Capital to Income Ratio

A Capital to Income Ratio, [math]\displaystyle{ \beta }[/math], is a ratio between a rate of return on capital [math]\displaystyle{ r }[/math] and an economic income [math]\displaystyle{ \alpha }[/math] (i.e. [math]\displaystyle{ \beta = r / \alpha }[/math]).

• AKA: Share of Capital to Income; [math]\displaystyle{ \beta }[/math].
• Context:
  • It can be correlated to the Savings to Growth Rate Ratio (i.e. [math]\displaystyle{ s/g = \beta = r / \alpha }[/math]). (Piketty's, via the First Fundamental Law of Capitalism).
  • It can range from being a National Capital/Income Ratio to being a Global Capital/Income Ratio.
  • It can be illustrated in a Capital to Income Ratio Timeseries.
  • …
• Example(s):
  • a U.S. Capital/Income Ratio for 2010.
  • if savings [math]\displaystyle{ s=12\% }[/math] and growth [math]\displaystyle{ g=2\% }[/math] then in the long run [math]\displaystyle{ \beta = 6 }[/math] (i.e. six years of national income would be required to match this economy's capital stock).
  • …
• Counter-Example(s):
  • a Labor/Income Ratio.
  • a Return on Capital.
• See: Income Inequality, Wealth Inequality.

---

---

References

2014

• (Piketty, 2014) ⇒ Thomas Piketty. (2014). “Capital in the Twenty-First Century." Harvard University Press. ISBN:9780674369559
  • QUOTE: Now that income and capital have been defined, I can move on to the first basic law tying these two ideas together. I begin by defining the capital/ income ratio. Income is a flow. It corresponds to the quantity of goods produced and distributed in a given period (which we generally take to be a year). Capital is a stock. It corresponds to the total wealth owned at a given point in time. This stock comes from the wealth appropriated or accumulated in all prior years combined.

    The most natural and useful way to measure the capital stock in a particular country is to divide that stock by the annual flow of income. This gives us the capital/ income ratio, which I denote by the Greek letter [math]\displaystyle{ \beta }[/math]. For example, if a country’s total capital stock is the equivalent of six years of national income, we write [math]\displaystyle{ \beta = 6 }[/math] (or [math]\displaystyle{ \beta = 600% }[/math]). …

    .... In the long run, the capital/income ratio [math]\displaystyle{ \beta }[/math] is related in a simple and transparent way to the savings rate [math]\displaystyle{ s }[/math] and the growth rate [math]\displaystyle{ g }[/math] according to the following formula [math]\displaystyle{ \beta = s / g }[/math] For example, if [math]\displaystyle{ s }[/math] = 12% and [math]\displaystyle{ g }[/math] = 2%, then [math]\displaystyle{ \beta = s / g = 600% }[/math].[2] In other words, if a country saves 12 percent of its national income every year, and the rate of growth of its national income is 2 percent per year, then in the long run the capital/ income ratio will be equal to 600 percent: the country will have accumulated capital worth six years of national income. This formula, which can be regarded as the second fundamental law of capitalism, reflects an obvious but important point: a country that saves a lot and grows slowly will over the long run accumulate an enormous stock of capital (relative to its income), which can in turn have a significant effect on the social structure and distribution of wealth. …

    … I will also use a few equations, such as [math]\displaystyle{ a = r × ß }[/math] (which says that the share of capital in national income is equal to the product of the return on capital and the capital/income ratio), or [math]\displaystyle{ \beta = s / g }[/math] (which says that the capital/income ratio is equal in the long run to the savings rate divided by the growth rate) …

    … I turn now from the analysis of the capital/income ratio to the division of national income between labor and capital. The formula [math]\displaystyle{ α = r × β }[/math], which in Chapter 1 I called the first fundamental law of capitalism, …

    … In the abstract, nothing prevents us from imagining a society in which the capital/income ratio [math]\displaystyle{ β }[/math] is quite high but the return on capital [math]\displaystyle{ r }[/math] is strictly zero. In that case, the share of capital in national income, [math]\displaystyle{ α = r × β }[/math], would also be zero. In such a society, all of national income and output would go to labor.

---