Businesses produce and sell a variety of products in different market structures at different price levels. To maximize their profit in the market, they have to take the costs of the production into account as well. To understand how the firms calculate the cost functions and derive their production plan, we should have a close look at two main cost types: marginal cost and average cost. In this article, we will learn all about the average cost, its equation, and what the average cost function looks like with various examples. Ready to deep dive, let’s go!
Average Cost Definition
Average Cost, also called average total cost (ATC), is the cost per output unit. We can calculate the average cost by dividing the total cost (TC) by the total output quantity (Q).
Average Cost equals the per-unit cost of production, which is calculated by dividing the total cost by the total output.
Total cost means the sum of all costs, including fixed and variable costs. Therefore, average Cost is also often called the total cost per unit or the average total cost.
For example, if a company produces 1,000 widgets at a total cost of $10,000, the average cost per widget would be $10 ($10,000 ÷ 1,000 widgets). This means that on average, it costs the company $10 to produce each widget.
Average Cost Formula
The average cost is important for firms since it shows them how much each unit of output costs them.
Remember, marginal cost shows how much an additional unit of output costs the firm to produce.
\(\hbox{Average total cost}=\frac{\hbox{Total cost}}{\hbox{Quantity of output}}\)
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?
Let's say the Willy Wonka chocolate firm produces chocolate bars. Their total costs and different levels of quantity are given in the following table. Using the average cost formula, we divide the total cost by the corresponding quantity for each level of quantity in the third column:
| Table 1. Calculating Average Cost |
|---|
Total Cost ($) | Quantity of Output | Average Cost ($) |
3000 | 1000 | 3 |
3500 | 1500 | 2.33 |
4000 | 2000 | 2 |
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:
\(\hbox{Average fixed cost}=\frac{\hbox{Fixed cost}}{\hbox{Quantity of output}}\)
\(AFC=\frac{FC}{Q}\)
Fixed costs are not connected to the quantity of produced output. Fixed costs the firms have to pay, even at a production level of 0. Let's say a firm has to spend $2000 a month for rent and it does not matter whether the firm is active that month or not. Thus, $2000, in this case, is a fixed cost.
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.
A firm decides to produce 200 units. If raw materials cost $300 and labor to refine them costs $500.
$300+$500=$800 variable cost.
$800/200(units) =$4 Average Variable Cost.
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.
You can think of the fixed cost as the amount of money you need to open a bakery. This includes, for instance, necessary machines, stands, and tables. In other words, fixed costs equal the required investment you need to make to start producing.
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.
Assume a firm has a fixed cost of 200 in the beginning. For the first 2 units of production, we would have a $100 average fixed cost. After the firm produces 4 units, the fixed cost decreases by half: $50. Therefore, the spreading effect has a strong influence on the lower levels of quantity.
At high levels of output, the average fixed cost is already spread over the produced quantity and has a very small influence on the average total cost. Therefore, we don't observe a strong spreading effect anymore. On the other hand, diminishing returns generally increase as quantity rises. Therefore, the diminishing returns effect dominates the spreading effect for a large number of quantities.
Average Cost Examples
It is very important to understand how to calculate the Average Cost using the total fixed cost and average variable cost. Let's practice calculating the Average Cost and have a closer look at the example of the Willy Wonka chocolate firm. After all, we all like chocolate, right?
In the below table, we have columns for the produced quantity, the total cost as well as the average variable cost, average fixed cost, and average total cost.
| Table 2. Average Cost Example |
|---|
Quantity (chocolate bar) | Average fixed cost ($) | Average variable cost ($) | Total costs ($) | Average total cost ($) |
1 | 54 | 6 | 60 | 60 |
2 | 27 | 8 | 70 | 35 |
4 | 13.5 | 10 | 94 | 23.5 |
8 | 6.75 | 12 | 150 | 18.75 |
10 | 5.4 | 14 | 194 | 19.4 |
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.
Fig 1. - Average Cost Function
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.
Fig 2. - Average Cost and Cost Minimization
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.
Average Cost - Key takeaways
- Average Cost equals the per-unit cost of production which is calculated by dividing the total cost by the total output.
- Average fixed cost (AFC) shows us the total fixed cost for each unit and Average variable cost (AVC) equals the total variable cost per unit of produced quantity.
- The average cost is the sum of the fixed cost and average variable cost. Thus, if we add the average fixed cost and average variable cost, we should find the average total cost.
- 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.
- The U-shape structure of the Average Cost Function is formed by two effects: the spreading effect and the diminishing returns effect.
- For lower levels of output, the spreading effect dominates the diminishing returns effect, and for higher levels of output, the contrary holds.
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