Why does average variable cost decrease then increase?

Fixed costs are those that do not vary with output and typically include rents, insurance, depreciation, set-up costs, and normal profit. They are also called overheads.

Variable costs are costs that do vary with output, and they are also called direct costs. Examples of typical variable costs include fuel, raw materials, and some labour costs.

Consider the following hypothetical example of a boat building firm. The total fixed costs, TFC, include premises, machinery and equipment needed to construct boats, and are £100,000, irrespective of how many boats are produced. Total variable costs (TVC) will increase as output increases.

Plotting this gives us Total Cost, Total Variable Cost, and Total Fixed Cost.

Total fixed costs

Given that total fixed costs (TFC) are constant as output increases, the curve is a horizontal line on the cost graph.

Total variable costs

The total variable cost (TVC) curve slopes up at an accelerating rate, reflecting the law of diminishing marginal returns.

Total costs

The total cost (TC) curve is found by adding total fixed and total variable costs. Its position reflects the amount of fixed costs, and its gradient reflects variable costs.

Average fixed costs

Average fixed costs are found by dividing total fixed costs by output. As fixed cost is divided by an increasing output, average fixed costs will continue to fall.

The average fixed cost (AFC) curve will slope down continuously, from left to right.

Average variable costs

Average variable costs are found by dividing total fixed variable costs by output.

The average variable cost (AVC) curve will at first slope down from left to right, then reach a minimum point, and rise again.

AVC is ‘U’ shaped because of the principle of variable Proportions, which explains the three phases of the curve:

1. Increasing returns to the variable factors, which cause average costs to fall, followed by:
2. Constant returns, followed by:
3. Diminishing returns, which cause costs to rise.

Average total cost

Average total cost (ATC) is also called average cost or unit cost. Average total costs are a key cost in the theory of the firm because they indicate how efficiently scarce resources are being used. Average variable costs are found by dividing total fixed variable costs by output.

Average total cost (ATC) can be found by adding average fixed costs (AFC) and average variable costs (AVC). The ATC curve is also ‘U’ shaped because it takes its shape from the AVC curve, with the upturn reflecting the onset of diminishing returns to the variable factor.

Areas for total costs

Total Fixed costs and Total Variable costs are the respective areas under the Average Fixed and Average Variable cost curves.

Marginal costs

Marginal cost is the cost of producing one extra unit of output.  It can be found by calculating the change in total cost when output is increased by one unit.

It is important to note that marginal cost is derived solely from variable costs, and not fixed costs.

The marginal cost curve falls briefly at first, then rises. Marginal costs are derived from variable costs and are subject to the principle of variable proportions.

The significance of marginal cost

The marginal cost curve is significant in the theory of the firm for two reasons:

1. It is the leading cost curve, because changes in total and average costs are derived from changes in marginal cost.
2. The lowest price a firm is prepared to supply at is the price that just covers marginal cost.

ATC and MC

Average total cost and marginal cost are connected because they are derived from the same basic numerical cost data.  The general rules governing the relationship are:

1. Marginal cost will always cut average total cost from below.
2. When marginal cost is below average total cost, average total cost will be falling, and when marginal cost is above average total cost, average total cost will be rising.
3. A firm is most productively efficient at the lowest average total cost, which is also where average total cost (ATC) = marginal cost (MC).

Total costs and marginal costs

Marginal costs are derived exclusively from variable costs, and are unaffected by changes in fixed costs. The MC curve is the gradient of the TC curve, and the positive gradient of the total cost curve only exists because of a positive variable cost. This is shown below:

Sunk costs

Sunk costs are those that cannot be recovered if a firm goes out of business. Examples of sunk costs include spending on advertising and marketing, specialist machines that have no scrap value, and stocks which cannot be sold off.

Sunk costs are a considerable barrier to entry and exit.

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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 familiar—they come from the Clip Joint example we saw earlier—but 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.

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 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.

The marginal cost curve intersects the average total 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 total 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 total 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.

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.

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

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