Short-Run Costs

business. By contrast, online sellers such as Amazon care only about maximizing overall e-book revenue. It should not be surprising that book publishers and online sellers experience the same kinds of conflicts as franchisers and franchisees (discussed earlier in Chapter 2). As the spreadsheet problem at the close of the chapter shows, book publishers must carefully balance the two competing revenue sources in setting print book and e-book prices.

THE COST OF PRODUCTION

As we noted in Chapter 5, production and cost are very closely related. In a sense, cost information is a distillation of production information: It combines the information in the production function with information about input prices. The end result can be summarized in the following important concept: The cost function indicates the firm’s total cost of producing any given level of output. The concept of a cost function was first introduced in Chapter 2. In this section, we take a much closer look at the factors that determine costs. A key point to remember is that the concept of the cost function presupposes that the firm’s managers have determined the least-cost method of producing any given level of output. (Clearly, inefficient or incompetent managers could contrive to produce a given level of output at some—possibly inflated—cost, but this would hardly be profit maximizing. Nor would the resulting cost schedule foster optimal managerial decision making.) In short, the cost function should always be thought of as a least-cost function. It usually is denoted as C C(Q) and can be described by means of a table, a graph, or an equation.

As in our study of production, our analysis of cost distinguishes between the short run and the long run. Recall that the short run is a period of time so limited that the firm is unable to vary the use of some of its inputs. In the long run, all inputs—labor, equipment, factories—can be varied freely. Our investigation of cost begins with the short run.

Short-Run Costs

In the basic model of Chapter 5, we focused on two inputs, capital and labor. In the short run, capital is a fixed input (i.e., cannot be varied) and labor is the sole variable input. Production of additional output is achieved by using additional hours of labor in combination with a fixed stock of capital equipment in the firm’s current plant. Of course, the firm’s cost is found by totaling its expenditures on labor, capital, materials, and any other inputs and including any relevant opportunity costs, as discussed in the previous section. For concreteness, consider a firm that provides a service—say, electronic repair. Figure 6.1 provides a summary of the repair firm’s costs as they vary for different quantities of output (number of repair jobs completed).

FIGURE 6.1

A Firm’s Total Costs

Total cost is the sum of fixed cost and variable cost. Total Cost (Thousands of Dollars) 3,000

2,000

1,000 Cost function

0 5 10 15 20 25 30 35

40 45 50 55 60 Output (Thousands of Units)

Annual Output Total Cost Fixed Cost Variable Cost (Repairs Thousands) ($ Thousands) ($ Thousands) ($ Thousands)

0 270.0 270 0.0 5 427.5 270 157.5 10 600.0 270 330.0 15 787.5 270 517.5 20 990.0 270 720.0 25 1,207.5 270 937.5 30 1,440.0 270 1,170.0 35 1,687.5 270 1,417.5 40 1,950.0 270 1,680.0 45 2,227.5 270 1,957.5 50 2,520.0 270 2,250.0 55 2,827.5 270 2,557.5 60 3,150.0 270 2,880.0

The total cost of achieving any given level of output can be divided into two parts: fixed and variable costs. As the term suggests, fixed costs result from the firm’s expenditures on fixed inputs. These costs are incurred regardless of the firm’s level of output. Most overhead expenses fall into this category. Such costs might include the firm’s lease payments for its factory, the cost of equipment, some portion of energy costs, and various kinds of administrative costs (payment for support staff, taxes, and so on). According to the table in Figure 6.1, the repair firm’s total fixed costs come to $270,000 per year. These costs are incurred regardless of the actual level of output (i.e., even if no output were produced).

Variable costs represent the firm’s expenditures on variable inputs. With respect to the short-run operations of the repair firm, labor is the sole variable input. Thus, in this example, variable costs represent the additional wages paid by the firm for extra hours of labor. To achieve additional output (i.e., to increase the volume of repair jobs completed), the firm must incur additional variable costs. Naturally, we observe that total variable costs rise with increases in the quantity of output. In fact, a careful look at Figure 6.1 shows that variable costs rise increasingly rapidly as the quantity of output is pushed higher and higher. Note that the firm’s total cost exhibits exactly the same behavior. (With fixed costs “locked in” at $270,000, total cost increases are due solely to changes in variable cost.) The graph in Figure 6.1 shows that the total cost curve becomes increasingly steep at higher output levels.

Average total cost (or simply average cost) is total cost divided by the total quantity of output. Figure 6.2 shows average costs for the repair company over different levels of output. (Check that the average cost values are computed as the ratio of total cost in column 2 of the table and total output in column 1.) The graph displays the behavior of average cost. Both the table and graph show that short-run average cost is U-shaped. Increases in output first cause average cost (per unit) to decline. At 30,000 units of output, average cost achieves a minimum (at the bottom of the U). As output continues to increase, average unit costs steadily rise. (We will discuss the factors underlying this average cost behavior shortly.) Finally, average variable cost is variable cost divided by total output. Because it excludes fixed costs, average variable cost is always smaller than average total cost.

Marginal cost is the addition to total cost that results from increasing output by one unit. We already are acquainted with the concept of marginal cost from the analyses of the firm’s output and pricing decisions in Chapters 2 and 3. Now we take a closer look at the determinants of marginal cost. The last column of the table in Figure 6.2 lists the repair company’s marginal costs for output increments of 5,000 units. For instance, consider an output increase from 25,000 to 30,000 units. According to Figure 6.2, the result is a total cost increase of 1,440,000 1,207,500 $232,500. Consequently, the marginal cost (on a perunit basis) is 232,500/5,000 $46.50/unit. The other entries in the last column are computed in an analogous fashion. From either the graph or the

FIGURE 6.2

A Firm’s Average and Marginal Costs Cost/Unit (Thousands of Dollars) 64

60

56

52

48

44 SMC

SAC

0 5 10 15 20 25 3530 40 45 50 55 60 Output (Thousands of Units)

Annual Output Total Cost Average Cost Marginal Cost (Repairs Thousands) (Thousands of Dollars) (Dollars/Unit) (Dollars/Unit)

0 270.0 5 427.5 85.5 31.5

10 600.0 60 34.5

15 20 25 30 35 40 45 50 55 60 787.5 990.0

52.5 49.5 1,207.5 48.3 1,440.0 48 1,687.5 48.2 1,950.0 48.8 2,227.5 49.5 2,520.0 50.4 2,827.5 51.4 3,150.0 52.5 37.5 40.5 43.5 46.5 49.5 52.5 55.5 58.5 61.5 64.5

table, we observe that the firm’s marginal cost rises steadily with increases in output. Expanding output starting from a level of 40,000 units per month is much more expensive than starting from 20,000 units.

What factors underlie the firm’s increasing short-run marginal cost (SMC)? The explanation is simple. With labor the only variable input, SMC can be expressed as

[6.1]

where PL denotes the price of hiring additional labor (i.e., wage per hour) and MPL denotes the marginal product of labor.5 To illustrate, suppose the prevailing wage is $20 per hour and labor’s marginal product is .5 unit per hour (one-half of a typical repair job is completed in one hour). Then the firm’s marginal (labor) cost is 20/.5 $40 per additional completed job. According to Equation 6.1, the firm’s marginal cost will increase if there is an increase in the price of labor or a decrease in labor’s marginal product. Moreover, as the firm uses additional labor to produce additional output, the law of diminishing returns applies. With other inputs fixed, adding increased amounts of a variable input (in this case, labor) generates smaller amounts of additional output; that is, after a point, labor’s marginal product declines. As a result, marginal cost rises with the level of output. (Clearly, material costs are also variable and, therefore, are included in SMC. However, because these costs typically vary in proportion to output, they do not affect the shape of SMC.)

Now we can explain the behavior of short-run average cost (SAC). When output is very low (say 5,000 units), total cost consists mainly of fixed cost (since variable costs are low). SAC is high because total cost is divided by a small number of units. As output increases, total costs (which are mostly fixed) are “spread over” a larger number of units, so SAC declines. In the graph in Figure 6.2, notice that SAC lies well above SMC for low levels of output. As long as extra units can be added at a marginal cost that is lower than the average cost of the current output level, increasing output must reduce overall average cost. But what happens to average cost as marginal cost continues to rise? Eventually there comes a point at which SMC becomes greater than SAC. As soon as extra units become more expensive than current units (on average), the overall average begins to increase. This explains the upward arc of the U-shaped SAC curve. This argument also confirms an interesting result: The firm’s marginal cost curve intersects its average cost curve at the minimum point of SAC. SMC PL/MPL,

5The mathematical justification is as follows. Marginal cost can be expressed as MC C/ Q ( C/ L)/( Q/ L) PL/MPL. As the notation indicates, here we are looking at discrete changes in output and input. The same relationship holds with respect to infinitesimal changes, (dC/dQ).