Long-Run Economic Growth

Per Worker Production Function

The per worker production function describes the relationship between Real GDP per hour worked and capital per hour worked, assuming the level of technology is constant. This function is fundamental for understanding how economies grow over time.

• Diminishing Returns: As capital per worker increases, the initial gains in output are large, but subsequent increases in capital yield progressively smaller increases in output. This phenomenon is known as diminishing returns.

• Formula: The typical form of the per worker production function is: where is output, is technology, is capital, and is labor.

• Graphical Representation: The production function curve becomes flatter as capital increases, illustrating diminishing returns.

Example: If a factory adds more machines (capital) for each worker, output rises, but each additional machine adds less to total output than the previous one.

Technological Change and Economic Growth

Unlike capital, technological change does not experience diminishing returns. Improvements in technology can continuously increase output per worker, even if capital per worker remains unchanged.

• Key Point: In the long run, a country can only achieve sustained increases in its standard of living through ongoing technological change.

• Formula (Solow Model with Technology): where represents technology, is capital, is labor, and .

Example: The introduction of computers and the internet led to significant increases in productivity across many industries.

New Growth Theory

New Growth Theory is a model of long-run economic growth that emphasizes the role of economic incentives in driving technological change. It highlights the importance of knowledge capital as a key determinant of economic growth.

• Knowledge Capital: Refers to the stock of knowledge, skills, and innovations that contribute to production. Unlike physical capital, knowledge capital is nonrival (one person's use does not reduce its availability to others) and nonexcludable (it is difficult to prevent others from using it).

• Public Good: Because knowledge capital is nonrival and nonexcludable, it is considered a public good. This leads to increasing returns at the economy-wide level, even if individual firms do not experience them.

Example: Once a new technology is invented, many firms can use it without diminishing its usefulness to others.

Government's Role in Promoting Economic Growth

Because knowledge capital is a public good, private firms may underinvest in research and development due to the problem of free riding—benefiting from goods and services without paying for them. Governments can help address this market failure in several ways:

• Protecting Intellectual Property: Through patents and copyrights, governments grant inventors exclusive rights to their creations for a limited time, encouraging innovation.

• Subsidizing Research and Development (R&D): Governments can provide grants, tax credits, or direct funding to support R&d activities.

• Subsidizing Education: By investing in education, governments help increase the stock of knowledge capital in the economy.

Example: The U.S. government funds basic scientific research at universities and national laboratories, which often leads to technological breakthroughs.

Catch-Up Effect

The catch-up effect (or convergence) refers to the tendency for poorer countries to grow more rapidly than richer countries, as they adopt existing technologies and benefit from higher returns to capital investment.

• Key Point: Countries with lower initial levels of capital and technology can "catch up" by adopting best practices and innovations developed elsewhere.

Example: Many East Asian economies experienced rapid growth in the late 20th century by adopting technologies from advanced economies.