Production is the creation of goods and services from inputs or resources, such as labor, machinery and other capital equipment, land, raw materials, and so on.
Obviously, when a company such as Ford makes a truck or car or when Exxon- Mobil refines a gallon of gasoline, the activity is production. But production goes much further than that. A doctor produces medical services, a teacher produces
production
The creation of goods and services from inputs or resources.
education, and a singer produces entertainment. So production involves services as well as making the goods people buy. Production is also undertaken by govern- ments and nonprofit organizations. A city police department produces protection, a public school produces education, and a hospital produces health care.
In the following chapters, we will analyze production within the framework of business firms using inputs to produce goods rather than services. It is con- ceptually easier to visualize the production of cars, trucks, or refrigerators than the production of education, health, or security, which are hard to measure and even harder to define. Nonetheless, throughout the discussion, remember that the concepts developed here apply to services as well as goods and to government production as well as firm production.
Production Functions
A production function is the link between levels of input usage and attainable levels of output. The production function formally describes the relation between physical rates of output and physical rates of input usage. With a given state of technology, the attainable quantity of output depends on the quantities of the vari- ous inputs employed in production. A production function is a schedule (or table or mathematical equation) showing the maximum amount of output that can be produced from any specified set of inputs, given the existing technology or state of knowledge concerning available production methods.
Many different inputs are used in production. So, in the most general case, we can define maximum output Q to be a function of the level of usage of the various inputs X. That is,
Q 5 f (X1, X2, . . . , Xn)
However, in our discussion we will generally restrict attention to the simpler case of a product whose production entails only one or two inputs. We will normally use capital and labor as the two inputs. Hence, the production function we will usually be concerned with is
Q 5 f (L, K)
where L and K represent, respectively, the amounts of labor and capital used in production. However, we must stress that the principles to be developed apply to situations with more than two inputs and, as well, to inputs other than capital and labor.
For most production functions, the same output can be produced using differ- ent combinations of capital and labor. For example, when less labor is used, more capital can be added to reach the same level of production. When input substitu- tion is possible, we call this kind of production variable proportions production.
In contrast, when there is one, and only one, ratio or mix of inputs that can be used to produce a good, we call this fixed proportions production. In this case, when output is expanded, usage of all inputs must be expanded at the same rate to main- tain the fixed input ratio. At first glance, this might seem to be the usual condition.
production function A schedule (or table or mathematical equation) showing the maximum amount of output that can be produced from any specified set of inputs, given the existing technology.
variable proportions production
Production in which a given level of output can be produced with more than one combination of inputs.
fixed proportions production
Production in which one, and only one, ratio of inputs can be used to produce a good.
However, real-world examples of fixed proportions production are hard to come by. As a consequence, we will concentrate on production with variable proportions throughout this book.
Technical and Economic Efficiency
Production engineers, who are responsible for designing and managing processes for transforming inputs into goods or services, frequently speak of “efficiency”
in a way that differs from managers, who are responsible for maximizing the profit generated from producing goods or services. To understand the nature and importance of this difference, we must distinguish between two types of efficiency:
technical efficiency and economic efficiency.
Technical efficiency is achieved when a firm produces the maximum pos- sible output for a given combination of inputs and existing technology. Since production functions show the maximum output possible for any particular combi- nation of inputs, it follows that production functions are derived assuming inputs are going to be employed in a technically efficient way. When a firm is technically efficient, every input is being utilized to the fullest extent possible, and there is no other way to get more output without using more of at least one input. And thus, for a technically efficient firm, reducing the usage of any input will necessarily cause output to fall.
Amergen Inc., a firm manufacturing electric generators, provides an excel- lent example of how engineers strive to achieve technical efficiency in produc- tion. Amergen’s assembly-line process begins with workers manually performing five steps before the generator reaches a computer-controlled drill press. Here, the computer-controlled machine drills 36 holes in the generator, and, in doing so, two pounds of iron are removed. Using this procedure, 10 assembly-line workers and one computer-controlled drill press were producing 140 generators each day.
Recently, however, a production engineer at Amergen discovered that moving the computer-controlled drill press to the beginning of the assembly line, ahead of the five steps performed manually, would save a significant amount of labor energy because each generator would weigh two pounds less as it moves downstream on the assembly line. The production engineer was unable to find any other change that would further increase output. Thus, Amergen’s production became techni- cally efficient: 150 generators was the maximum number of generators that could be produced using 10 laborers and one drill press.
Like the Amergen example above, engineers at most firms focus on ensuring that production takes place in a technically efficient manner. Business managers, however, are not only interested in technical efficiency but also plan to achieve economic efficiency in production. Economic efficiency is achieved when the firm produces its chosen level of output at the lowest-possible total cost. The reason managers focus on economic efficiency is simple: profit cannot be maximized unless the firm’s output is produced at the lowest-possible total cost.
We can now explain the relationship between technical and economic efficiency. When a firm is economically efficient it must also be technically
technical efficiency Producing the maximum output for any given combination of inputs and existing technology.
economic efficiency Producing a given level of output at the lowest- possible total cost.
efficient, because minimizing total cost cannot happen if the amount of any input could be reduced without causing output to fall. However, it is possible to produce in a technically efficient way without achieving economic efficiency.
Typically there are numerous technically efficient input combinations capable of producing any particular output level. While production engineers might be satisfied using any one of the technically efficient combinations of inputs, managers want to use only the combination with the lowest total cost—the economically efficient one. The input combination that turns out to be econom- ically efficient depends crucially on the prices of the inputs. For a different set of input prices, a different technically efficient input combination will become the economically efficient one. This point is illustrated in Technical Problem 2 at the end of this chapter.
Inputs in Production
When analyzing a firm’s production process and the associated costs of producing the good or service, it is important for tactical decision making and strategic anal- ysis of market competition to distinguish between several major types of inputs:
variable, fixed, or quasi-fixed. A variable input is one for which the level of usage may be readily varied in order to change the level of output. Many types of labor services as well as raw materials and energy to run production facilities are vari- able inputs. Payments for variable inputs are called variable costs. Producing more output is accomplished by using greater amounts of the variable inputs, and output is reduced by using smaller amounts of the variable inputs. Thus, variable costs are directly related to the level of output.
In contrast to variable inputs, the usage of some inputs remains constant or fixed as the level of output rises or falls. There are two primary reasons why input usage may be fixed as output varies. First, when the cost of adjusting the level of input usage is prohibitively high, a manager will treat the level of usage of that input as fixed at its current level of usage. No matter how much output the firm produces—even when output is zero—the firm uses a constant amount of the input and must pay for the input even if the firm ceases production. This kind of input is called a fixed input, and payments for fixed inputs are called fixed costs.
As an example of a fixed input, consider the number of aircraft operated by a commercial airline. Most airlines choose to lease, rather than buy, the aircraft in their fleets. A Boeing 737 aircraft, one of the most widely used jets, leases for about
$400,000 per month, depending on the age of the aircraft and the number of pas- sengers it can carry. Although the lengths of aircraft leases vary, 10-year leases are common for new aircraft. During this 10-year period, it is very costly to break a lease agreement and return a plane. For this reason, airlines almost always con- tinue to pay the $400,000 per-month lease payments when demand for air travel decreases, forcing some of their planes to sit in hangars until demand picks up again. And, when airlines wish to increase the number of planes in their fleets, it can take up to 24 months to lease a new aircraft. Typically, airline managers view aircraft as fixed inputs over a one- to two-year time period.
Now try Technical Problems 1–2.
variable input
Input for which the level of usage may be varied to increase or decrease output.
fixed input
An input for which the level of usage cannot be changed and which must be paid even if no output is produced.
The second reason for input fixity arises when, in order to produce any posi- tive amount of output, a necessary input must be purchased in some fixed size or lump amount. Because of the inherent lumpiness or indivisibility of such inputs, producing the first unit of output requires the firm to pay for an entire “lump” of the indivisible input. Further expansion of output can be accomplished without using any more of the lumpy input. This type of fixed input is called a quasi-fixed input to distinguish it from an ordinary fixed input, and payments for quasi-fixed inputs are called quasi-fixed costs. Although fixed and quasi-fixed inputs are both used in constant amounts as output varies, fixed inputs must be paid even if out- put is zero while quasi-fixed inputs need not be purchased if output is zero.
Quasi-fixed inputs are rather common in many industries. Consider a broad- cast radio station: To broadcast the first minute of radio news and entertainment, one entire radio antenna tower must be purchased and installed. Increasing trans- mission time from one minute all the way up to 24 hours, seven days a week, still requires only one antenna tower. Or consider a doctor’s office: The amount of electricity used for lighting the office and examination rooms does not vary with the number of patients the doctor examines—unless the lights are turned off when examination rooms are empty.
Even though examples can be found in a wide variety of industries, quasi-fixed inputs only play an important role in business strategy when these costs are rela- tively large in relation to variable costs of production. For the rest of this chapter and most of the remaining chapters in this book, we will largely ignore quasi-fixed inputs in our production and cost analysis to avoid any confusion about the nature of fixed costs. Unless we specifically state that an input is a quasi-fixed input, we will treat all fixed inputs as “ordinary” fixed inputs: a fixed amount of the input is employed for all output levels, and must be paid for even when output is zero. We must, however, discuss quasi-fixed inputs again in Chapter 9. There, we will explain how quasi-fixed inputs can affect the shape of firms’ long-run average cost curves, which in turn play a crucial role in determining the number and size of the firms that compete in an industry. And then in Chapters 12 and 13, you will learn about the role quasi-fixed costs play in both a firm’s decision to enter a new market and an incumbent firm’s ability to strategically deter new firms from entering a market.
Short-Run and Long-Run Production Periods
As mentioned in the introduction, economists distinguish between the short-run and the long-run periods of production. The short run refers to the current time span during which one or more inputs are fixed inputs and must be paid whether or not any output is produced. Changes in output during the short-run period must be accomplished exclusively by changes in the use of the variable inputs.
The long run refers to the time period far enough in the future to allow all fixed inputs to become variable inputs. Possibly the simplest statement capturing the dif- ference between short-run and long-run production periods is: “Firms operate in the short run and plan for the long run.”
quasi-fixed input A lumpy or indivisible input for which a fixed amount must be used for any positive level of output, and none is purchased when output is zero.
Now try Technical Problem 3.
short run
Current time span during which at least one input is a fixed input.
long run
Time period far enough in the future to allow all fixed inputs to become variable inputs.
Using the simplified production function discussed previously for a firm using only two inputs, labor (L) and capital (K), we can view the production function Q 5 f (L, K) as the long-run production function, because output in the long run varies by changing the amounts of the variable inputs L and K. Once a firm chooses to purchase and install a particular amount of capital, __K , the firm then begins operat- ing in a short-run situation with the chosen fixed amount of capital. The short-run production function can be expressed as Q 5 f (L, __K ), where capital is fixed at the current level K __. In the short run, with capital fixed at its current level, output varies only as the level of labor usage varies, and we can express the short-run produc- tion function more simply as Q 5 f (L), where we have dropped the term __K because capital usage cannot vary. The firm will continue to operate with this particular short-run production function until a time in the future is reached when it is pos- sible to choose a different amount of capital. The length of time it takes to make a change in K (i.e., the length of the short-run period) varies widely across firms and industries. Consequently, we cannot give you a particular amount of time for the short-run production period. The short-run period lasts as long as it takes for the firm to be able to change the current levels of usage of its fixed inputs.
Now it should be clear to you why the firm’s current short-run production condition is different for every possible level of capital the firm might choose in the long run. Simply stated, the long run consists of all possible future short-run situations—one for every level of capital the firm can employ in the future. For this reason, the long-run production period is frequently called the firm’s planning horizon. A firm’s planning horizon is the collection of all possible short-run situa- tions the firm can face in the future composed of one short-run situation for every level of capital the firm can choose in the long run.
planning horizon Set of all possible short- run situations the firm can face in the future.
Relation In the short run at least one input is a fixed input, and in the long run all fixed inputs become variable inputs. The long-run planning horizon is the set of all possible short-run situations from which the firm may choose to operate in the long run.
In the long run managers will choose the most advantageous (i.e., the optimal) amount of capital based on the price of capital relative to other inputs and the intended output level. However, when production levels or input prices change, a firm may find itself positioned with too much or too little capital in the current short- run period. When the firm has too much or too little capital in the short run, it will be able to reduce total production costs in the future by making long-run adjustments in capital usage. We will have much more to say about restructuring costs in the next chapter.
Sunk Costs versus Avoidable Costs
We first introduced the concept of sunk costs in Chapter 3 when we developed rules for finding the optimal level of any activity in general. We will now apply the concept of sunk costs to a firm’s costs of production and explain how sunk costs differ from avoidable costs of production. A sunk cost in production is a pay- ment for an input that, once made, cannot be recovered should the firm no longer
Now try Technical Problem 4.
sunk cost in production
Payment for an input that, once made, cannot be recovered should the firm no longer wish to employ that input. Fixed costs are sunk costs.
wish to employ that input. To keep matters clear, you should think of the firm’s production occurring over a series of time periods: days, weeks, months, quarters, or years, for example. An input payment made in any particular time period is a sunk cost if that input payment cannot be recovered if it turns out in later time periods the firm no longer needs that input. For this reason, fixed costs are sunk costs of production.
Once a sunk cost is incurred, a manager should ignore the sunk cost for decision-making purposes. After an unrecoverable payment is made, it is irrelevant for all future decisions and is in no way a part of the economic cost of production in future time periods. Recall that the economic cost to the owners of a business for using a resource is equal to the opportunity cost to the business owners for using the resource. After a business makes a sunk payment for an input, the cost of using the input thereafter is zero, because the input cannot be returned for a refund nor can it be sold, rented, or leased to some other business to recover the sunk cost. Under some circumstances, a portion of the payment can be recovered, either as a refund or by renting or subleasing the input to another firm. In that case, only the nonrecoverable portion of the input payment is a sunk cost.
An example should be quite helpful here. Suppose that at 8:00 a.m. on January 1, a homebuilder pays $10,000 to a local government agency for an annual, nontransferable building license that permits the firm to build homes from January 1 to December 31. The $10,000 building license is part of the annual total cost of building homes. Although the $10,000 must be paid to start doing business for the year, once the license is paid for on January 1, it then immediately becomes a sunk cost for the rest of that year; there is no opportunity cost for using this nontransferable license for the remainder of the year. Thus, after January 1, the opportunity cost of owning this license is zero and should not be considered for decision-making purposes during the rest of the year. We wish to stress here that even though the sunk cost does not matter after January 1 for decision-making purposes, it does matter for computing the annual cost and profit of the firm: the cost of the license reduces profit by $10,000.
Now let’s suppose that on July 1 the builder decides to quit building new homes for the rest of the year. When making the decision to cease production on July 1, the builder should completely ignore the $10,000 sunk cost of the license, because none of the sunk payment can be recovered when deciding to shut down new construction. But consider this twist: What if the local building agency offers a one-time bailout for distressed homebuilders by refunding one-fourth of the an- nual license fee (i.e., $2,500) at any time during the year for builders that cease production. With this bailout option, the sunk cost of the license drops to $7,500 and the economic cost of using the license for the remainder of the year rises from zero to $2,500.
Avoidable costs are the opposite of sunk costs. An avoidable cost in production is an input payment that a firm can recover or avoid paying should the manager no longer wish to use that input. Avoidable costs do matter in decision making and should not be ignored. In our previous example, when the building agency
avoidable cost in production
Payment for an input that a firm can recover or avoid paying should the firm no longer wish to use that input. Variable costs and quasi-fixed costs are avoidable costs.