Economic Growth in the Long Run

Economic wealth grows as the economy grows. All the conveniences and benefits of modern life, such as entertainment, fast and efficient transportation and communications, advanced healthcare, and a longer and healthier life, are all possible because of the economy. And the benefits continue to accrue as the economy grows. Economic growth expands the production possibilities frontier, which is simply the possible combinations of output that can be produced with the given resources and technology available. Economic growth increases living standards, increasing the real GDP per capita, but only if the output is distributed equitably.

Brief History of Economic Growth

Before 1750, the economy was mostly agrarian, since technology was primitive, almost everyone was needed to produce enough food to survive. Then, in England, starting in 1750, new inventions greatly increased the productivity of agriculture and textiles, providing more efficient methods of farming, spinning, and weaving. Since a smaller portion of the population was needed for agriculture and textiles, much of the rural agrarian society was transforming into an urban industrial society, allowing workers to produce many more things other than food.

Advances in metallurgy, especially steel production, greatly enhanced manufacturing in many areas. The invention of the telegraph in the 1800s and the telephone a few decades later allowed much faster communication than what was previously possible, allowing worldwide trade, which enabled economies to profit from the comparative advantages of different countries.

Nowadays, technology is improving much more rapidly than any time in history, especially with the advent of the Internet, computerization, robotics, and artificial intelligence, which will improve productivity in every area of the economy. Indeed, robotics and artificial intelligence may eliminate the need for labor.

Pace of Economic Growth

Worldwide statistics clearly show that small economies grow faster than larger economies, not only because they are growing from a smaller base, but also because they can learn about new technologies from advanced economies, without having to fund their own research and development. Indeed, many investors in the modern economies invest in emerging economies simply because such investments can yield a higher return that would be likely in the slower growing larger economies. However, economic growth eventually converges to a steady-state, ranging from about 2% to 4% annually.

The growth rate of the economy can make a major difference in the well-being of its citizens. For instance, an economy growing 2% will double in 35 years and double again in another 35 years. An economy growing at 3% will double in 23 years 4 months, resulting in a octupling within the same 70 years, which is slightly less than an average lifespan. The economy will be twice as large with a mere 1% increase in the growth rate. Hence, economists would like to know what causes economic growth, how it can be accelerated, and what are the best policies promoting growth.

Economic Growth Models

Economic growth occurs through the acquisition of more resources or by discovering how to use available resources more efficiently. Thomas Malthus, and David Ricardo, who were early economists, thought that economic growth would be limited by the supply of land, because the marginal utility of land would decrease as less productive land must be used. However, they could not foresee how technology would alleviate many of the problems in agriculture nor did they foresee the enormous expansion of the nonagricultural economy.

The basic model of economic growth is based on the Solow-Swan model of economic growth, 1st published independently by Robert Solow and Trevor Swan in 1956.

Economic Growth Depends on Increases in Capital and Labor

Economic growth depends on business growth. Businesses want to grow to maximize profits. Businesses use capital and labor to produce their output.

Because labor and capital produce economic output, economic growth obviously depends on increases in capital and labor. It also depends in the productivity of the inputs. The productivity of an input is the amount of output produced per unit of input, and can be increased by technological improvements, economies of scale, and advances in knowledge.

Labor productivity is often measured as output per worker-hour, which is the amount of output produced by an average worker in 1 hour.

Capital can be classified as physical capital or human capital. Physical capital is the equipment and structures used in the production of products and services. Human capital is the knowledge and skills acquired through education, training, and experience which allows workers to produce products and services.

An obvious example of physical capital is the infrastructure of modern economies, including roads, bridges, the electrical grid, and the energy distribution infrastructure. Without this physical capital, labor productivity would be considerably less.

Human capital is also a major source of economic growth. Human capital is increased with schooling, on-the-job training, vocational training programs, and college education.

Capital has been increasing much faster than labor recently, a pace that will only accelerate with the development of robotics and artificial intelligence. Since population is slowing in most modern parts of the world, most of the future productivity will come from the investment of physical and human capital.

Other Factors Affecting Economic Growth

Although capital and labor are the major determinants of economic growth, other factors may also affect the growth rate. Weather can affect productivity, especially in agriculture. Major disasters, such as earthquakes and hurricanes can also reduce economic growth temporarily, but usually leads to greater economic growth for some time thereafter, as the population rebuilds.

Major impediments to growth could be the result of political mismanagement and mismanaging the economy, where the output is less than the full potential.

Production Function, Marginal Product of Capital and Labor

The aggregate production function represents the relationship between the GDP (Y) and the inputs of labor (L) and capital (K).

Y = F(K, L)

Under this simple model, increases in output depend on increases in labor and capital. If both are doubled, then output is doubled:

2Y = F(2K, 2L)

However, if either capital or labor is increased while the other factor input remains constant, then there will be diminishing returns for each unit input of the increasing factor. The marginal product of capital (MPK) is the additional output created by additional capital while keeping labor constant.

As long as the increases in profit exceed the additional cost of capital, a business can increase its profit by increasing its capital. However, if labor is constant, then the marginal product of capital will increase quickly at 1st, but then level off, until there are no additional increases in profits. This occurs because labor becomes more productive with capital, but only up to a certain point. Thereafter, profits can only be increased by also increasing labor.

Since labor is an input to any business, labor also has a marginal product, referred to, naturally enough, as the marginal product of labor (MPL), which is the additional output that can be created with increased labor while keeping capital constant. As with capital, profits can be increased with additional labor as long as the marginal product of labor exceeds its cost, which are workers' wages.

Graph showing output per worker or per unit of capital while the other input is held constant.
There is always a diminishing marginal return when increasing capital per worker or increasing the number of workers per unit of capital.

Comparing the output of labor and capital to its costs shows an optimal combination of inputs that will yield the highest profits. Thus, business profits can be maximized when the capital-to-labor ratio (k) is optimized.

Graph showing the steady-state equilibrium of output per worker when the investment in capital per worker equals its rate of depreciation.
A steady-state equilibrium is reached when the capital investment per worker equals the rate of its depreciation.


Capital Formation Depends on Savings, Investments, and Depreciation

GDP depends on household consumption, business investment, government expenditures, and international trade:

Y = C + I + G + NX

Over the long run, imports and exports can be assumed to net to 0; otherwise, trade surpluses or deficits would increase indefinitely, which is not tenable, so the above equation can be simplified by eliminating NX.

GDP can also be measured in terms of what households do with their income: spend for consumer goods, pay taxes, and save:

Y = C + T + S

Hence, funding for business investments will depend on the amount of household savings. Since households only have so much money, and tax rates are set by the government, there is a trade-off between consumption and saving. The more household consumes, the less it saves, leaving less funds for investment.

Private savings is also supplemented by public savings. The government invests some of the tax money, such as for the national infrastructure, i.e., roads, bridges, and water supplies and waste disposal. Governments also pay for research and development, especially for those projects that would not otherwise be financed by private enterprises. It also pays for training and education that is more general than on-the-job training provided by private firms. As with private savings, there is a trade-off between public spending and public savings: the more the government spends, the less it can invest.

Hence, the total funds available for capital formation depend on both private and public savings.

Capital Accumulation

Economic growth depends on the total available capital, so capital accumulation can increase economic growth. Capital has a limited lifetime, so the accumulation of capital not only depends on the investment rate, but also on the depreciation rate of capital. All capital has a limited lifetime, so at least some portion of new capital must be used to replace old capital. Economic models assume that depreciation is a constant percentage of the total capital. So if δ is the rate of depreciation, then capital accumulation can be represented thus:

Net Capital Accumulation for Next Period =

or, using common economics notation:

Kt+1 = It + Kt (1 − δ)

If the growth rate of capital exceeds the depreciation rate, then capital will accumulate; otherwise, it will decline. In most economies, the economy converges to a steady-state, where investment equals depreciation. This steady-state depends on the savings rate.

The savings rate determines the level of GDP per capita in the long run, but it has no effect on the long-run growth rate in GDP per capita. Increases in the savings rate will increase the growth rate GDP per capita, but only temporarily, until it reaches a higher steady-state.

Technology will also significantly affect depreciation, since technology helps to produce better quality products at last much longer. Cars, for instance, are much better quality and last significantly longer than cars of yesteryear. LED light bulbs last more than 30 times longer than incandescent bulbs and yield the same light output using less than 10% of the electricity. Because technology improves the useful life of capital, more capital will accumulate per unit of investment.

The Rate of Economic Growth Is Proportional to the Rate of Capital Growth, Labor Growth, and Technological Progress

Since economic growth depends on capital, labor, and technology, the economic growth rate also depends on the growth rate of these inputs. Capital growth can be increased with increased savings and investments, but the growth in labor supply depends on the fertility rate of the population. It is further constrained by the labor force participation rate (LFPR). Labor statistics are gathered in most economies, and in modern economies, the LFPR usually ranges from 60% to 67%, which is a narrow range. Hence, increases in labor is proportional to the LFPR percentage of increases in population. In economics, the labor growth rate is usually depicted as gL.

The growth in capital and labor does not explain all economic growth. Technology is also a significant factor in economic growth, but the quantitative effects of technology are not easily measured. Instead, technological progress is represented by the total factor productivity, which is added to increases in capital and labor to explain economic growth.

Output Growth =

Steady-State Economy

Since labor grows at a relatively constant rate, and because productivity is maximized at some amount of capital per worker, i.e. the K/L ratio, the growth of the economy reaches a steady-state with a constant growth rate. Moreover, since the savings rate is also relatively constant as a percentage of GDP, the growth in capital must also be relatively constant. Combining that with a constant rate of labor growth yields a constant growth in GDP. The actual value of the K/Y ratio will depend on the savings rate. If the savings rate increases, then the K/Y ratio will also increase, temporarily increasing the rate of economic growth to a higher level; thereafter, the economy again reaches a steady-state, but at a higher constant growth level.

Problems in Measuring Economic Growth

The success of an economy is measured by how well it improves people's lives. The easiest thing to measure is quantities, which is why most economies are measured in terms of their gross domestic product, the value of all goods and services provided by a domestic industry. In improving people's lives, the quality of the products and services matters, but quality cannot be easily measured. For instance, phones have greatly improved since their invention in 1876, especially in the last 10 years, since computer technology has enabled phones to do much more than just communicate. And even for communication, telephones have become much more efficient and portable, enabling people and businesses to communicate not only with voice, but also with text messaging and through social networks. While it is simple to count how many phones have been produced and what their price is, it is much more difficult to measure the improvements in quality, such as the many features provided by apps, like GPS. Indeed, if GDP were measured only with respect to phones, it probably would not have increased over the years, or the growth in GDP would be far more erratic, rather than the constant growth exhibited by the economy. This is because both the quantity and prices of phones have changed over the years. For instance, portable phones were far more expensive in the 1980s than the mobile devices of today, and had far less capability, but there are also many more mobile phones today than ever before. So, measuring the price and quantity of phones over the years would be highly misleading, but it does provide some indication of economic output. Of course, some improvements in equality can be measured more easily than others, and government agencies do account for quality improvements where it can be consistently measured, but quality measurement will never be perfect.

Public Policies to Promote Economic Growth

Since the formation of both human and physical capital leads to greater economic growth, governments generally have policies to promote saving and investing, which provides funding for expanding capital. Most governments provide extensive funding for the development of their human capital. In the United States, considerable state and municipal tax revenues are used to fund schools, but the federal government also promotes education through tax deductions and credits, allowing more people to afford education.

Since saving is needed for investments, there are many tax policies promoting retirement savings, which will stimulate the economy by providing more funds for capital. Popular tax-advantaged retirement funds include individual retirement accounts and 401(k)s.

The most significant benefit that any government can provide the economy is the rule of law, especially an equitable law, where private property cannot be taken by the government or by others arbitrarily without the due process of law. Even if there is a rule of law, it is often unjust, if the elites or special interests of society control the government, passing laws to their benefit and at the expense of everyone else. People can also be discouraged from seeking opportunities if there are significant, artificial legal barriers set up so that existing businesses can stifle competition.

An efficient business and tax code is also required to allow business to be conducted efficiently. Contracts need to be enforced, ownership of property must be respected, and red tape should be minimized.

The government provides significant funding for research and development, but also has a patent system that allows companies to gain a legal monopoly over any new inventions that they develop and patent. The drawback of patents is that they can stifle innovation, since large companies accumulate many patents and use the threat of patent infringement lawsuits to set up artificial barriers of entry, to thwart the entries of any companies unable or unwilling to spend the large sums of money required to defend such cases, even when the lawsuits are meritless.

Some countries use an industrial policy, to promote certain industries, where the government takes an active role in deciding how capital is allocated across manufacturing sectors. Industrial policies are enacted through tax credits, subsidies, and special deductions. Japan, for instance, had an industrial policy promoting the automobile manufacturing sector, at which it has become very successful. However, critics of industrial policies have argued that the government is choosing winners and losers, for which it is ill-equipped. And because investments involve a lot of risk, it is better to leave the allocation of resources to private industries, who know better how to develop a profitable enterprise and how to handle its associated risks.