The concept of macroeconomics is hard for most people. The most valuable books are often written at a high level. If this series is popular (comments and page views), I will bring readers an easy summary of macroeconomics. These pieces should average 750 words. Assuming 150 words per minute, that means five minutes of material.
I found my wife was fascinated by these concepts. However, she had no interest in economics books. I learned to describe the concepts quickly. These concepts are covered in-depth in Thomas Piketty's book: Capital in the Twenty-First Century.
What is the Second Fundamental Law?
I will get rid of all Greek letters. Variables will be named in English.
You need to know these terms:
B requires further work. The Capital/Income Ratio is the total wealth of the country divided by the earnings and interest generated by the wealth. This is like EV/EBIT (enterprise value/earnings before interest and taxes) for an entire country. However, houses are included as capital and the equivalent rent cost is included as earnings.
The next formula was created by Roy Harrod and Evsey Domar in the late 1930s.
G = S/B
This formula says that the growth rate of the economy is equal to the savings rate divided by the capital/income ratio. This premise was widely accepted for decades. However, it only applies to long-term planning.
Using the Law
It is easier to watch the math:
Since the formula is a math equation, it can be written in different formats. I picked the start values. Don't rely on 2% growth on a 10% savings rate in the real world.
The math is easiest to verify in the second formula. Assume that the total capital of the country is valued at $400 and that national income is $100. The value for B would be 400%, calculated as $400/$100. However, what happens if S is 10% and G is 2%?
The 10% savings rate will lead to capital increasing from $400 to $410. Meanwhile, the 2% growth rate would increase income from $100 to $102. The value for B the next year is $440/102 = 402% (rounded). The value for B would continue to grow until it reached 500%.
Solving for G was a Problem
In the 1930s and 1940s, economists were trying to use the formula to solve for G. Initially, they even assumed that B was fixed. Because they thought B was static, they believed that savings was the primary driver of growth. The capital/income ratio (that is B) changes over time.
Imagine if G was 0
It is not impossible for an economy to have no growth. However, dividing by 0 is generally viewed as "impossible". It is only impossible if people refuse to treat "infinity" as an acceptable answer.
Imagine that B = 500 and S = 10. What happens if G is equal to 0?
The capital of the country is worth $500. The income is equal to $100.
After one year, savings adds $10 to the capital base. Capital is worth $510. Since there is no growth, income still equals $100 the next year. The capital/income ratio is now $510/$100 = 510%.
After two years, savings adds another $10 to the capital base. Capital is worth $520 and income remains at $100. The capital/income ratio is now $520/$100 = 520%.
In this zero growth scenario, the value of B increases every year.
If there is zero growth in the economy, but the savings rate is positive, B increases. The growth in B requires one of two things to happen. Either capital receives a larger share of the $100 of income, or the return on capital decreases. Remember that income will be split between labor and capital (before taxes). If the share of income going to capital increases, the share going to labor decreases. If we start this scenario with capital earning $30 and labor earning $70, then the return on capital in the first year was 6% ($30/$500). If capital does not consume more of the income in the subsequent years, then in the third year, the return on capital would only be 5.77% ($30/$520). If capital maintains a 6% return, it would require $31.2 in the third year ($520*.06).
This is why so much emphasis is placed on generating economic growth.
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