8: Production and cost

The productivity-cost relationship

Consider the average variable cost - average product relationship, as developed in column 7 of Table 8.2; its corresponding variable cost curve is plotted in Figure 8.4. In this example, AVC first decreases and then increases. The intuition behind its shape is straightforward (and realistic) if you have understood why productivity varies in the short run: The variable cost, which represents the cost of labour, is constant per unit of labour, because the wage paid to each worker does not change. However, each worker's productivity varies. Initially, when we hire more workers, they become more productive, perhaps because they have less 'down time' in switching between tasks. This means that the labour costs per snowboard must decline. At some point, however, the law of diminishing returns sets in: As before, each additional worker is paid a constant amount, but as productivity declines the labour cost per snowboard increases.

Figure 8.4 Average and marginal cost curves

The MC intersects the ATC and AVC at their minimum values. The AFC declines indefinitely as fixed costs are spread over a greater output.

In this numerical example the AP is at a maximum when six units of labour are employed and output is 175. This is also the point where the AVC is at a minimum. This maximum/minimum relationship is also illustrated in Figures 8.2 and 8.4.

Now consider the marginal cost - marginal product relationship. The marginal cost (MC) defines the cost of producing one more unit of output. In Table 8.2, the marginal cost of output is given in the final column. It is the additional cost of production divided by the additional number of units produced. For example, in going from 15 units of output to 40, total costs increase from $4,000 to $5,000. The MC is the cost of those additional units divided by the number of additional units. In this range of output, MC is . We could also calculate the MC as the addition to variable costs rather than the addition to total costs, because the addition to each is the same—fixed costs are fixed. Hence:

MC

Just as the behaviour of the AVC curve is determined by the AP curve, so too the behaviour of the MC is determined by the MP curve. When the MP of an additional worker exceeds the MP of the previous worker, this implies that the cost of the additional output produced by the last worker hired must be declining. To summarize:

If the marginal product of labour increases, then the marginal cost of output declines;
If the marginal product of labour declines, then the marginal cost of output increases.

In our example, the reaches a maximum when the fourth unit of labour is employed (or 110 units of output are produced), and this also is where the MC is at a minimum. This illustrates that the marginal cost reaches a minimum at the output level where the marginal product reaches a maximum.

The average total cost is the sum of the fixed cost per unit of output and the variable cost per unit of output. Typically, fixed costs are the dominant component of total costs at low output levels, but become less dominant at higher output levels. Unlike average variable costs, note that the average fixed cost must always decline with output, because a fixed cost is being spread over more units of output. Hence, when the ATC curve eventually increases, it is because the increasing variable cost component eventually dominates the declining AFC component. In our example, this occurs when output increases from 220 units (8 workers) to 235 (9 workers).

Finally, observe the interrelationship between the MC curve on the one hand and the ATC and AVC on the other. Note from Figure 8.4 that the MC cuts the AVC and the ATC at the minimum point of each of the latter. The logic behind this pattern is analogous to the logic of the relationship between marginal and average product curves: When the cost of an additional unit of output is less than the average, this reduces the average cost; whereas, if the cost of an additional unit of output is above the average, this raises the average cost. This must hold true regardless of whether we relate the MC to the ATC or the AVC.

When the marginal cost is less than the average cost, the average cost must decline;
When the marginal cost exceeds the average cost, the average cost must increase.

Notation: We use both the abbreviations and to denote average total cost. The term 'average cost' is understood in economics to include both fixed and variable costs.

Teams and services

The choice faced by the producer in the example above is slightly 'stylized', yet it still provides an appropriate rule for analyzing hiring decisions. In practice, it is quite difficult to isolate or identify the marginal product of an individual worker. One reason is that individuals work in teams within organizations. The accounting department, the marketing department, the sales department, the assembly unit, the chief executive's unit are all composed of teams. Adding one more person to human resources may have no impact on the number of units of output produced by the company in a measurable way, but it may influence worker morale and hence longer-term productivity. Nonetheless, if we consider expanding, or contracting, any one department within an organization, management can attempt to estimate the net impact of additional hires (or layoffs) on the contribution of each team to the firm's profitability. Adding a person in marketing may increase sales, laying off a person in research and development may reduce costs by more than it reduces future value to the firm. In practice this is what firms do: they attempt to assess the contribution of each team in their organization to costs and revenues, and on that basis determine the appropriate number of employees.

The manufacturing sector of the macro economy is dominated, sizewise, by the services sector. But the logic that drives hiring decisions, as developed above, applies equally to services. For example, how does a law firm determine the optimal number of paralegals to employ per lawyer? How many nurses are required to support a surgeon? How many university professors are required to teach a given number of students?

All of these employment decisions involve optimization at the margin. The goal of the decision maker is not always profit, but she should attempt to estimate the cost and value of adding personnel at the margin.

R & D as a sunk cost

Sunk costs in the modern era are frequently in the form of research and development costs, not the cost of building a plant or purchasing machinery. The prototypical example is the pharmaceutical industry, where it is becoming progressively more challenging to make new drug breakthroughs – both because the 'easier' breakthroughs have already been made, and because it is necessary to meet tighter safety conditions attaching to new drugs. Research frequently leads to drugs that are not sufficiently effective in meeting their target. As a consequence, the pharmaceutical sector regularly writes off hundreds of millions of dollars of lost sunk costs – unfruitful research and development.

Finally, we need to keep in mind the opportunity costs of running the business. The owner pays himself a salary, and ultimately he must recognize that the survival of the business should not depend upon his drawing a salary that is less than his opportunity cost. As developed in Section 7.2, if he underpays himself in order to avoid shutting down, he might be better off in the long run to close the business and earn his opportunity cost elsewhere in the marketplace.

A dynamic setting

We need to ask why it might be possible to cover all costs in a longer run horizon, while in the near-term costs are not covered. The principal reason is that demand may grow, particularly for a new product. For example, in 2019 numerous cannabis producing firms were listed on the Canadian Securities Exchange, and collectively were valued at about fifty billion dollars. None had revenues that covered costs, yet investors poured money into this sector. Investors evidently envisaged that the market for legal cannabis would grow. As of 2020 it appears that these investors were excessively optimistic. Sales growth has been slow and stock valuations have plummeted.

Average costs in the long run

Figure 8.5 illustrates a possible relationship between the ATC curves for four different scales of operation. is the average total cost curve associated with a small-sized plant; think of it as the plant built in the entrepreneur's garage. is associated with a somewhat larger plant, perhaps one she has put together in a rented industrial or commercial space. The further a cost curve is located to the right of the diagram the larger the production facility it defines, given that output is measured on the horizontal axis. If there are economies associated with a larger scale of operation, then the average costs associated with producing larger outputs in a larger plant should be lower than the average costs associated with lower outputs in a smaller plant, assuming that the plants are producing the output levels they were designed to produce. For this reason, the cost curve and the cost curve each have a segment that is lower than the lowest segment on . However, in Figure 8.5 the cost curve has moved upwards. What behaviours are implied here?

Figure 8.5 Long-run and short-run average costs

The long-run ATC curve, LATC, is the lower envelope of all short-run ATC curves. It defines the least cost per unit of output when all inputs are variable. Minimum efficient scale is that output level at which the LATC is a minimum, indicating that further increases in the scale of production will not reduce unit costs.

In many production environments, beyond some large scale of operation, it becomes increasingly difficult to reap further cost reductions from specialization, organizational economies, or marketing economies. At such a point, the scale economies are effectively exhausted, and larger plant sizes no longer give rise to lower (short-run) ATC curves. This is reflected in the similarity of the and the curves. The pattern suggests that we have almost exhausted the possibilities of further scale advantages once we build a plant size corresponding to . Consider next what is implied by the position of the curve relative to the and curves. The relatively higher position of the curve implies that unit costs will be higher in a yet larger plant. Stated differently: If we increase the scale of this firm to extremely high output levels, we are actually encountering diseconomies of scale. Diseconomies of scale imply that unit costs increase as a result of the firm's becoming too large: Perhaps co-ordination difficulties have set in at the very high output levels, or quality-control monitoring costs have risen. These coordination and management difficulties are reflected in increasing unit costs in the long run.

The terms increasing, constant, and decreasing returns to scale underlie the concepts of scale economies and diseconomies: Increasing returns to scale (IRS) implies that, when all inputs are increased by a given proportion, output increases more than proportionately. Constant returns to scale (CRS) implies that output increases in direct proportion to an equal proportionate increase in all inputs. Decreasing returns to scale (DRS) implies that an equal proportionate increase in all inputs leads to a less than proportionate increase in output.

These are pure production function relationships, but, if the prices of inputs are fixed for producers, they translate directly into the various cost structures illustrated in Figure 8.5. For example, if a 40% increase in capital and labour use allows for better production flows than when in the smaller plant, and therefore yields more than a 40% increase in output, this implies that the cost per snowboard produced must fall in the new plant. In contrast, if a 40% increase in capital and labour leads to say just a 30% increase in output, then the cost per snowboard in the new larger plant must be higher. Between these extremes, there may be a range of relatively constant unit costs, corresponding to where the production relation is subject to constant returns to scale. In Figure 8.5, the falling unit costs output region has increasing returns to scale, the region that has relatively constant unit costs has constant returns to scale, and the increasing cost region has decreasing returns to scale.

Increasing returns to scale characterize businesses with large initial costs and relatively low costs of producing each unit of output. Computer chip manufacturers, pharmaceutical manufacturers, vehicle rental agencies, booking agencies such as booking.com or hotels.com, intermediaries such as airbnb.com, even brewers, all benefit from scale economies. In the beer market, brewing, bottling and shipping are all low-cost operations relative to the capital cost of setting up a brewery. Consequently, we observe surprisingly few breweries in any brewing company, even in large land-mass economies such as Canada or the US.

In addition to the four short-run average total cost curves, Figure 8.5 contains a curve that forms an envelope around the bottom of these short-run average cost curves. This envelope is the long-run average total cost (LATC) curve, because it defines average cost as we move from one plant size to another. Remember that in the long run both labour and capital are variable, and as we move from one short-run average cost curve to another, that is exactly what happens—all factors of production are variable. Hence, the collection of short-run cost curves in Figure 8.5 provides the ingredients for a long-run average total cost curve1.

The particular range of output on the LATC where it begins to flatten out is called the range of minimum efficient scale. This is an important concept in industrial policy, as we shall see in later chapters. At such an output level, the producer has expanded sufficiently to take advantage of virtually all the scale economies available.

In view of this discussion and the shape of the LATC in Figure 8.5, it is obvious that economies of scale can also be defined in terms of the curvature of the LATC. Where the LATC declines there are IRS, where the LATC is flat there are CRS, where the LATC slopes upward there are DRS.

Table 8.3 LATC elements for two plants (thousands $)

Q
20	50	30	80	100	25	125
40	25	30	55	50	25	75
60	16.67	30	46.67	33.33	25	58.33
80	12.5	30	42.5	25	25	50
100	10	30	40	20	25	45
120	8.33	30	38.33	16.67	25	41.67
140	7.14	30	37.14	14.29	25	39.29
160	6.25	30	36.25	12.5	25	37.5
180	5.56	30	35.56	11.11	25	36.11
200	5	30	35	10	25	35
220	4.55	30	34.55	9.09	25	34.09
240	4.17	30	34.17	8.33	25	33.33
260	3.85	30	33.85	7.69	25	32.69
280	3.57	30	33.57	7.14	25	32.14

Plant 1 m. Plant 2 m. For Q<200, ; for Q>200, ; and for Q=200, ATC₁=ATC₂. LATC defined by data in bold font.

Long-run costs – a simple numerical example

Kitt is an automobile designer specializing in the production of off-road vehicles sold to a small clientele. He has a choice of two (and only two) plant sizes; one involving mainly labour and the other employing robots extensively. The set-up (i.e. fixed) costs of these two assembly plants are $1 million and $2 million respectively. The advantage to having the more costly plant is that the pure production costs (variable costs) are less. The cost components are defined in Table 8.3. The variable cost (equal to the marginal cost here) is $30,000 in the plant that relies primarily on labour, and $25,000 in the plant that has robots. The ATC for each plant size is the sum of AFC and AVC. The AFC declines as the fixed cost is spread over more units produced. The variable cost per unit is constant in each case. By comparing the fourth and final columns, it is clear that the robot-intensive plant has lower costs if it produces a large number of vehicles. At an output of 200 vehicles the average costs in each plant are identical: The higher fixed costs associated with the robots are exactly offset by the lower variable costs at this output level.

The ATC curve corresponding to each plant size is given in Figure 8.6. There are two short-run ATC curves. The positions of these curves indicate that if the manufacturer believes he can produce at least 200 vehicles his unit costs will be less with the plant involving robots; but at output levels less than this his unit costs would be less in the labour-intensive plant.

Figure 8.6 LATC for two plants in $000

The long-run average cost curve for this producer is the lower envelope of these two cost curves: ATC₁ up to output 200 and ATC₂ thereafter. Two features of this example are to be noted. First we do not encounter decreasing returns – the LATC curve never increases. ATC₁ tends asymptotically to a lower bound of , while ATC₂ tends towards . Second, in the interests of simplicity we have assumed just two plant sizes are possible. With more possibilities on the introduction of robots we could imagine more short-run ATC curves which would form the lower-envelope LATC.

Globalization

The modern communications revolution has reduced costs, just like its predecessors. But it has also greatly sped up globalization, the increasing integration of national markets.

Globalization has several drivers: lower transportation and communication costs; reduced barriers to trade and capital mobility; the spread of new technologies that facilitate cost and quality control; different wage rates between developed and less developed economies. New technology and better communications have been critical in both increasing the minimum efficient scale of operation and reducing diseconomies of scale; they facilitate the efficient management of large companies.

The continued reduction in trade barriers in the post-World War II era has also meant that the effective marketplace has become the globe rather than the national economy for many products. Companies like Apple, Microsoft, and Facebook are visible worldwide. Globalization has been accompanied by the collapse of the Soviet Union, the adoption of an outward looking philosophy on the part of China, and an increasing role for the market place in India. These developments together have facilitated the outsourcing of much of the West's manufacturing to lower-wage economies.

But new technology not only helps existing companies grow large; it also enables new ones to start up. It is now cheaper for small producers to manage their inventories and maintain contact with their own suppliers.

The impact of technology is to reduce the cost of production, hence it will lower the average cost curve in both the short and long run. First, decreasing returns to scale become less probable due to improved communications, so the upward sloping section of the LRAC curve may disappear altogether. Second, capital costs are now lower than in earlier times, because much modern technology has transformed some fixed costs into variable cost: Both software and hardware functions can be subcontracted to specialty firms, who in turn may use cloud computing services, and it is thus no longer necessary to have a substantial in-house computing department. The use of almost-free software such as Skype, Hangouts and WhatsApp reduces communication costs. Advertising on social media is more effective and less costly than in traditional hard-print form. Hiring may be cheaper through LinkedIn than through a traditional human resources department. These developments may actually reduce the minimum efficient scale of operation because they reduce the need for large outlays on fixed capital. On the other hand, changes in technology may induce producers to use more capital and less labor, with the passage of time. That would increase the minimum efficient scale. An example of this phenomenon is in mining, or tunnel drilling, where capital investment per worker is greater than when technology was less developed. A further example is the introduction of robotic assistants in Amazon warehouses. In these scenarios the minimum efficient scale should increase, and that is illustrated in Figure 8.7.

Figure 8.7 Technological change and LAC

Technological change reduces the unit production cost for any output produced and may also increase the minimum efficient scale (MES) threshold.

The local diffusion of technology

The impacts of technological change are not just evident in a global context. Technological change impacts every sector of the domestic economy. For example, the modern era in dentistry sees specialists in root canals (endodentists) performing root canals in the space of a single hour with the help of new technology; dental implants into bone, as an alternative to dentures, are commonplace; crowns can be machined with little human intervention; and X-rays are now performed with about one hundredth of the power formerly required. These technologies spread and are adopted through several channels. Dental practices do not usually compete on the basis of price, but if they do not adopt best practices and new technologies, then community word of mouth will see patients shifting to more efficient operators.

Some technological developments are protected by patents. But patent protection rarely inhibits new and more efficient practices that in some way mimic patent breakthroughs.

Clusters

The phenomenon of a grouping of firms that specialize in producing related products is called a cluster. For example, Ottawa has more than its share of software development firms; Montreal has a disproportionate share of Canada's pharmaceutical producers and electronic game developers; Calgary has its 'oil patch'; Hollywood has movies; Toronto is Canada's financial capital, San Francisco and Seattle are leaders in new electronic products. Provincial and state capitals have most of their province's bureaucracy. Clusters give rise to externalities, frequently in the form of ideas that flow between firms, which in turn result in cost reductions and new products.

The most famous example of clustering is Silicon Valley, surrounding San Francisco, in California, the original high-tech cluster. The presence of a large group of firms with a common focus serves as a signal to workers with the right skill set that they are in demand in such a region. Furthermore, if these clusters are research oriented, as they frequently are, then knowledge spillovers benefit virtually all of the contiguous firms; when workers change employers, they bring their previously-learned skills with them; on social occasions, friends may chat about their work and interests and share ideas. This is a positive externality.

Learning by doing

Learning from production-related experiences frequently reduces costs: The accumulation of knowledge that is associated with having produced a large volume of output over a considerable time period enables managers to implement more efficient production methods and avoid errors. We give the term learning by doing to this accumulation of knowledge.

Examples abound, but the best known may be the continual improvement in the capacity of computer chips, whose efficiency has doubled about every eighteen months for several decades – a phenomenon known as Moore's Law. As Intel Corporation continues to produce chips it learns how to produce each succeeding generation of chips at lower cost. Past experience is key. Economies of scale and learning by doing therefore may not be independent: Large firms usually require time to grow or to attain a dominant role in their market, and this time and experience enables them to produce at lower cost. This lower cost in turn can solidify their market position further.

Economies of scope

Economies of scope define a production process if the production of multiple products results in lower unit costs per product than if those products were produced alone. Scope economies, therefore, define the returns or cost reductions associated with broadening a firm's product range.

Corporations like Proctor and Gamble do not produce a single product in their health line; rather, they produce first aid, dental care, and baby care products. Cable companies offer their customers TV, high-speed Internet, and telephone services either individually or packaged. A central component of some new-economy multi-product firms is a technology platform that can be used for multiple purposes. We shall analyze the operation of these firms in more detail in Chapter 11.