Structure of Production: Stages of Capital
Production of the temple was a hugely complex task, and the result was highly commended by both God and man. God chose to ensure that the description of the building process occupied several chapters of the Bible, suggesting its importance.
Yet as complex as this task was, Solomon was not building a temple in the manner Robinson Crusoe would have—he didn’t start from scratch. He was able to rely on many institutions and resources that were previously available. Why was there a saw available to cut timber? Why were there boats available to ship the timber from Lebanon down to Israel? How did Hiram know the value of wheat against the timber he was asked to trade for? As we focus on the specific factors of production in this chapter, do not forget they are applied in a given institutional setting (legal framework, tax laws, morals, culture, norms/values, etc.) which will significantly alter how productive a given set of factors can be employed. For example, the former Soviet Union had land, labor, and capital, but its lack of entrepreneur-friendly institutions was a large contributor to its ultimate failure.
Neither the institutions of market exchange nor the capital equipment of saws, hammers, and boats were initiated with any expectation of Solomon’s requirement to build a temple; yet they were there and indispensable to its creation. In the production process, we begin to see a whole hierarchy of production activities that support the ultimate consumer’s goods that you and I purchase and use.
Consider the temple as a final good, a good of the first order—something that is used for its own sake and not to produce something else. This is a consumer good; we use and buy them routinely. The house you live in, the car you drive or ride in, the iPod you listen to, the TV you watch—these are all goods of the first order, or consumer goods. They are goods used in immediate satisfaction of human wants.
All of these first order goods are dependent upon higher order goods that are used to produce them. For instance, most of our houses have a refrigerator. All of our refrigerators have compressors. All of our compressors have a metal case. All the metal cases were fashioned from some metal ore product. The entire metal ore product was mined. All the mines used tractors. All the tractors had tires…etc. Obviously this process goes on and on and on. There are whole series of spider web relationships and interdependencies between various products and goods. I recently took up the hobby of metalwork and welding. I have a welder, but it is a higher order good; I don’t value the welder for the welder’s sake, but rather the products that I can produce with it. Further, I value the welder not only according to the value of the finished product, but also complementary goods that are necessary to produce the final product. Were the price of steel to astronomically skyrocket, the value I would place on the welder would go down, since I would not have anything on which to weld.
Figure 7.3 and Figure 7.4 provide two different ways to think about the structure of production in practice. In Figure 7.3, we see that consumer goods are the lowest order good, with capital goods as increasingly higher order goods the further they are from the final consumer good production. For each final consumer good (goods of the first order) there are multiple capital goods at each stage of production. In our example of Solomon’s Temple, we see that the 2nd stage of production requires both finished timbers and cut stones, while the 3rd stage of production (further away from the final consumer good of the temple) had raw cut logs and stones. Further back from these were saws and axes used in the cutting of saw logs.
Figure 7.4 illustrates a slightly different way of thinking about the same thing. The most basic of materials are the raw commodities that come from land; they are usually the highest order good because they are the furthest away from being a consumer good. Those commodities are acted upon by manufacturers, who add both value and time to the production process by shaping the raw commodities into something closer to a final consumer’s good. Perhaps iron ore is processed in steel, and subsequently fashioned into a fender that you will use to replace the one you dented. The wholesale trade will both (1) take more time, and (2) provide additional value by grouping the assets in a way that makes it easier to ultimately get in the hands of a consumer. Recall from our discussion of the middleman in the last chapter that every stage is involved in production— they are part of an overall production process that ultimately delivers a finished good or service in the way a consumer wants it. That final stage is for goods to enter retail stores where consumers may purchase them.
Derived Factor Demand
As we see the interrelationships between various levels of goods and final consumer products, we begin to see that the value we place on higher order goods is inextricably linked to the value we place on the goods of the 1st order (final consumer goods). Imagine a consumer good with only one higher order good; for arguments sake let’s say that a type of apple is the final consumer good and the higher order good is the corresponding apple tree. This particular apple is "mushy," and prone to spoil quickly. Now assume researchers have come up with a new tree that produces very crisp, sweet apples that don’t spoil, such that the demand for the original mushy apple drops dramatically. What will happen to the demand for the mushy apple fruit tree? Of course, as we learned in our chapter on demand, demand for any good depends on complements and substitutes. But in this case, the substitution effect is in the final consumer good (the apple); there is no substitution effect here with the tree—no substitute that can also produce mushy apples. But as your intuition undoubtedly tells you, the demand for fruit trees that produce mushy apples will go down when the demand for mushy apples goes down.
Higher order goods derive their value from the value placed on the goods they are able to produce. For example, in the recent recession, demand for houses went down and the prices for commodities such as copper (for plumbing) also went down. As consumers, we don’t usually value copper directly, but indirectly through the value we place on products that use copper. This logic applies to the demand for all of the factors of production. Land, labor, capital, and entrepreneurship all derive their exchange value from the value of the products that they produce. We call this derived demand, since our demand for any of the factors of production is derived from the products they produce. How does this work out in practice? What do you think happened to the demand for blacksmiths vs. the demand for auto assemblers during the early 1900s? As the demand for horseshoe service fell and the demand for automobiles rose, we can understand that the derived demand for supporting labor in each category fell (horseshoe service) and rose (automobiles). Blacksmiths saw their income fall, and automobile assemblers saw their income rise as demand for the products they produced changed.
The derived factor demand helps explain some of the "injustices" we see in the labor market. Why are doctors paid so well, and veterinarians are paid quite a bit less? The answer is that as much as we love our pets, we don’t value their medical care nearly as much as we value our family’s medical care. If the vet told you that your dog had cancer and needed a $50,000 treatment process for a possible cure (but Fido might still die), very few of you would spend it. Yet, if a family member were similarly diagnosed, you’d do whatever you could to raise the money. Consequently, veterinarians are paid much less than medical doctors. Why are teachers paid less than rock stars? Supply and demand for each labor market in part explains it, but the demand in the labor market is derived from how highly we value the consumer good or service that labor produces.
Let's narrow our focus on production to create a simple economic model. Assume that Megan is an entrepreneur, and she has her own (fixed) entrepreneurial skill and land. She can adjust the amount of labor or capital she wants to put into her business. The simple model would be:
"Q," here, stands for the amount of goods she is able to produce and capital (K), which means that there is a positive relationship to capital and/or labor with output. So increasing either capital or labor (or both) will increase output, while decreasing either input (or both) will reduce output. The right hand side of the equation simply means that the product is a function (f) of the amount of labor (L) and capital (K).
Let’s say Megan’s business is a new competitor to SUBWAY, where she can employ workers (L) and/or purchase machinery (K) to make sandwiches. We don’t need to be specific on what type of capital; in her world it could include toasters, electric knives, perhaps a moving sandwich line which automatically adds condiments. Let’s simply assume that she currently has five units of capital and three workers, and therefore she is able to produce 300 sandwiches per day. If Megan wants to increase her production, she can hire more workers, buy more efficient machinery, or some combination of both options. If she hires another worker, she might be able to produce 125 more sandwiches, for a total of 425. Hiring a fifth might yield 75 more sandwiches, and a sixth an additional 25. Can you think why subsequent workers don’t produce as many additional sandwiches as earlier workers? Production is subject to the law of diminishing returns, where adding more of one input while keeping others fixed will ultimately lead to increased output at a diminishing rate. The law of diminishing returns is operative over the short run, when at least one productive input is fixed.
When an entrepreneur adds more labor to the sandwich line without more equipment, the workers have to share both the equipment and the work space to operate. Additional workers lead to more sandwiches, but less additional sandwiches with each additional worker. We call this the diminishing marginal product of labor (MPL). At some point, there may be so many workers behind the counter that they are simply in each other’s way, and each marginal (additional) worker actually causes a decrease in production output.
The same thing will happen with capital. Initially adding more capital will result in increased production, perhaps at an increasing rate because of the gains from specialization as the capital may allow each worker to concentrate on a specific task. But eventually, without adding more workers to operate the machines, the returns will begin to decrease and we will see diminishing marginal product of capital (MPK). Graphically we can see how this operates in Figure 7.5. As Megan increases the number of workers (or alternatively capital), while holding all other production inputs fixed, we see that the total product (sandwich output) increases. Adding more and more workers initially leads to output gains at an increasing rate due to gains from specialization as shown by the curve rising at an increasing rate. Eventually, however, successive gains begin to get smaller and smaller due to the law of diminishing returns, as shown by the increase growing at a slower rate (the curve flattens out).
How does Megan know whether it would be more profitable to add another unit of machinery or another worker? She would need to compare the marginal product (additional output from adding one more unit of labor or capital) of each, divided by the cost of one more unit. This provides a way to compare each of the two inputs; you can think of it as the best “bang for the buck.” For example, an additional worker may cost $1,500 per month, while creating 500 sandwiches per month. A new automated condiment dispenser may have a cost of $5,000 per month but allow an additional 2,000 sandwiches per month in production. So the marginal product of labor divided by its price is less than the marginal product of capital divided by its price.
The relative price of capital is less than the relative price of labor since the output per dollar is higher with an investment in capital. Megan should therefore expand with capital rather than labor.
The important point here is not necessarily the calculation itself, but rather that you understand that the various inputs to the production process can often be substitutes for one another. The relative price of each will determine the demand for each factor. Thus, any change in either the costs or productivity of each factor will eventually lead to a change in the production process as entrepreneurs seek to maximize their profits.
Returns to Scale
Our initial production function allows us to model what one firm could do to produce goods and services, and we begin to see the tradeoff between productive inputs. Yet another question may quickly come to mind: how big should the firm be? Or what should the scale of production be? This can be more formally treated with the concept of returns to scale. Let’s say General Motors wants to build a new car such as they did in 2016 with the new Camaro SS. Demand is expected to be high, and they’d like to build 300,000 units each year. Should they build one large factory, and produce them all? Or should they build three smaller factories and have them build 100,000 units each? Or should they have one factory in each state and build 6,000 cars each?
If GM has 100,000 plants, each producing three cars per year, there is a lot of overhead in order to maintain all the different buildings. GM would only have a few workers in each "plant" (more like a garage!), and each worker would have to perform many parts of the production process. Imagine all the extra delivery work to supply the parts to all those "plants." By increasing the scale of production to only three plants, each producing 100,000 cars, GM is able to concentrate its managerial focus on how to use the resources in those three plants. The workers are able to specialize in a given task and become very efficient. Their increased efficiency will result in additional production as well as higher quality—the benefits of increasing returns to scale. It’s possible that a single plant may be even more efficient, or conversely, the span of control might be too much and it might be less efficient. Or there might not be enough quality workers at one location, and it is better to have plants in multiple locations. Entrepreneurs have a financial incentive to size their production facilities at the optimal size; you can bet they will carefully consider this choice.
There are three types of returns to scale that we might see (and the mathematical formulas which express them):
- Constant Returns to Scale
- Increasing Returns to Scale
- Decreasing Returns to Scale
If a company (1) faces constant returns to scale, as it doubles its productive inputs, its output will exactly double, (i.e., 2Q = f(2L,2K)). This might be the case where there are no resource conflicts (i.e., all the productive inputs are readily available on the market at the same price and capability). This gets more and more difficult as a firm’s size increases. With (2) increasing returns to scale, as a company doubles productive inputs, output will more than double, or 2Q < f(2L,2K). This would be the case where the business sees gains from specialization from the division of labor, and is able to use more specialized capital equipment. Smaller firms may especially find increasing returns to scale. Finally, (3) decreasing returns to scale occur when increasing the productive inputs will lead to a less than proportional increase in output, or 2Q > f(2L,2K). All firms will eventually get to the point of decreasing returns to scale due to diminishing returns to the quality of productive inputs.
We may not see decreasing returns in practice; demand may not require high enough production to get to that point. But the conceptual law is still there: we know logically that eventually production would require inferior inputs resulting in decreased gains. You can think of any number of reasons why: the additional workers may not have the same skill level as the initial workers; the facility may not be in as good an area; or capital may not be as readily available or in the same quality as it was initially. This is a natural result of the fact that when an entrepreneur builds the first factory, he or she will pick the expected best location first— the best of every productive input at the cheapest cost to make sure this first factory is a success. Just as with the gains from specialization, it is possible that initial factory increases could lead to increased production at an increasing rate due to lessons learned in how to build and equip a factory. Eventually, however, the inputs used at subsequent factories will be less efficient than prior inputs, as illustrated in Figure 7.6.
The concept of returns to scale helps us think about how productive efficiency may change depending on the scale of production. But another aspect of the size of a firm is also crucial for entrepreneurs: the size of the firm may drive differential cost structures. If a firm’s costs falls per unit of production, we say a firm is experiencing economies of scale. Many firms find this to be true—if they can buy resource inputs in bulk they can bargain for a cheaper price. Or similarly, if they can contract for a sustained rate of purchase they can likewise obtain a lower price. For example, United Airlines may contract with Boeing to purchase ten 777 aircrafts per year for the next ten years. This allows Boeing to likewise "right size" its production and gain efficiencies. Firms also become more efficient as they grow by spreading fixed costs across more units that are produced. If a firm sees costs rising as production increases, we say that firm is experiencing diseconomies of scale. Diseconomies of scale can be the result of increased communication costs, additional layers of management, or any other bureaucratic inefficiency. As firms get larger and larger, it becomes harder to innovate and gain approval through additional layers of management that often accompanies growth. In some cases, it may not be bureaucracy, but rather the difficulty in scaling inputs. Many fine artisans do not become a chain; they cannot duplicate the original genius at similar costs. For example, you can get your car painted at any Maaco nationwide, but getting Chip Foose to overhaul your ’55 Chevy will be difficult!
Both returns to scale and economies to scale are important for firms to consider; returns to scale capture how efficiently a firm can produce as it grows larger, and economies of scale capture the costs of growing larger. They are obviously similar concepts, and yet distinct—entrepreneurs must consider both.
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