As they plan for the future, business owners and managers make every effort to avoid undertaking operations or making strategic plans that will result in losses or negative profits. When managers foresee market conditions that will not gen- erate enough total revenue to cover long-run total costs, they will plan to cease production in the long run and exit the industry by moving the firm’s resources to their best alternative use. Similarly, decisions to add new product lines or enter new geographic markets will not be undertaken unless managers are reasonably sure that long-run costs can be paid from revenues generated by entering those new markets. Because the long-run viability of a firm—as well as the number of product lines and geographic markets a firm chooses—depends crucially on the likelihood of covering long-run costs, managers need to understand the various economic forces that can affect long-run costs. We will now examine several im- portant forces that affect the long-run cost structure of firms. While some of these factors cannot be directly controlled by managers, the ability to predict costs in the long run requires an understanding of all forces, internal and external, that affect a firm’s long-run costs. Managers who can best forecast future costs are likely to make the most profitable decisions.
Economies and Diseconomies of Scale
The shape of a firm’s long-run average cost curve (LAC) determines the range and strength of economies and diseconomies of scale. Economies of scale occur when
economies of scale Occurs when long-run average cost (LAC) falls as output increases.
F I G U R E 9.9 Long-Run Average and Marginal Cost Curves
LMC
LAC
Output Q2
Average and marginal cost (dollars)
Q1
long-run average cost falls as output increases. In Figure 9.10, economies of scale exist over the range of output from zero up to Q2 units of output. Diseconomies of scale occur when long-run average cost rises as output increases. As you can see in the figure, diseconomies of scale set in beyond Q2 units of output.
The strength of scale economies or diseconomies can been seen, respectively, as the reduction in unit cost over the range of scale economies or the increase in LAC above its minimum value LACmin beyond Q2. Recall that average cost falls when marginal cost is less than average cost. As you can see in the figure, over the out- put range from 0 to Q2, LAC is falling because LMC is less than LAC. Beyond Q2, LMC is greater than LAC, and LAC is rising.
Reasons for scale economies and diseconomies Before we begin discussing reasons for economies and diseconomies of scale, we need to remind you of two things that cannot be reasons for rising or falling unit costs as quantity increases along the LAC curve: changes in technology and changes in input prices. Recall that both technology and input prices are held constant when deriving expansion paths and long-run cost curves. Consequently, as a firm moves along its LAC curve to larger scales of operation, any economies and diseconomies of scale the firm experiences must be caused by factors other than changing technology or changing input prices. When technology or input prices do change, as we will show you later in this section, the entire LAC curve shifts upward or downward, perhaps even changing shape in ways that will alter the range and strength of existing scale economies and diseconomies.
Probably the most fundamental reason for economies of scale is that larger-scale firms have greater opportunities for specialization and division of labor. As an
diseconomies of scale Occurs when long-run average cost (LAC ) rises as output increases.
specialization and division of labor Dividing production into separate tasks allows workers to specialize and become more productive, which lowers unit costs.
Average and marginal cost (dollars)
LACmin
Quantity Economies
of scale Diseconomies
of scale
Q2
LMC LAC
F I G U R E 9.10 Economic and Disecomies of Scale.
Now try Technical Problem 7.
example, consider Precision Brakes, a small-scale automobile brake repair shop ser- vicing only a few customers each day and employing just one mechanic. The single mechanic at Precision Brakes must perform every step in each brake repair: moving the car onto a hydraulic lift in a service bay, removing the wheels, removing the worn brake pads and shoes, installing the new parts, replacing the wheels, moving the car off the lift and out of the service bay, and perhaps even processing and col- lecting a payment from the customer. As the number of customers grows larger at Precision Brakes, the repair shop may wish to increase its scale of operation by hir- ing more mechanics and adding more service bays. At this larger scale of operation, some mechanics can specialize in lifting the car and removing worn out parts, while others can concentrate on installing the new parts and moving cars off the lifts and out of the service bays. And, a customer service manager would probably process each customer’s work order and collect payments. As you can see from this rather straightforward example, large-scale production affords the opportunity for divid- ing a production process into a number of specialized tasks. Division of labor allows workers to focus on single tasks, which increases worker productivity in each task and brings about very substantial reductions in unit costs.
A second cause of falling unit costs arises when a firm employs one or more quasi-fixed inputs. Recall that quasi-fixed inputs must be used in fixed amounts in both the short run and long run. As output expands, quasi-fixed costs are spread over more units of output causing long-run average cost to fall. The larger the con- tribution of quasi-fixed costs to overall total costs, the stronger will be the down- ward pressure on LAC as output increases. For example, a natural gas pipeline company experiences particularly strong economies of scale because the quasi- fixed cost of its pipelines and compressor pumps accounts for a very large portion of the total costs of transporting natural gas through pipelines. In contrast, a truck- ing company can expect to experience only modest scale economies from spread- ing the quasi-fixed cost of tractor-trailer rigs over more transportation miles, because the variable fuel costs account for the largest portion of trucking costs.
A variety of technological factors constitute a third force contributing to econo- mies of scale. First, when several different machines are required in a production process and each machine produces at a different rate of output, the operation may have to be quite sizable to permit proper meshing of equipment. Suppose only two types of machines are required: one that produces the product and one that packages it. If the first machine can produce 30,000 units per day and the second can package 45,000 units per day, output will have to be 90,000 units per day to fully utilize the capacity of each type of machine: three machines making the good and two machines packaging it. Failure to utilize the full capacity of each machine drives up unit production costs because the firm is paying for some amount of machine capacity it does not need or use.
Another technological factor creating scale economies concerns the costs of capital equipment: The expense of purchasing and installing larger machines is usually proportionately less than for smaller machines. For example, a printing press that can run 200,000 papers per day does not cost 10 times as much as one that can run 20,000 per day—nor does it require 10 times as much building space,
10 times as many people to operate it, and so forth. Again, expanding size or scale of operation tends to reduce unit costs of production.
A final technological matter might be the most important technological factor of all: As the scale of operation expands, there is usually a qualitative change in the optimal production process and type of capital equipment employed. For a simple example, consider ditch digging. The smallest scale of operation is one worker and one shovel. But as the scale expands, the firm does not simply continue to add workers and shovels. Beyond a certain point, shovels and most workers are re- placed by a modern ditch-digging machine. Furthermore, expansion of scale also permits the introduction of various types of automation devices, all of which tend to reduce the unit cost of production.
You may wonder why the long-run average cost curve would ever rise. After all possible economies of scale have been realized, why doesn’t the LAC curve become horizontal, never turning up at all? The rising portion of LAC is generally attributed to limitations to efficient management and organization of the firm. As the scale of a plant expands beyond a certain point, top management must neces- sarily delegate responsibility and authority to lower-echelon employees. Contact with the daily routine of operation tends to be lost, and efficiency of operation declines. Furthermore, managing any business entails controlling and coordinat- ing a wide variety of activities: production, distribution, finance, marketing, and so on. To perform these functions efficiently, a manager must have accurate infor- mation, as well as efficient monitoring and control systems. Even though informa- tion technology continues to improve in dramatic ways, pushing higher the scale at which diseconomies set in, the cost of monitoring and controlling large-scale businesses eventually leads to rising unit costs.
As an organizational plan for avoiding diseconomies, large-scale businesses sometimes divide operations into two or more separate management divisions so that each of the smaller divisions can avoid some or all of the diseconomies of scale.
Unfortunately, division managers frequently compete with each other for allocation of scarce corporate resources—such as workers, travel budget, capital outlays, office space, and R & D expenditures. The time and energy spent by division managers trying to influence corporate allocation of resources is costly for division managers, as well as for top-level corporate managers who must evaluate the competing claims of division chiefs for more resources. Overall corporate efficiency is sacrificed when lobbying by division managers results in a misallocation of resources among divi- sions. Scale diseconomies, then, remain a fact of life for very large-scale enterprises.
Constant costs: Absence of economies and diseconomies of scale In some cases, firms may experience neither economies nor diseconomies of scale, and instead face constant costs. When a firm experiences constant costs in the long run, its LAC curve is flat and equal to its LMC curve at all output levels.
Figure 9.11 illustrates a firm with constant costs of $20 per unit: Average and marginal costs are both equal to $20 for all output levels. As you can see by the flat LAC curve, firms facing constant costs experience neither economies nor diseconomies of scale.
constant costs Neither economies nor diseconomies of scale occur, thus LAC is flat and equal to LMC at all output levels.
Instances of truly constant costs at all output levels are not common in practice. However, businesses frequently treat their costs as if they are constant even when their costs actually follow the more typical U-shape pattern shown in Figure 9.9. The primary reason for assuming constant costs, when costs are in fact U-shaped, is to simplify cost (and profit) computations in spread- sheets. This simplifying assumption might not adversely affect managerial decision making if marginal and average costs are very nearly equal. However, serious decision errors can occur when LAC rises or falls by even modest amounts as quantity rises. In most instances in this textbook, we will assume a representative LAC, such as that illustrated earlier in Figure 9.9. Nonetheless, you should be familiar with this special case because many businesses treat their costs as constant.
Minimum efficient scale (MES) In many situations, a relatively modest scale of operation may enable a firm to capture all available economies of scale, and dis- economies may not arise until output is very large. Figure 9.12 illustrates such a situation by flattening LAC between points m and d to create a range of output over which LAC is constant. Once a firm reaches the scale of operation at point m on LAC, it will achieve the lowest possible unit costs in the long run, LACmin. The minimum level of output (i.e., scale of operation) that achieves all available economies of scale is called minimum efficient scale (MES), which is output level QMES in Figure 9.12. After a firm reaches minimum efficient scale, it will enjoy the lowest possible unit costs for all output levels up to the point where diseconomies set in at QDIS in the figure.
Firms can face a variety of shapes of LAC curves, and the differences in shape can influence long-run managerial decision making. In businesses where economies of scale are negligible, diseconomies may soon become of paramount importance, as LAC turns up at a relatively small volume
minimum efficient scale (MES)
Lowest level of output needed to reach minimum long-run average cost.
Quantity 0
Average and marginal cost (dollars)
LAC 5 LMC 20
Now try Technical Problem 8.
F I G U R E 9.11 The Special Case of Constant Costs:
LMC 5 LAC
of output. Panel A of Figure 9.13 shows a long-run average cost curve for a firm of this type. Panel B illustrates a situation in which the range and strength of the available scale economies are both substantial. Firms that must have low unit costs to profitably enter or even just to survive in this market will need to operate at a large scale when they face the LAC in Panel B. In many real-world situations, Panel C typifies the long-run cost struc- ture: MES is reached at a low level of production and then costs remain constant for a wide range of output until eventually diseconomies of scale take over.
Before leaving this discussion of scale economies, we wish to dispel a commonly held notion that all firms should plan to operate at minimum efficient scale in the long run. As you will see in Part IV of this book, the long run profit- maximizing output or scale of operation can occur in a region of falling, constant,
Constant LAC
m d
LAC
Quantity QMES
0 QDIS
Long-run average cost (dollars)
LACmin F I G U R E 9.12
Minimum Efficient Scale
QMES
Panel A — Early diseconomies
m
LAC
Average cost (dollars)
QMES Panel B — Extended
economies m LAC
Average cost (dollars)
QMES
Panel C — Extended constant LAC
m d
LAC
Average cost (dollars)
F I G U R E 9.13 MES with Various Shapes of LAC
or rising long-run average cost, depending on the shape of LAC and the intensity of market competition. Decision makers should ignore average cost and focus instead on marginal cost when trying to reach the optimal level of any activity.
For now, we will simply state that profit-maximizing firms do not always oper- ate at minimum efficient scale in the long run. We will postpone a more detailed statement until Part IV, where we will examine profit-maximization in various market structures.
Economies of Scope in Multiproduct Firms
Many firms produce a number of different products. Typically, multiproduct firms employ some resources that contribute to the production of two or more goods or services: Citrus orchards produce both oranges and grapefruit, oil wells pump both crude oil and natural gas, automotive plants produce both cars and trucks, commercial banks provide a variety of financial services, and hospitals perform a wide array of surgical operations and medical procedures. Economies of scope are said to exist whenever it is less costly for a multiproduct firm to produce two or more products together than for separate single-product firms to produce identical amounts of each product. Economists believe the prevalence of scope economies may be the best explanation for why we observe so many multiproduct firms across most industries and in most countries.
Multiproduct cost functions and scope economies Thus far, our analysis of production and costs has focused exclusively on single-product firms. We are now going to examine long-run total cost when a firm produces two or more goods or services. Although we will limit our discussion here to just two goods, the analysis applies to any number of products.
A multiproduct total cost function is derived from a multiproduct expansion path.
To construct a multiproduct expansion path for two goods X and Y, production engineers must work with a more complicated production function—one that gives technically efficient input combinations for various pairs of output quantities (X, Y). For a given set of input prices, engineers can find the economically efficient input combination that will produce a particular output combination (X, Y) at the lowest total cost. In practice, production engineers use reasonably complicated computer algorithms to repeatedly search for and identify the efficient combi- nations of inputs for a range of output pairs the manager may wish to produce.
This process, which you will never undertake as a manager, typically results in a spreadsheet or table of input and output values that can be rather easily used to construct a multiproduct total cost function: LTC(X, Y ). A multiproduct total cost function—whether expressed as an equation or as a spreadsheet—gives the lowest total cost for a multiproduct firm to produce X units of one good and Y units of some other good.
While deriving multiproduct cost functions is something you will never actually do, the concept of multiproduct cost functions nonetheless proves quite
economies of scope Exist when the joint cost of producing two or more goods is less than the sum of the separate costs of producing the goods.
Now try Technical Problem 9.
multiproduct total cost function:
LTC(X,Y)
Gives the lowest total cost for a multiproduct firm to produce X units of one good and Y units of another good.
useful in defining scope economies and explaining why multiproduct efficiencies arise. Economies of scope exist when
LTC(X, Y) , LTC(X, 0) 1 LTC(0, Y)
where LTC(X,0) and LTC(0,Y) are the total costs when single-product firms special- ize in production of X and Y, respectively. As you can see from this mathematical expression, a multiproduct firm experiencing scope economies can produce goods X and Y together at a lower total cost than two single-product firms, one firm spe- cializing in good X and the other in good Y.
Consider Precision Brakes and Mufflers—formerly our single-product firm known as Precision Brakes—that now operates as a multiservice firm repairing brakes and replacing mufflers. Precision Brakes and Mufflers can perform 4 brake jobs (B) and replace 8 mufflers (M) a day for a total cost of $1,400:
LTC(B, M) 5 LTC(4, 8) 5 $1,400
A single-service firm specializing in muffler replacement can install 8 replacement mufflers daily at a total cost of $1, 000: LTC(0, 8) 5 $1,000. A different single-service firm specializing in brake repair can perform 4 brake jobs daily for a total cost of
$600: LTC(4, 0) 5 $600. In this example, a multiproduct firm can perform 4 brake jobs and replace 8 mufflers at lower total cost than two separate firms producing the same level of outputs:
LTC(4, 8) , LTC(0, 8) 1 LTC(4, 0)
$1,400 , $1,000 1 $600
$1,400 , $1,600
Thus, Precision Brakes and Mufflers experiences economies of scope for this com- bination of muffler repair services.
An important consequence of scope economies for managerial decision making concerns the incremental or marginal cost of adding new product or service lines:
Firms that already produce good X can add production of good Y at lower cost than a specialized, single-product firm can produce Y. You can quickly confirm the validity of this statement by subtracting LTC(X, 0) from both sides of the origi- nal mathematical expression for economies of scope:
LTC(X, Y) 2 LTC(X, 0) , LTC(0, Y)
The left side of this expression shows the marginal cost of adding Y units at a firm already producing good X, which, in the presence of scope economies, costs less than having a single-product firm produce Y units. To illustrate this point, suppose Precision Brakes, the single-product firm specializing in brake jobs, is performing 4 brake jobs daily. If Precision Brakes wishes to become a multiservice company by adding 8 muffler repairs daily, the marginal or incremental cost to do so is $800:
LTC(4, 8) 2 LTC(4, 0) 5 $1,400 2 $600 5 $800