Piketty_LawsOfCapitalism.sagews

Piketty's Fundamental Laws of Capitalism

1st Law of Capitalism

α = r × β

$\alpha$: Share of capital in national income

r: rate of return on capital (ROI)

$\beta$: capital income ratio - Total available capital in terms of yearly income

Typically $\beta \sim 6, r \sim 5\%$

$\implies \alpha \sim 30\%$ of income comes from capital returns

2nd Law of Capitalism

β = s / g

s: savings rate

g: growth rate

Growth can come through demographic growth (more capita) or increased productivity pro capita With low growth, capital's role in income inceases

Typically $s \sim 10\%$ and $g \sim 1.5\%$ in the long term

$\implies \beta \sim 6$ (as assumed above)

alpha = var('alpha')
beta = var('beta')
r = var('r')
s = var('s')
g = var('g')
alpha = r * beta
beta = s / g