Understanding the total cost curve (and its fixed and variable cost components) is an important part of analyzing firms’ production behavior. To see why, we introduce two other cost concepts that play a key role in production decisions: average cost and marginal cost. In our Chapter 6 analysis of a firm’s production decisions, we took the firm’s desired output level as given. In the next few chapters, we will see that average and marginal costs are important in determining a firm’s desired output level.

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Average cost is fairly straightforward. It’s just cost divided by quantity. Because there are three costs (total, fixed, and variable), there are three kinds of average cost. Each of these measures examines the per-unit cost at that level of output. We compute these measures in Table 7.2 and illustrate them in Figure 7.2. Average fixed cost (AFC) is measured as fixed cost per unit of output, or

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AFC = FC/Q

Column (6) of Table 7.2 shows average fixed cost AFC for Fleet Foot (FF). AFC falls as output rises. The numerator (fixed cost) is constant while the denominator (quantity) rises, so average fixed cost becomes smaller and smaller as quantity goes up. (The fixed cost is spread over more and more units of output.) Thus, as FF manufactures more running shoes, the average fixed cost it pays per pair of shoes declines.

Average variable cost measures the per-unit variable cost of production. It is calculated by dividing variable cost by the quantity of output:

AVC = VC/Q

Unlike average fixed cost, average variable cost can go up or down as quantity changes. In this case, it declines until five units are produced, after which it rises, leading to a U-shaped average variable cost curve.

Average total cost is total cost TC per unit of output Q:

ATC = TC/Q

Average total cost for Fleet Foot is shown in the last column of Table 7.2. For FF, average total cost at first falls and then rises as output rises. Firms’ average total costs often exhibit this sort of U-shaped pattern. To see why, first note that average total cost (ATC) is the sum of average fixed cost (AFC) and average variable cost (AVC):

ATC = TC/Q = (FC + VC)/Q

= FC/Q + VC/Q

= AFC + AVC

Average total cost first falls as output rises because the dominant influence on average total cost is the rapidly declining average fixed cost. But as output continues to rise, average variable cost keeps increasing, first slowing the rate at which average total cost is falling and eventually causing average total cost to increase with output. These changes create a U-shaped average total cost curve.

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The other key cost concept is marginal cost, a measure of how much it costs a firm to produce one more unit of output:

MC = ΔTC/ΔQ

where ΔTC is the change in total cost and ΔQ is a 1-unit change in output.

Fleet Foot’s marginal cost is shown in the fifth column of Table 7.2. It is the difference in total cost when output increases by 1 pair of shoes. But notice something else: Marginal cost also equals the difference in variable cost when one additional unit is produced. That’s because, by definition, fixed cost does not change when output changes. Therefore, fixed cost does not affect marginal cost; only variable cost changes when the firm produces one more unit. This means marginal cost can also be defined as the change in variable cost from producing another unit of output:

MC = ΔVC/ΔQ (= ΔTC/ΔQ)

For this reason, marginal cost is not split into fixed and variable cost components, as is average cost. Marginal cost is only marginal variable cost.

Fleet Foot’s marginal cost initially declines as output increases. After a certain output level (4 units in Table 7.2), marginal cost begins to rise, and at even higher output levels, it rises steeply. Why? Marginal cost may initially fall at low quantities because complications may arise in producing the first few units that can be remedied fairly quickly, or because having more scale allows workers to specialize in those tasks that they are best at. As output continues to increase, however, these marginal cost reductions stop and marginal cost begins to increase with the quantity produced, as seen in Figure 7.3. There are many reasons why it becomes more and more expensive to make another unit as output rises: Capacity constraints may occur, inputs may become more expensive as the firm uses more of them, it may be harder for the company to coordinate its operations, and so on.

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Understanding the concept of marginal cost is critical: It is one of the most central concepts in all of economics, and it is the only cost that matters for many of the key decisions a firm makes.

Because average cost and marginal cost are both derived from total cost, they are directly related. If the marginal cost of output is less than the average cost at a particular quantity, producing an additional unit will reduce the average cost because the extra unit’s cost is less than the average cost of making all the units before it. (This relationship is the same as that between the average and marginal products of labor we learned about in Chapter 6.) Suppose, for example, that a firm had produced 9 units of output at an average cost of $100 per unit. If the marginal cost of the next unit is $90, the average cost will fall to ($900 + $90)/10 = $99, because the marginal cost of that extra unit is less than the average cost of the previous units.

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This means that if the marginal cost curve is below an average cost curve at some quantity, average cost must be falling—that is, the average cost curve is downward-sloping. This is true whether we’re talking about average total cost or average variable cost, because the marginal cost of producing another unit of output creates the same increment to both total and variable cost. This is also true even if, as is often the case, marginal costs are rising while they are below average costs. Producing another unit of output at a cost below the firm’s current average will still bring down the average even if that marginal cost is rising with output. Just remember that the marginal cost curve is the cost at a specific output level—how much it costs to produce that specific unit—while average costs are averaging over all the previous units’ costs, too.

You can see this relationship in Figure 7.4, which shows an average total cost curve, an average variable cost curve, and a marginal cost curve all derived from a single total cost curve. At lower quantities, when the marginal cost curve is below the average cost curves, the average cost curves are downward-sloping.

When the marginal cost of the additional unit is above average cost, then producing it increases the average cost. Therefore, if the marginal cost curve is above an average cost curve at a quantity level, average cost is rising, and the average cost curve slopes up at that quantity. Again, this is true for both average total cost and average variable cost. This property explains why average variable cost curves and average total cost curves often have a U-shape. If marginal cost continues to increase as quantity increases, it eventually rises above average cost and begins pulling up the average variable and average total cost curves.

The only point at which there is no change in average cost from producing one more unit occurs at the minimum point of the average variable and average total cost curves, where marginal and average cost are equal. These minimum points are indicated on Figure 7.4. (In the next chapter, we see that the point at which average and marginal costs are equal and average total cost is minimized has a special significance in competitive markets.)

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