1.2 Module 18: Productivity and Growth

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The Aggregate Production Function

Productivity is higher, other things equal, when workers are equipped with more physical capital, more human capital, better technology, or any combination of the three. But can we put numbers to these effects? To do this, economists make use of the aggregate production function, which shows how productivity depends on the quantities of physical capital per worker and human capital per worker as well as the state of technology. In general, all three factors tend to rise over time, as workers are equipped with more machinery, receive more education, and benefit from technological advances.

In analyzing historical economic growth, economists have discovered a crucial fact about the estimated aggregate production function: it exhibits diminishing returns to physical capital. That is, when the amount of human capital per worker and the state of technology are held fixed, each successive increase in the amount of physical capital per worker leads to a smaller increase in productivity. Figure 18-1 and the accompanying table give a hypothetical example of how the level of physical capital per worker might affect the level of real GDP per worker, holding human capital per worker and the state of technology fixed. In this example, we measure the quantity of physical capital in dollars.

The aggregate production function shows how, in this case holding human capital per worker and technology fixed, productivity increases as physical capital per worker rises. Other things equal, a greater quantity of physical capital per worker leads to higher real GDP per worker but is subject to diminishing returns: each successive addition to physical capital per worker produces a smaller increase in productivity. Starting at the origin, 0, a $20,000 increase in physical capital per worker leads to an increase in real GDP per worker of $30,000, indicated by point A. Starting from point A, another $20,000 increase in physical capital per worker leads to an increase in real GDP per worker but only of $20,000, indicated by point B. Finally, a third $20,000 increase in physical capital per worker leads to only a $10,000 increase in real GDP per worker, indicated by point C.

To see why the relationship between physical capital per worker and productivity exhibits diminishing returns, think about how having farm equipment affects the productivity of farmworkers. A little bit of equipment makes a big difference: a worker equipped with a tractor can do much more than a worker without one. And a worker using more expensive equipment will, other things equal, be more productive: a worker with a $40,000 tractor will normally be able to cultivate more farmland in a given amount of time than a worker with a $20,000 tractor because the more expensive machine will be more powerful, perform more tasks, or both.

But will a worker with a $40,000 tractor, holding human capital and technology constant, be twice as productive as a worker with a $20,000 tractor? Probably not: there’s a huge difference between not having a tractor at all and having even an inexpensive tractor; there’s much less difference between having an inexpensive tractor and having a better tractor. And we can be sure that a worker with a $200,000 tractor won’t be 10 times as productive: a tractor can be improved only so much. Because the same is true of other kinds of equipment, the aggregate production function shows diminishing returns to physical capital.

Diminishing returns to physical capital imply a relationship between physical capital per worker and output per worker like the one shown in Figure 18-1. As the productivity curve for physical capital and the accompanying table illustrate, more physical capital per worker leads to more output per worker. But each $20,000 increment in physical capital per worker adds less to productivity. As you can see from the table, there is a big payoff for the first $20,000 of physical capital: real GDP per worker rises by $30,000. The second $20,000 of physical capital also raises productivity, but not by as much: real GDP per worker goes up by only $20,000. The third $20,000 of physical capital raises real GDP per worker by only $10,000.

By comparing points along the curve you can also see that as physical capital per worker rises, output per worker also rises—but at a diminishing rate. Going from the origin at 0 to point A, a $20,000 increase in physical capital per worker, leads to an increase of $30,000 in real GDP per worker. Going from point A to point B, a second $20,000 increase in physical capital per worker, leads to an increase of only $20,000 in real GDP per worker. And from point B to point C, a $20,000 increase in physical capital per worker increased real GDP per worker by only $10,000.

It’s important to realize that diminishing returns to physical capital is an “other things equal” phenomenon: additional amounts of physical capital are less productive when the amount of human capital per worker and the technology are held fixed. Diminishing returns may disappear if we increase the amount of human capital per worker, or improve the technology, or both at the same time the amount of physical capital per worker is increased.

For example, a worker with a $40,000 tractor who has also been trained in the most advanced cultivation techniques may in fact be more than twice as productive as a worker with only a $20,000 tractor and no additional human capital. But diminishing returns to any one input—regardless of whether it is physical capital, human capital, or number of workers—is a pervasive characteristic of production.

Growth Accounting

In practice, all the factors contributing to higher productivity rise during the course of economic growth: both physical capital and human capital per worker increase, and technology advances as well. To disentangle the effects of these factors, economists use growth accounting, which estimates the contribution of each major factor in the aggregate production function to economic growth. For example, suppose the following are true:

• The amount of physical capital per worker grows 3% a year.
• Each 1% rise in physical capital per worker, holding human capital and technology constant, raises output per worker by one-third of 1%, or 0.33%.

In that case, we would estimate that growing physical capital per worker is responsible for 3% × 0.33 = 1 percentage point of productivity growth per year. A similar but more complex procedure is used to estimate the effects of growing human capital. The procedure is more complex because there aren’t simple dollar measures of the quantity of human capital.

Growth accounting allows us to calculate the effects of greater physical and human capital on economic growth. But how can we estimate the effects of technological progress? We do so by estimating what is left over after the effects of physical and human capital have been taken into account. For example, let’s imagine that there was no increase in human capital per worker so that we can focus on changes in physical capital and in technology.

Technological progress is central to economic growth.

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In Figure 18-2, the lower curve shows the same hypothetical relationship between physical capital per worker and output per worker shown in Figure 18-1. Let’s assume that this was the relationship given the technology available in 1942. The upper curve also shows a relationship between physical capital per worker and productivity, but this time given the technology available in 2012. (We’ve chosen a 70-year stretch to allow us to use the Rule of 70.) The 2012 curve is shifted up compared to the 1942 curve because technologies developed over the previous 70 years made it possible to produce more output for a given amount of physical capital per worker than was possible with the technology available in 1942. (Note that the two curves are measured in constant dollars.)

Technological progress raises productivity at any given level of physical capital per worker, and therefore shifts the aggregate production function upward. Here we hold human capital per worker fixed. We assume that the lower curve (the same curve as in Figure 18-1) reflects technology in 1942 and the upper curve reflects technology in 2012. Holding technology and human capital fixed, tripling physical capital per worker from $20,000 to $60,000 leads to a doubling of real GDP per worker, from $30,000 to $60,000. This is shown by the movement from point A to point C, reflecting an approximately 1% per year rise in real GDP per worker. In reality, technological progress raised productivity at any given level of physical capital—shown here by the upward shift of the curve—and the actual rise in real GDP per worker is shown by the movement from point A to point D. Real GDP per worker grew 2% per year, leading to a quadrupling during the period. The extra 1% in growth of real GDP per worker is due to higher total factor productivity.

Let’s assume that between 1942 and 2012 the amount of physical capital per worker rose from $20,000 to $60,000. If this increase in physical capital per worker had taken place without any technological progress, the economy would have moved from A to C: output per worker would have risen, but only from $30,000 to $60,000, or 1% per year (using the Rule of 70 tells us that a 1% growth rate over 70 years doubles output). In fact, however, the economy moved from A to D: output rose from $30,000 to $120,000, or 2% per year. There was an increase in both physical capital per worker and technological progress, which shifted the aggregate production function.

In this case, 50% of the annual 2% increase in productivity—that is, 1% in annual productivity growth—is due to higher total factor productivity, the amount of output that can be produced with a given amount of factor inputs. So when total factor productivity increases, the economy can produce more output with the same quantity of physical capital, human capital, and labor.

Most estimates find that increases in total factor productivity are central to a country’s economic growth. We believe that observed increases in total factor productivity in fact measure the economic effects of technological progress. All of this implies that technological change is crucial to economic growth. The Bureau of Labor Statistics estimates the growth rate of both labor productivity and total factor productivity for nonfarm business in the United States. According to the Bureau’s estimates, during the past 70 years, only about half of the productivity in the economy is explained by increases in physical and human capital per worker; the rest is explained by rising total factor productivity—that is, by technological progress.

THE INFORMATION TECHNOLOGY PARADOX

From the early 1970s through the mid-1990s, the United States went through a slump in total factor productivity growth. Figure 18-3 shows Bureau of Labor Statistics estimates of annual total factor productivity growth, averaged for each 10-year period from 1948 to 2010. As you can see, there was a large fall in the total factor productivity growth rate beginning in the early 1970s. Because higher total factor productivity plays such a key role in long-run growth, the economy’s overall growth was also disappointing, leading to a widespread sense that economic progress had ground to a halt.

Source: Bureau of Labor Statistics.

Many economists were puzzled by the slowdown in total factor productivity growth after 1973, since in other ways the era seemed to be one of rapid technological progress. Modern information technology really began with the development of the first microprocessor—a computer on a chip—in 1971. In the 25 years that followed, a series of inventions that seemed revolutionary became standard equipment in the business world: computers, the Internet, cell phones, and e-mail.

Yet the rate of growth of total factor productivity remained stagnant. In a famous remark, MIT economics professor and Nobel laureate Robert Solow, a pioneer in the analysis of economic growth, declared that the information technology revolution could be seen everywhere except in the economic statistics. Why didn’t information technology show large rewards?

Paul David, a Stanford University economic historian, offered a theory and a prediction. He pointed out that 100 years earlier another miracle technology—electric power—had spread through the economy, again with surprisingly little impact on productivity growth at first. The reason, he suggested, was that a new technology doesn’t yield its full potential if you use it in old ways.

For example, a traditional factory around 1900 was a multistory building, with the machinery tightly crowded together and designed to be powered by a steam engine in the basement. This design had problems: it was very difficult to move people and materials around. Yet owners who electrified their factories initially maintained the multistory, tightly packed layout. Only with the switch to spread-out, one-story factories that took advantage of the flexibility of electric power—most famously Henry Ford’s auto assembly line—did productivity take off.

David suggested that the same phenomenon was happening with information technology. Productivity, he predicted, would take off when people really changed their way of doing business to take advantage of the new technology—such as replacing letters and phone calls with e-mail. Sure enough, productivity growth accelerated dramatically in the second half of the 1990s as companies discovered how to effectively use information technology. (The business case at the end of the section details Walmart’s innovative practices.)

What About Natural Resources?

In our discussion so far, we haven’t mentioned natural resources, which certainly have an effect on productivity. Other things equal, countries that are abundant in valuable natural resources, such as highly fertile land or rich mineral deposits, have higher real GDP per capita than less fortunate countries. The most obvious modern example is the Middle East, where enormous oil deposits have made a few sparsely populated countries very rich. For example, Kuwait has about the same level of real GDP per capita as Germany, but Kuwait’s wealth is based on oil, not manufacturing, the source of Germany’s high output per worker.

But other things are often not equal. In the modern world, natural resources are a much less important determinant of productivity than human or physical capital for the great majority of countries. For example, some nations with very high real GDP per capita, such as Japan, have very few natural resources. Some resource-rich nations, such as Nigeria (which has sizable oil deposits), are very poor.

Historically, natural resources played a much more prominent role in determining productivity. In the nineteenth century, the countries with the highest real GDP per capita were those abundant in rich farmland and mineral deposits: the United States, Canada, Argentina, and Australia. As a consequence, natural resources figured prominently in the development of economic thought.

In a famous book published in 1798, An Essay on the Principle of Population, the English economist Thomas Malthus made the fixed quantity of land in the world the basis of a pessimistic prediction about future productivity. As population grew, he pointed out, the amount of land per worker would decline. And this, other things equal, would cause productivity to fall.

His view, in fact, was that improvements in technology or increases in physical capital would lead only to temporary improvements in productivity because they would always be offset by the pressure of rising population and more workers on the supply of land. In the long run, he concluded, the great majority of people were condemned to living on the edge of starvation. Only then would death rates be high enough and birth rates low enough to prevent rapid population growth from outstripping productivity growth.

It hasn’t turned out that way, although many historians believe that Malthus’s prediction of falling or stagnant productivity was valid for much of human history. Population pressure probably did prevent large productivity increases until the eighteenth century. But in the time since Malthus wrote his book, any negative effects on productivity from population growth have been far outweighed by other, positive factors—advances in technology, increases in human and physical capital, and the opening up of enormous amounts of cultivatable land in the New World.

Is World Growth Sustainable?

Some skeptics have expressed doubt about whether sustainable long-run economic growth is possible—whether it can continue in the face of the limited supply of natural resources and the impact of growth on the environment.

In 1972 a group of scientists made a big splash with a book titled The Limits to Growth, which argued that long-run economic growth wasn’t sustainable due to limited supplies of nonrenewable resources such as oil and natural gas.

These concerns at first seemed to be validated by a sharp rise in resource prices in the 1970s, then came to seem foolish when resource prices fell sharply in the 1980s. After 2005, however, resource prices rose sharply again, leading to renewed concern about resource limitations to growth. Figure 18-4 shows the real price of oil—the price of oil adjusted for inflation in the rest of the economy. The rise, fall, and rise of concern about resource-based limits to growth have more or less followed the rise, fall, and rise of oil prices shown in the figure.

The real price of natural resources, like oil, rose dramatically in the 1970s and then fell just as dramatically in the 1980s. Since 2005, however, the real prices of natural resources have soared.

Sources: Energy Information Administration; Bureau of Labor Statistics.

Differing views about the impact of limited natural resources on long-run economic growth turn on the answers to the following three questions:

1. How Large are The Supplies of Key Natural Resources?It’s mainly up to geologists to answer this question. And the response changes as new technologies, such as hydraulic fracking, are developed, allowing access to previously inaccessible oil and natural gas resources. Unfortunately, there’s wide disagreement among the experts, especially about the prospects for future oil production.

Some analysts believe that there is enough untapped oil in the ground that world oil production can continue to rise for several decades. Others, including a number of oil company executives, believe that the growing difficulty of finding new oil fields will cause oil production to plateau—that is, stop growing and eventually begin a gradual decline—in the fairly near future. Some analysts believe that we have already reached that plateau.

2. How Effective Will Technology Be At Finding Alternatives to Natural Resources?This question will have to be answered by engineers. There’s no question that there are many alternatives to the natural resources currently being depleted, some of which are already being exploited. For example, oil extracted from Canadian tar sands is making a significant contribution to world oil supplies, and the amount of electricity generated by wind and solar power continues to grow.

3. Can Long-Run Economic Growth Continue in The Face of Resource Scarcity?This is mainly a question for economists. And most, though not all, economists are optimistic: they believe that modern economies can find ways to work around limits in the supply of natural resources. One reason for this optimism is the fact that resource scarcity leads to high resource prices. These high prices in turn provide strong incentives to conserve the scarce resource and to find alternatives.

For example, after the sharp oil price increases of the 1970s, American consumers turned to smaller, more fuel-efficient cars, and U.S. industry also greatly intensified its efforts to reduce energy bills. The result is shown in Figure 18-5, which compares U.S. real GDP per capita and oil consumption before and after the 1970s energy crisis. In the United States before 1973, there seemed to be a more or less one-to-one relationship between economic growth and oil consumption.

Until 1973, the real price of oil was relatively cheap and there was a more or less one-to-one relationship between economic growth and oil consumption. Conservation efforts increased sharply after the spike in the real price of oil in the mid-1970s. Yet the U.S. economy was still able to deliver growth despite cutting back on oil consumption.

Sources: Energy Information Administration; Bureau of Economic Analysis.

One response to resource scarcity.

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However, after 1973 the U.S. economy continued to deliver growth in real GDP per capita even as it substantially reduced the use of oil. This move toward conservation paused after 1990, as low real oil prices encouraged consumers to shift back to gas-guzzling larger cars and SUVs. But a sharp rise in oil prices since 2005 encouraged renewed shifts toward oil conservation.

Given such responses to prices, economists generally tend to see resource scarcity as a problem that modern economies handle fairly well, and so not as a fundamental limit to long-run economic growth. Environmental issues, however, pose a more difficult problem because dealing with them requires effective political action.

Economic Growth and the Environment

Economic growth, other things equal, tends to increase the human impact on the environment. For example, China’s spectacular economic growth has also brought a spectacular increase in air pollution in that nation’s cities. But again, other things aren’t necessarily equal: countries can and do take action to protect their environments.

In fact, air and water quality in today’s advanced countries is generally much better than it was a few decades ago. London’s famous “fog”—actually a form of air pollution, which killed more than 4,000 people during a two-week episode in 1952—is gone, thanks to regulations that virtually eliminated the use of coal heat. The equally famous smog of Los Angeles, although not extinguished, is far less severe than it was in the 1960s and early 1970s, again thanks to pollution regulations.

Despite these past environmental success stories, there is widespread concern today about the environmental impacts of continuing economic growth, reflecting a change in the scale of the problem. Environmental success stories have mainly involved dealing with local impacts of economic growth, such as the effect of widespread car ownership on air quality in the Los Angeles basin. Today, however, we are faced with global environmental issues—the adverse impacts on the environment of the Earth as a whole by worldwide economic growth.

The biggest of these issues involves the impact of fossil-fuel consumption on the world’s climate. Burning coal and oil releases carbon dioxide into the atmosphere. There is broad scientific consensus that rising levels of carbon dioxide and other gases are causing a greenhouse effect on the Earth, trapping more of the sun’s energy and raising the planet’s overall average temperature. And rising temperatures may impose high human and economic costs: rising sea levels may flood coastal areas; changing climate may disrupt agriculture, especially in poor countries; and so on.

The problem of climate change is clearly linked to economic growth. Figure 18-6 shows carbon dioxide emissions from the United States, Europe, and China since 1980. Historically, the wealthy nations have been responsible for the bulk of these emissions because they have consumed far more energy per person than poorer countries. As China and other emerging economies have grown, however, they have begun to consume much more energy and emit much more carbon dioxide.

Greenhouse gas emissions are positively related to growth. As shown here by the United States and Europe, wealthy countries have historically been responsible for the great bulk of greenhouse gas emissions because of their richer and faster-growing economies. As China and other emerging economies have grown, they have begun to emit much more carbon dioxide.

Source: Energy Information Administration.

Is it possible to continue long-run economic growth while curbing the emissions of greenhouse gases? The answer, according to most economists who have studied the issue, is yes. It should be possible to reduce greenhouse gas emissions in a wide variety of ways, ranging from the use of non-fossil-fuel energy sources such as wind, solar, and nuclear power, to preventive measures such as capturing the carbon dioxide from power plants and storing it, to simpler things like designing buildings so that they’re easier to keep warm in winter and cool in summer. Such measures would impose costs on the economy, but the best available estimates suggest that even a large reduction in greenhouse gas emissions over the next few decades would only modestly dent the long-term rise in real GDP per capita.

The big question is how to make all of this happen. Unlike resource scarcity, environmental problems don’t automatically provide incentives for changed behavior. Pollution is an example of a negative externality, a cost that individuals or firms impose on others without having to offer compensation. In the absence of government intervention, individuals and firms have no incentive to reduce negative externalities, which is why it took regulation to reduce air pollution in America’s cities.

So there is a broad consensus among economists—although there are some dissenters—that government action is needed to deal with climate change. There is also broad consensus that this action should take the form of market-based incentives, either in the form of a carbon tax—a tax per unit of carbon emitted—or a cap and trade system in which the total amount of emissions is capped, and producers must buy licenses to emit greenhouse gases. There is, however, considerable dispute about how to proceed.

Emissions from coal-fired municipal heating systems contribute to the heavy smog that has become a problem in many Chinese cities.

ChinaFotoPress/Getty Images

There are also several aspects of the climate change problem that make it much more difficult to deal with than, say, smog in Los Angeles. One is the problem of taking the long view. The impact of greenhouse gas emissions on the climate is very gradual: carbon dioxide put into the atmosphere today won’t have its full effect on the climate for several generations. As a result, there is the political problem of persuading voters to accept pain today in return for gains that will benefit future generations.

There is also a difficult problem of international burden sharing. As Figure 18-6 shows, rich economies have historically been responsible for most greenhouse gas emissions, but newly emerging economies like China are responsible for most of the recent growth. Inevitably, rich countries are reluctant to pay the price of reducing emissions only to have their efforts frustrated by rapidly growing emissions from new players. At the same time, countries like China, which are still relatively poor, consider it unfair that they should be expected to bear the burden of protecting an environment threatened by the past actions of rich nations.

The general moral of this story is that it is possible to reconcile long-run economic growth with protecting the environment. The main question is one of getting political consensus around the necessary policies.

Module 18 Review

Check Your Understanding

Assume that between 1942 and 2012:

• The amount of physical capital per worker grows at 2% per year.
• Each 1% rise in physical capital per worker (holding human capital and technology constant) raises output per worker by ½ of a percent, or 0.5%.
• There is no growth in human capital.
• Real GDP per capita rises from $30,000 to $60,000.

PITFALLS: IT MAY BE DIMINISHED…BUT IT’S STILL POSITIVE

IT MAY BE DIMINISHED…BUT IT’S STILL POSITIVE

If there are diminishing returns to physical capital per worker, does it mean that GDP per worker is falling?

NO, it does not. An increase in physical capital per worker will never reduce productivity. but due to diminishing returns, at some point increasing the amount of physical capital per worker will no longer produce an economic payoff: at that point, the increase in output will be so small that it won’t be worth the cost of the additional physical capital.

To answer the question, keep in mind what diminishing returns to physical capital per worker means and what it doesn’t mean. As we’ve seen, it is an “other things equal” statement: holding the amount of human capital per worker and the technology fixed, each successive increase in the amount of physical capital per worker results in a smaller increase in real GDP per worker. But this doesn’t mean that real GDP per worker eventually falls as more and more physical capital is added. It’s just that the increase in real GDP per worker gets smaller and smaller, while remaining at or above zero.

To learn more, see pages 179–181.