## Average Costs and Curves

### Learning Objectives

• Describe and calculate average total costs and average variable costs
• Calculate and graph marginal cost
• Analyze the relationship between marginal and average costs

The cost of producing a firm’s output depends on how much labor and capital the firm uses. A list of the costs involved in producing cars will look very different from the costs involved in producing computer software or haircuts or fast-food meals. However, the cost structure of all firms can be broken down into some common underlying patterns. When a firm looks at its total costs of production in the short run, a useful starting point is to divide total costs into two categories: fixed costs that cannot be changed in the short run and variable costs that can be changed.

The breakdown of total costs into fixed and variable costs can provide a basis for other insights as well. The first five columns of Table 1 should look familiarthey come from the Clip Joint example we saw earlierbut there are also three new columns showing average total costs, average variable costs, and marginal costs. These new measures analyze costs on a per-unit (rather than a total) basis.

Table 1. Different Types of Costs
Labor Quantity Fixed Cost Variable Cost Total Cost Marginal Cost Average Total Cost Average Variable Cost
1 16 $160$80 $240$5.00 $15.00$5.00
2 40 $160$160 $320$3.30 $8.00$4.00
3 60 $160$240 $400$4.00 $6.60$4.00
4 72 $160$320 $480$6.60 $6.60$4.40
5 80 $160$400 $560$10.00 $7.00$5.00
6 84 $160$480 $640$20.00 $7.60$5.70

### Watch It

Watch this clip as a continuation from the video on the previous page to see how average variable cost, average fixed costs, and average total costs are calculated.

Average total cost is total cost divided by the quantity of output. Since the total cost of producing 40 haircuts at “The Clip Joint” is $320, the average total cost for producing each of 40 haircuts is$320/40, or $8 per haircut. Average cost curves are typically U-shaped, as Figure 1 shows. Average total cost starts off relatively high, because at low levels of output total costs are dominated by the fixed cost; mathematically, the denominator is so small that average total cost is large. Average total cost then declines, as the fixed costs are spread over an increasing quantity of output. In the average cost calculation, the rise in the numerator of total costs is relatively small compared to the rise in the denominator of quantity produced. But as output expands still further, the average cost begins to rise. At the right side of the average cost curve, total costs begin rising more rapidly as diminishing returns kick in. Figure 1. Cost Curves at the Clip Joint. The information on total costs, fixed cost, and variable cost can also be presented on a per-unit basis. Average total cost (ATC) is calculated by dividing total cost by the total quantity produced. The average total cost curve is typically U-shaped. Average variable cost (AVC) is calculated by dividing variable cost by the quantity produced. The average variable cost curve lies below the average total cost curve and is typically U-shaped or upward-sloping. Marginal cost (MC) is calculated by taking the change in total cost between two levels of output and dividing by the change in output. The marginal cost curve is upward-sloping. Average variable cost obtained when variable cost is divided by quantity of output. For example, the variable cost of producing 80 haircuts is$400, so the average variable cost is $400/80, or$5 per haircut. Note that at any level of output, the average variable cost curve will always lie below the curve for average total cost, as shown in Figure 1. The reason is that average total cost includes average variable cost and average fixed cost. Thus, for Q = 80 haircuts, the average total cost is $8 per haircut, while the average variable cost is$5 per haircut. However, as output grows, fixed costs become relatively less important (since they do not rise with output), so average variable cost sneaks closer to average cost. Average total and variable costs measure the average costs of producing some quantity of output. Marginal cost is somewhat different.

Recall that marginal cost, which we introduced on the previous page, is the additional cost of producing one more unit of output.  So it is not the cost per unit of all units being produced, but only the next one (or next few). Marginal cost can be calculated by taking the change in total cost and dividing it by the change in quantity. For example, as quantity produced increases from 40 to 60 haircuts, total costs rise by 400 – 320, or 80. Thus, the marginal cost for each of those marginal 20 units will be 80/20, or $4 per haircut. The marginal cost curve may fall for the first few units of output but after that are generally upward-sloping, because diminishing marginal returns implies that additional units are more costly to produce. A small range of increasing marginal returns can be seen in the figure as a dip in the marginal cost curve before it starts rising. ### Watch It Watch this video to learn how to draw the various cost curves, including total, fixed and variable costs, marginal cost, average total, average variable, and average fixed costs. ### Where do marginal and average costs meet? The marginal cost curve intersects the average cost curve exactly at the bottom of the average cost curve—which occurs at a quantity of 72 and cost of$6.60 in Figure 1. The reason why the intersection occurs at this point is built into the economic meaning of marginal and average costs. If the marginal cost of production is below the average cost for producing previous units, as it is for the points to the left of where MC crosses ATC, then producing one more additional unit will reduce average costs overall—and the ATC curve will be downward-sloping in this zone. Conversely, if the marginal cost of production for producing an additional unit is above the average cost for producing the earlier units, as it is for points to the right of where MC crosses ATC, then producing a marginal unit will increase average costs overall—and the ATC curve must be upward-sloping in this zone. The point of transition, between where MC is pulling ATC down and where it is pulling it up, must occur at the minimum point of the ATC curve.

The same relationship is true for marginal cost and average variable cost. The reasoning is the same also. This does not hold for average fixed cost. Do you know why not? It’s because marginal cost affects variable cost, but it does not affect fixed cost.

This idea of the marginal cost “pulling down” the average cost or “pulling up” the average cost may sound abstract, but think about it in terms of your own grades. If the score on the most recent quiz you take is lower than your average score on previous quizzes, then the marginal quiz pulls down your average. If your score on the most recent quiz is higher than the average on previous quizzes, the marginal quiz pulls up your average. In this same way, low marginal costs of production first pull down average costs and then higher marginal costs pull them up.

The numerical calculations behind average cost, average variable cost, and marginal cost will change from firm to firm. However, the general patterns of these curves, and the relationships and economic intuition behind them, will not change.

### Why are total cost and average cost not on the same graph?

Total cost, fixed cost, and variable cost each reflect different aspects of the cost of production over the entire quantity of output being produced. These costs are measured in dollars. In contrast, marginal cost, average cost, and average variable cost are costs per unit. In the previous example, they are measured as cost per haircut. Thus, it would not make sense to put all of these numbers on the same graph, since they are measured in different units ($versus$ per unit of output).

It would be as if the vertical axis measured two different things. In addition, as a practical matter, if they were on the same graph, the lines for marginal cost, average cost, and average variable cost would appear almost flat against the horizontal axis, compared to the values for total cost, fixed cost, and variable cost. Using the figures from the previous example, the total cost of producing 40 haircuts is $320. But the average cost is$320/40, or \$8. If you graphed both total and average cost on the same axes, the average cost would hardly show.

### Try It

These questions allow you to get as much practice as you need, as you can click the link at the top of the first question (“Try another version of these questions”) to get a new set of questions. Practice until you feel comfortable doing the questions.

### Try It

These questions allow you to get as much practice as you need, as you can click the link at the top of the first question (“Try another version of these questions”) to get a new set of questions. Practice until you feel comfortable doing the questions.

### Glossary

average total cost:
for any quantity of output, total cost divided by the quantity of output
average variable cost:
for any quantity of output, variable cost divided by the quantity of output