6.1 The Basics of Production

production

The process by which a person, company, government, or non-profit agency creates a good or service that others are willing to pay for.

intermediate good

A good that is used to produce another good.

final good

A good that is bought by a consumer.

Before anyone can consume a good, someone must first produce it (duh). Production is the process by which a person, company, government, or non-profit agency uses inputs to create a good or service for which others are willing to pay. Production can take many forms. Some producers make final goods that are bought by consumers.1 Others make intermediate goods that are inputs into another firm’s production, such as electricity, sugar, or advertising services. The range of products is so extensive that formulating a general model of production is hard—not unlike building the model of consumer behavior in the previous two chapters.

production function

A mathematical relationship that describes how much output can be made from different combinations of inputs.

We begin our model of production by laying out the assumptions that economists typically adopt to simplify firms’ decisions.2 Then, we introduce the idea of a production function, which relates the amount of output a firm can create from different combinations of inputs. We show how a firm, given that production function, makes its choice about which inputs to use in production—how many workers to hire, how much equipment to buy, and so on. We will see how this input mix depends on the prices of the inputs and the properties of the production function itself. Finally, we explore some specific topics about production functions, including how they reflect technological progress and differences in the scale of operations.

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Before we begin this analysis, a word of advice: Students often find it more difficult to understand production and supply than consumption and demand because they have more experience consuming than producing. But as you’ll see in this chapter, there are a lot of parallels in the economics of consumers’ and producers’ decisions. For example, a firm’s task of minimizing the cost of producing its desired quantity of output is very much like a consumer’s desire to maximize utility subject to a budget constraint.

Simplifying Assumptions about Firms’ Production Behavior

In the real world, production is complicated. Think about a restaurant. It sells dozens, maybe hundreds, of items. It has multiple suppliers (meat, fish, drinks, glasses, paper umbrellas, silverware), many employees, and it must constantly make decisions about tables, menu, advertising, and more. At large firms like Walmart, Apple, or BMW, with tens of thousands of employees and billions of dollars of annual revenues from sales all over the globe, the production process is even more complicated.

To make general conclusions about optimal production behavior when reality is so complicated, we need to make some simplifying assumptions so we can focus on just the essentials. We do not want to assume away so much reality that the model becomes useless as a tool to understand real-world behavior. In our attempt to model producer behavior in this chapter, we assume the following:

  1. The firm produces a single good. If a firm sells many products, then the decisions a firm makes about each product get intertwined in complicated ways. In the basic model of the firm, we can avoid these complications by assuming that the firm makes just one good.

  2. The firm has already chosen which product to produce. The firms we study already know what they want to produce; we just decide how they can make it most efficiently. Deciding what to produce is an important aspect of a real firm’s success, but that analysis is beyond the scope of what we analyze here. The branch of economics called industrial organization studies many aspects of firm behavior, including product choice.

  3. For whatever quantity it makes, the firm’s goal is to minimize the cost of producing it.

    Note the assumption is not to minimize cost completely, just for a given quantity level. The firm can always reduce its total production cost by producing nothing. In building our model, we want to analyze how a firm produces a specific quantity of output. (A firm’s choice about the specific quantity of output to make depends on the characteristics of the market for its product, including the demand for the product and the number and type of its competitors. We discuss firms’ choices of output quantities in Chapter 8, Chapter 9, Chapter 10 and Chapter 11.)

    Second, cost minimization is necessary for the firm to maximize its profits, another standard assumption economists make about firm behavior. We can think of cost minimization as a first step in profit maximization. Remember, however, that we don’t need to assume a firm is maximizing profits for it to be minimizing costs. Producers such as non-profits or governments might have priorities other than profits, but they would still want to minimize their costs; they gain nothing from wasting resources to make their products.

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  4. The firm uses only two inputs to make its product: capital and labor. Capital encompasses the buildings, machinery, and raw materials needed to make the product. Labor refers to all of the human resources (such as factory workers, salespeople, and CEOs) that are used to produce the firm’s output. In building our model, we lump together all different kinds of capital under one single label, and do the same for labor.3

    short run

    In production economics, the period of time during which one or more inputs into production cannot be changed.

    fixed inputs

    Inputs that cannot be changed in the short run.

    variable inputs

    Inputs that can be changed in the short run.

    long run

    In production economics, the period of time during which all inputs into production are fully adjustable.

  5. In the short run, a firm can choose to employ as much or as little labor as it wants, but it cannot rapidly change how much capital it uses. In the long run, the firm can freely choose the amounts of both labor and of capital it employs. We will consider the short run here to be the period of time during which one or more inputs into production cannot be changed. Inputs that cannot be changed in the short run are fixed inputs; inputs that can be changed in the short run are variable inputs. The long run, then, is the amount of time necessary for all inputs to be fully adjustable; in the long run all inputs are variable. The assumption here captures the fact that it takes time to put capital into use. For example, between acquiring permits and undertaking construction, it can take many years for an electric company to build a new power plant. During this time, then, the electric company’s capital input is fixed, and we can consider this period (even though it could be several years long) as the short run in terms of the company’s production decisions. In comparison to this, the electric company and firms in general can much more easily adjust worker hours by allowing employees to leave early or asking them to work overtime. Hiring new employees and putting them to work are also relatively easy. Even though companies must take time to find and train these workers, such tasks do not usually take as long as building or integrating new capital.

  6. The more inputs the firm uses, the more output it makes. This assumption is similar to the “more is better” assumption for consumers’ utility functions that we discussed in Chapter 4. Here, the analogous implication for production is that if the firm uses more labor or capital, its total output rises.

  7. A firm’s production exhibits diminishing marginal returns to labor and capital. If the amount of capital is held constant, each additional worker eventually generates less output than the one before. The same diminishing returns exist for capital when labor is held constant. This assumption captures a basic idea of production: A mix of labor and capital is more productive than labor alone or capital alone. Capital helps workers to be productive, and vice versa. Even hundreds of workers will make little progress digging if they have no shovels to dig with. Similarly, a large amount of fancy digging equipment won’t work without people to operate it. The two inputs work best when combined in the right amounts. This assumption parallels the assumption in consumer theory that consumers derive diminishing marginal utility from additional units of each good.

  8. The firm can buy as many capital or labor inputs as it wants at fixed prices. Just as we assumed consumers could buy as much of any good as they wanted at a fixed price, we assume the firm can do the same for buying its capital and labor. Most firms are small relative to the markets for the inputs they use. Even the largest companies employ only a small fraction of an economy’s workers. Further, as long as the markets that produce a firm’s inputs are reasonably competitive, even the largest firms can likely acquire as much capital and labor as they desire at a fixed price.

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  9. If there is a well-functioning capital market (e.g., banks and investors), the firm does not have a budget constraint. As long as the firm can make profits, it will be able to obtain the resources necessary to acquire the capital and labor it needs to produce. If a firm doesn’t have the cash necessary to finance its input expenditures, it can raise funds by issuing stock or by borrowing. Outside investors should be willing to finance a firm’s expenditures if they expect it to be profitable. Notice that this assumption about a firm’s production does not have a counterpart in consumer choice theory. Consumers always have a budget constraint that limits the maximum level of utility they can obtain.

You may have noticed that there are more simplifying assumptions for the production model than for the consumption model. This is because producer behavior is a bit more complicated. For example, we need to consider producer behavior in two time frames, the short run and the long run. The added levels of complication require us to simplify things a little more.

Production Functions

A firm’s task is to turn capital and labor inputs into outputs. A production function is a mathematical relationship that describes how much output can be made from different combinations of inputs.

As noted above, we simplify things in our model of production so that we can shrink the many outputs made and inputs used by real-world firms into something that we can get a better handle on. Namely, our firm makes one product as its output and uses two inputs, capital and labor, to do so. Capital includes the equipment and structures that firms use—an enormous range of inputs, from the machinery on assembly lines, to office buildings, to the iPhone that the CEO uses to keep abreast of what’s happening at the firm while she’s on the road. Labor includes the human inputs a firm uses, ranging from miners to computer programmers to summer interns and executive vice presidents. The production function summarizes how a firm transforms these capital and labor inputs into output. A production function is a formula that describes output (which we label Q for quantity) as a function of our two inputs, capital (K) and labor (L):

Q = f(K, L)

In this production function, f is a mathematical function that describes how capital and labor are combined to produce the output. Production functions can take a form such as Q = 10K + 5L in which the inputs are separate, or Q = K0.5L0.5 (a different way of writing that would be image in which the inputs are multiplied together. They can also take many other forms depending on the technology a firm uses to produce its output. The type of production function in which capital and labor are each raised to a power and then multiplied together (as in Q = K0.5L0.5 above) is known as a Cobb–Douglas production function. It is named after mathematician Charles Cobb and University of Chicago economist (and later, U.S. Senator) Paul Douglas. The Cobb–Douglas production function is one of the most common types of production functions used by economists.