Toolkit: Section 16.15 "The Aggregate Production Function"
The aggregate production function describes how aggregate output (real gross domestic product [real GDP]) in an economy depends on available inputs. The most important inputs are as follows:
- Physical capital: machines, production facilities, and so forth used in production
- Labor: the number of hours that are worked in the entire economy
- Human capital: the skills and education embodied in the work force of the economy
- Knowledge: the blueprints that describe the production process
- Natural resources: oil, coal, and other mineral deposits; agricultural and forest lands; and other resources
- Social infrastructure: the general business climate, the legal environment, and any relevant features of the culture
Output increases whenever there is an increase in one of these inputs, all else being the same.
Physical capital refers to goods—such as factory buildings, machinery, and 18-wheel trucks—that have two essential features. First, capital goods are used in the production of other goods. The production of physical capital does not increase our well-being in and of itself. It allows us to produce more goods in the future, which permits us to enjoy more consumption at some future date. Second, capital goods are long lasting, which means we accumulate a capital stock over time. Capital goods are thus distinct from intermediate goods, which are fully used up in the production process.
The capital stock of an economy is the total amount of physical capital in the economy. As well as factories and machines, the capital stock includes physical infrastructure—road networks, airports, telecommunications networks, and the like. These are capital goods that are available for multiple firms to use. Sometimes these goods are supplied by governments (roads, for example); sometimes they are provided by private firms (cellular telephone networks are an example). For brevity, we often simply refer to “capital” rather than “physical capital.” When you see the word capital appearing on its own in this book you should always understand it to mean physical capital.
Labor hours are the total number of hours worked in an economy. This depends on the size of the workforce and on how many hours are worked by each individual. [***We use the term workforce rather than labor force deliberately because the term labor force has a precise definition—those who are unemployed as well as those who are working. We want to include only those who are working because they are the ones supplying the labor hours that go into the production function. Chapter 8 "Jobs in the Macroeconomy" discusses this distinction in more detail.***]
Human capital is the term that economists use for the skills and training of an economy’s workforce. It includes both formal education and on-the-job training. It likewise includes technical skills, such as those of a plumber, an electrician, or a software designer, and managerial skills, such as leadership and people management.
Knowledge is the information that is contained in books, software, or blueprints. It encompasses basic mathematics, such as calculus and the Pythagorean theorem, as well as more specific pieces of knowledge, such as the map of the human genome, the formula for Coca-Cola, or the instructions for building a space shuttle.
Natural resources include land; oil and coal reserves; and other valuable resources, such as precious metals.
Social infrastructure refers to the legal, political, social, and cultural frameworks that exist in an economy. An economy with good social infrastructure is relatively free of corruption, has a functional and reliable legal system, and so on. Also included in social infrastructure are any relevant cultural variables. For example, it is sometimes argued that some societies are—for whatever reason—more entrepreneurial than others. As another example, the number of different languages that are spoken in a country influences GDP.
We show the production function schematically in ***Figure 5.2 "The Aggregate Production Function".
The idea of the production function is simple: if we put more in, we get more out.
- With more physical capital, we can produce more output. If you want to dig a foundation for a house, you will be more productive with a backhoe than a shovel; if you want to deliver documents from Chicago to St. Louis, you will be more productive using a truck than a bicycle.
- With more labor hours, we can produce more output. If there are more workers in an economy, or if they work longer hours, the economy will produce more real GDP.
- With more education and skills, we can produce more output. Skilled workers can produce more from an hour’s work than unskilled workers can produce.
- With more knowledge, we can produce more output. Inventions and innovations make an economy more productive.
- With more natural resources, we can produce more output. For example, if an economy discovers additional oil reserves, it can produce more with given labor and capital than can economies without such resources. Of course, this input more often decreases rather than increases over time, as economies use up their existing stocks of natural resources.
- With better institutions, we can produce more output. Economies in which it is easy to establish businesses, where corruption is limited, and where the laws are reliable get more out of their workers and capital.
We call the extra output that we get from one more unit of an input, holding all other inputs fixed, the marginal product of that input. For example, the extra output we obtain from one more unit of capital is the marginal product of capital, the extra output we get from one more unit of labor is the marginal product of labor, and so on.
Physical capital and labor hours are relatively straightforward to understand and measure. To measure labor hours, we simply count the number of workers and the number of hours worked by an average worker. Output increases if we have more workers or if they work longer hours. For simplicity, we imagine that all workers are identical. Aggregate differences in the type and the quality of labor are captured in our human capital variable. For physical capital, we similarly imagine that there are a number of identical machines (pizza ovens). Then, just as we measure labor as the number of worker hours, so also we could measure capital by the total number of machine hours. [***If this were literally true, we could measure capital stock by simply counting the number of machines in an economy. In reality, however, the measurement of capital stock is trickier. Researchers must add together the value of all the different pieces of capital in an economy. In practice, capital stock is usually measured indirectly by looking at the flow of additions to capital stock.***] We can produce more output by having more machines or by using each machine more intensively. The other inputs that we listed—human capital, knowledge, social infrastructure, and natural resources—are trickier to define and much harder to quantify. Economists have used measures of educational attainment (e.g., the fraction of the population that completes high school) to compare human capital across countries. [***We use an index of human capital in Chapter 6 "Global Prosperity and Global Poverty".***] There are likewise some data that provide some indication of knowledge and social infrastructure—such as spending on research and development (R&D) and survey measures of perceived corruption.
The measurement of natural resources is problematic for different reasons. Land is evidently an input to production: factories must be put somewhere, and agriculture requires fields and orchards, so the value of land can be measured in principle. But what about reserves of oil or underground stocks of coal, uranium, or gold? First, such reserves or stocks contribute to real GDP only if they are extracted from the earth. An untapped oil field is part of a nation’s wealth but makes no contribution to current production. Second, it is very hard to measure such stocks, even in principle. For example, the amount of available oil reserves in an economy depends on mining and drilling technologies. Oil that could not have been extracted two decades ago is now available; it is likely that future advances in drilling techniques will further increase available reserves in the economy.
We simply accept that, as a practical matter, we cannot directly measure an economy’s knowledge, social infrastructure, and natural resources. As we see later in this chapter, however, there is a technique for indirectly measuring the combined influence of these inputs.
One thing might strike you as odd. Our description of production does not include as inputs the raw materials that go into production. The production process for a typical firm takes raw materials and transforms them into something more valuable. For example, a pizza restaurant buys flour, tomatoes, pepperoni, electricity, and so on, and transforms them into pizzas. The aggregate production function measures not the total value of these pizzas but the extra value that is added through the process of production. This equals the value of the pizzas minus the value of the raw materials. We take this approach to avoid double counting and be consistent with the way real GDP is actually measured. [***Reserves of natural resources are not counted as raw materials. The output of the mining sector is the value of the resources that have been extracted from the earth.***]
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