $54 for the 1 unit of chocolate, the average fixed cost is $54. As we learn, the average fixed costs decrease as the total quantity increase.

At a quantity level of 8, we see that fixed costs have spread out across the total output($13.5). While the average variable cost is increasing($12), it increases less than the average fixed cost decreases. This results in a lower average total cost($18.75). This is the most efficient quantity to produce, as the average total cost is minimized.

Similarly, at a quantity level of 10, we can observe that despite the average fixed cost ($5.4) being minimized, the variable cost ($14) has increased as a result of diminishing returns. This results in a higher average total cost($19.4), which shows that the efficient production quantity is lower than 10.

The surprising aspect is the average total cost, which is first decreasing and then increasing as the quantity rises. It is important to distinguish between the total cost and the average total cost since the former always increases with additional quantity. However, the average total cost function has a U-shape and first falls and then rises as the quantity increases.

Average Cost Function

The average total cost function has a U-shape, which means it is decreasing for low levels of output and increases for larger output quantities.

In Figure 1, we will analyze the Average Cost Function of the Bakery ABC. Figure 1 illustrates how the average cost changes with different levels of quantity. The quantity is shown on the x-axis, whereas the cost in dollars is given on the y-axis.

On the first look, we can see that the Average Total Cost Function has a U-shape and decreases up to a quantity (Q) and increases after this quantity (Q). The average fixed cost decreases with the increasing quantity and the average variable cost has an increasing path in general.

The U-shape structure of the Average Cost Function is formed by two effects: the spreading effect and the diminishing returns effect. The average fixed cost and average variable cost are responsible for these effects.

Average Cost and Cost Minizimation

At the point Q where the diminishing returns effect and the spreading effect balance each other, the average total cost is at its minimum level.

The relationship between the average total cost curve and marginal cost curve is illustrated in Figure 2 below.

The corresponding quantity where the average total cost is minimized is called the minimum-cost output, which equals Q in Figure 2. Further, we see that the bottom of the U-shaped average total cost curve is also the point where the marginal cost curve intersects the average total cost curve. This is in fact not a coincidence but a general rule in the economy: the average total cost equals marginal cost at the minimum-cost output.