Question

How do gains in labor productivity lead to gains in GDP per capita?

Short answer

Gains in labor productivity lead to gains in GDP per capita by increasing the total output (GDP) produced with the same labor input. As labor productivity grows, workers produce more goods and services in the same amount of time. This increase in output raises GDP, and when the population remains constant, GDP per capita also increases. Consequently, the higher GDP per capita reflects an improvement in the average income per person, ultimately indicating a higher standard of living.

Step-by-step solution

Define labor productivity and GDP per capita

Labor productivity is defined as the amount of output produced per unit of labor input. It can be measured as output per worker or output per hour worked. A higher labor productivity means that workers produce more goods and services in the same amount of time. GDP per capita is the Gross Domestic Product divided by the total population of a given area, and it reflects the average income per person in that area.

Explain the role of labor productivity in the production function

The production function in economics relates the output of goods and services to the inputs used in the production process, including labor, capital, and technology. An increase in labor productivity means that the same amount of labor input produces more output. The production function can be represented as: $$Y=A\ast F(L,K,H,N)$$ Where: Y = output (GDP), A = total factor productivity (technology), F = a function describing the relationship between inputs and output, L = labor input, K = capital input, H = human capital, N = natural resources Labor productivity can be affected by various factors such as human capital (e.g., education and skills) and technology.

Show how increased labor productivity impacts GDP

When labor productivity increases, output per worker (or per hour worked) grows as well. If the labor force does not change, the total output (GDP) will increase. This increase in GDP reflects the fact that more goods and services are being produced with the same amount of labor input.

Connect the increase in GDP to GDP per capita

As we have seen, higher labor productivity leads to higher output (GDP). To evaluate the effect on GDP per capita, we will now consider the population: $$GDPpercapita=\frac{GDP}{population}$$ When GDP increases and population remains the same, GDP per capita also increases. This means that the average income per person in the country goes up, which is indicative of an improvement in the standard of living.

Conclusion

In conclusion, gains in labor productivity lead to gains in GDP per capita by increasing the total output produced with the same labor input. This results in higher average income per person, which ultimately indicates improved living standards.