# 05.03.14

## Piketty

It’s amazing how many bloggers on both the left and right (including actual economists) are butchering Piketty’s actual argument.

Piketty’s argument comes down to 3 pretty simple points.

1) β = s/g

β is the ratio of total capital in the economy to national income or GDP (K/Y). s is the savings rate in the economy. g is the growth rate of the economy.

It’s pretty easy to see how this works. Assume a capital stock of 500, national income of 100, economic growth of 2 percent, and a savings rate of 10 percent. 500/100 = 10/2. The following year, 510/102 = 10/2. Etc. Technically this is not an equation, but rather an equilibrium condition. If you plug in a different value for one of the variables you can get an inequality, but the result will be unstable and will tend back toward equality as you iterate through it several times.

2) α = r*β

α represents capital’s share of the national income. r is the rate of return on capital.

Using the example above, in the first year if the rate of return on capital was 4%, capital’s share of national income would be 0.04 * (500/100) or 20%. Labor’s share would then just be 1 – α or 80%.

3) Neither of the above propositions is particularly controversial or insightful. In fact, you could probably call them downright obvious. But then Piketty substitutes the first equation into the second to get:

α = r*(s/g)

Pretty simple, but what this is saying is that so long as the rate of return on capital exceeds the growth rate (r > g) then capital’s share of national income (α) will be increasing. Piketty then looks at some empirical economic data over the past couple hundred years which shows that over the long term the rate of return on capital has exceeded the rate of economic growth by a few percentage points per year (with the exception of the period 1910-1950). Thus increasing inequality is not some aberration, rather it’s a fundamental feature of capitalism.

More to come…………………..