## Production Choices and Costs: The Short Run

Read this section to learn about the behavior of the producer in the short run. Attempt the "Try It" problems at the end of the section before checking your answers. Take a moment to read through the stated learning outcomes for this chapter of the text, which you can find at the beginning of each section. These outcomes should be your goals as you read through the chapter.

### Costs in the Short Run

#### Marginal and Average Costs

Marginal and average cost curves, which will play an important role in the analysis of the firm, can be derived from the total cost curve. Marginal cost shows the additional cost of each additional unit of output a firm produces. This is a specific application of the general concept of marginal cost presented earlier. Given the marginal decision rule's focus on evaluating choices at the margin, the marginal cost curve takes on enormous importance in the analysis of a firm's choices. The second curve we shall derive shows the firm's average total cost at each level of output. Average total cost (ATC) is total cost divided by quantity; it is the firm's total cost per unit of output:

Equation 8.4

A T C = T C / Q

We shall also discuss average variable costs (AVC), which is the firm's variable cost per unit of output; it is total variable cost divided by quantity:

Equation 8.5

AVC=TVC/Q

We are still assessing the choices facing the firm in the short run, so we assume that at least one factor of production is fixed. Finally, we will discuss average fixed cost (AFC), which is total fixed cost divided by quantity:

Equation 8.6

AFC=TFC/Q

Marginal cost (MC) is the amount by which total cost rises with an additional unit of output. It is the ratio of the change in total cost to the change in the quantity of output:

Equation 8.7

MC=ΔTC/ΔQ

It equals the slope of the total cost curve. Figure 8.7 "Total Cost and Marginal Cost" shows the same total cost curve that was presented in Figure 8.6 "From Variable Cost to Total Cost". This time the slopes of the total cost curve are shown; these slopes equal the marginal cost of each additional unit of output. For example, increasing output from 6 to 7 units (  Δ Q = 1 ) increases total cost from $480 to$500 (  Δ T C = $20 ). The seventh unit thus has a marginal cost of$20 (  Δ T C / Δ Q = $20 / 1 =$ 20 ). Marginal cost falls over the range of increasing marginal returns and rises over the range of diminishing marginal returns.

Notice that the various cost curves are drawn with the quantity of output on the horizontal axis. The various product curves are drawn with quantity of a factor of production on the horizontal axis. The reason is that the two sets of curves measure different relationships. Product curves show the relationship between output and the quantity of a factor; they therefore have the factor quantity on the horizontal axis. Cost curves show how costs vary with output and thus have output on the horizontal axis.

Figure 8.7 Total Cost and Marginal Cost

Marginal cost in Panel (b) is the slope of the total cost curve in Panel (a).

Figure 8.8 "Marginal Cost, Average Fixed Cost, Average Variable Cost, and Average Total Cost in the Short Run" shows the computation of Acme's short-run average total cost, average variable cost, and average fixed cost and graphs of these values. Notice that the curves for short-run average total cost and average variable cost fall, then rise. We say that these cost curves are U-shaped. Average fixed cost keeps falling as output increases. This is because the fixed costs are spread out more and more as output expands; by definition, they do not vary as labor is added. Since average total cost (ATC) is the sum of average variable cost (AVC) and average fixed cost (AFC), i.e.,

Equation 8.8

AVC+AFC=ATC

the distance between the ATC and AVC curves keeps getting smaller and smaller as the firm spreads its overhead costs over more and more output.

Figure 8.8 Marginal Cost, Average Fixed Cost, Average Variable Cost, and Average Total Cost in the Short Run

Total cost figures for Acme Clothing are taken from Figure 8.7 "Total Cost and Marginal Cost". The other values are derived from these. Average total cost (ATC) equals total cost divided by quantity produced; it also equals the sum of the average fixed cost (AFC) and average variable cost (AVC) (exceptions in table are due to rounding to the nearest dollar); average variable cost is variable cost divided by quantity produced. The marginal cost (MC) curve (from Figure 8.7 "Total Cost and Marginal Cost") intersects the ATC and AVC curves at the lowest points on both curves. The AFC curve falls as quantity increases.

Figure 8.8 "Marginal Cost, Average Fixed Cost, Average Variable Cost, and Average Total Cost in the Short Run" includes the marginal cost data and the marginal cost curve from Figure 8.7 "Total Cost and Marginal Cost". The marginal cost curve intersects the average total cost and average variable cost curves at their lowest points. When marginal cost is below average total cost or average variable cost, the average total and average variable cost curves slope downward. When marginal cost is greater than short-run average total cost or average variable cost, these average cost curves slope upward. The logic behind the relationship between marginal cost and average total and variable costs is the same as it is for the relationship between marginal product and average product.

We turn next in this chapter to an examination of production and cost in the long run, a planning period in which the firm can consider changing the quantities of any or all factors.