Economic growth, which consists in an increase in the production of economic goods and services compared from one period of time to another, and is measured by the change in GDP (Gross Domestic Product), is probably the main aspect on which we focus when talking about economics and the goals of government policies. This happens because almost everyone has among its goals that of increasing economic growth, but however, it seems that not everybody has clear in mind what it is necessary in order to achieve a higher rate of economic growth.

To reach sustained economic growth, which means economic growth in the long term, the amount of output produced by the average worker should increase steadily, and it can be measured with the real GDP per capita, which is the real GDP divided by the number of people.

To make it clear, higher productivity is not the only source of long-run growth, in fact, as some point out, other measures like putting more people at work can, of course, increase real GDP per capita, as it is happened in various countries during or immediately after World War II when millions of women who previously worked only at home entered the paid workforce. However, this measure is not something that can make real GDP per capita grow in the long term, it can be effective only for short periods of time because, in the long run, the rate of employment growth is never very different from the rate of population growth.

This means that, as pointed out by Paul Krugman and Robin Wells in their book Macroeconomics, “overall real GDP can grow because of population growth, but any large increase in real GDP per capita must be the result of increased output per worker”, and it is confirmed by the fact that in the U.S. over the course of the twentieth century, GDP per capita rose 1.9% per year, and 1.7% of that was the result of rising productivity.

What Leads to Higher Productivity?

Various factors can lead to an increased level of productivity, the three most relevant ones are without any doubt the increase in physical capital, the increase in human capital, and the accumulation of technical advancements.

Physical Capital, which is defined as manufactured resources such as buildings and machines, can have a great impact on making workers more productive. For example, a worker operating a backhoe can dig a lot more feet of trench per day than one equipped only with a shovel.

Human Capital, which refers to the improvement in labor created by the education and knowledge embodied in the workforce, is considered of having a greater impact on productivity than increases in physical capital.

Technical advancements. The advances in the technical means of the production of goods and services have a strong impact on productivity growth. One notable factor is that not only major inventions that rely on “cutting-edge” science have been very relevant, but also other more modest inventions like the Post-it note, that by making it easier to perform everyday activities have helped organizations to reach a higher level of productivity.

These are not ideas, the impact of physical capital, human capital, and technology on productivity can be proved using numbers and facts.

The Aggregate Production Function

As we have seen in the previous section, productivity tends to be higher, other things being equal, when physical and human capital increase, or when technology gets better, but it is not clear how we can measure their effects.

This is when the aggregate production function comes into play. It is a function used by economists to understand the true impact of the three factors above in determining the entity of productivity, allowing them to disentangle the effects of physical capital, human capital, and technical advancements on overall productivity.

This key attribute of the aggregate production function has allowed economists to understand that, even though in general all three factors tend to rise over time, they don’t have the same level of impact in every circumstance, and particularly they have been able to study the behavior of these factors in relation to the behavior of one another.

One interesting finding is that the aggregate production function exhibits diminishing returns to physical capital, which means that “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” (P.Krugman, Robin Wells).

This is a pretty simple relationship and, to better understand it, you can think of a tailor who is used to sewing by hand. In this case, buying a sewing machine could greatly increase its productivity, so we could estimate that if hand sewing can make a dress every day, using a sewing machine could take 2 hours.

However, if now he has a $500 sewing machine and we give him a new $1000 sewing machine, his productivity is likely to go up but not with the same intensity. He could make the same dress in an hour and a half instead of two hours. This means that there is a bigger difference between not having a sewing machine at all and having an inexpensive sewing machine, rather than the difference between having a cheap sewing machine and an expensive one.

As you can see in the graph, sewing by hand the tailor can make one dress per day (point A), then by using a $500 machine he can make three dresses per day, increasing productivity by 300% (point B), and finally by using a $1.000 machine he can now make 4 dresses per day, increasing productivity by 33% (point C). This represents the fact that additional amounts of physical capital are less productive keeping the value of the other two factors equal.

But what happens when the amount of human capital per worker and the technology change? What researchers have found is that, if the amount of human capital per worker or the amount of technology increase, separately or at the same time, we may see diminishing returns disappear.

So, by looking at the previous example, if the tailor receives a new and incredibly advanced sewing machine that, combined with an advanced course about how to use it at best, and exploiting all its features, can allow him to make the same dress in 40 minutes or less. The jump in productivity, in this case, is definitely greater than in the previous one.

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