# 5.5: Average Total Cost

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So far, we have been examining how costs, overall, change with output. We will see in latter sessions how total profit depends, in part, on total costs. Additionally, it is also useful to measure average profit per unit. Since total cost is needed to measure total profit, it follows that average total cost is needed to measure average profit per unit.

## Calculating Average Total Cost (ATC)

Total costs of production are calculated by adding fixed costs to variable costs.

$\mathrm{TC}=\mathrm{FC}+\mathrm{VC} \nonumber$

Dividing total costs, fixed costs, and variable costs by the quantity of output yields the average costs:

\begin{aligned} & \mathrm{ATC}=\mathrm{TC} / \mathrm{Q} \\ & \mathrm{AFC}=\mathrm{FC} / \mathrm{Q} \\ & \mathrm{AVC}=\mathrm{VC} / \mathrm{Q} \end{aligned} \nonumber

The $$\mathrm{ATC}$$ at any given rate of output will show how much, on average, it costs to produce every individual unit. Keep in mind that over a range of output some units may have cost more and some cost less than the $$\mathrm{ATC}$$.

Insight into average total cost can be had using the data in table 2. The first column production ranges from 0 to 10. The second column is the total cost of producing each quantity, ranging from $3 to$65. If 5 units are produced, then the total cost of production is $16.50. The production of 9 units, in comparison, incurs a total cost of$46.

Figure 2 Table 2

Deriving average total cost is as simple as dividing the second column of total cost values by the first column of output quantity values. The average total cost of producing 1 unit is relatively easy--divide $9 by 1 unit. The average total cost of two units might be a little less obvious, but not much. The average total cost is$6.00, which is $12 divided by 2 units. The average total cost of producing 3 units is$4.67, $14 divided by 3. Given all the average total costs, what interesting insight into average total cost can be had? First, the average total cost is relatively high for the first unit produced, then declines. However, it reaches a low, then rises with production of the last few units. Second, average total cost remains positive, it never reaches a zero value and never turns negative. The only way for negative average total cost is for negative total cost, which makes no theoretical or practical sense. Third, the average total cost values in this table are comprised of two parts--average variable cost and average fixed cost. In other words, the$6.50 average total cost of producing 10 units can be broken down into something like $6.20 of average variable cost and$0.30 of average fixed cost.

The curve in Figure 3 shows the relationship between the average total cost and the quantity of production.

The key feature of this average total cost is the shape. It is U-shaped, meaning it has a negative slope for small quantities of output, reaches a minimum value, then has a positive slope for larger quantities. This U-shape is indirectly attributable to the law of diminishing marginal returns.

While it would be easy to attribute the U-shape of the average total cost curve to increasing, then decreasing marginal returns (and the law of diminishing marginal returns), such is not completely true. While the law of diminishing marginal returns is indirectly responsible for the positively sloped portion of the average total cost curve, the negatively sloped portion is attributable to increasing marginal returns, and perhaps more importantly to declining average fixed cost.

Figure 3 shows that the curve is at a low point above the output rate of six. The low point signifies the rate of output with the lowest average cost. Keep in mind that just because average costs are minimized, this does not mean profits are maximized. But being able to measure the impact production has on total average cost is of great importance to a profit maximizing firm.

This page titled 5.5: Average Total Cost is shared under a not declared license and was authored, remixed, and/or curated by Martin Medeiros.