5 ideas
When the return on capital (r) persistently exceeds the growth rate of output (g), wealth holders who reinvest enough of their capital income can see their fortunes grow faster than the economy. Past wealth can then outpace earnings and tend to concentrate. Piketty treats r > g as the usual historical condition, with r around 4–5% against long-run growth of 1–2%, and not as a market imperfection.
The capital-income ratio (β) measures total private wealth as a multiple of annual national income, which is about six to seven years in 19th-century Europe. In the long run it tends toward the savings rate divided by the growth rate (β = s/g). Slower growth with steady saving therefore mechanically raises the weight of accumulated wealth relative to current income.
Piketty attributes the 1914–1970s compression of wealth and income inequality mainly to shocks and policy: two world wars, depression, inflation, nationalizations and steep progressive taxation. He does not attribute it to a natural equalizing tendency of mature capitalism. Since 1980 the capital-income ratio has climbed back toward 19th-century levels, but wealth concentration has recovered much less fully, so the U-shape is clearer for aggregate wealth than for top wealth shares.
In Balzac's Le Père Goriot, the criminal Vautrin tells the ambitious young law student Rastignac that study and hard work will earn him far less than marrying an heiress. In 19th-century France the income from inherited capital dwarfed the top professional salaries. Piketty uses the scene to show a society where inheritance, not merit, set life outcomes, and warns that r > g can recreate that 'patrimonial' order.
Piketty proposes an annual progressive tax on net wealth, for example rates near 0–2% rising with fortune size. It would be backed by automatic cross-border exchange of bank information so wealth cannot escape into tax havens. Its main purpose is transparency and restraining divergence between r and g, rather than raising revenue. He concedes it is utopian at global scale but argues regional versions, such as a European one, are feasible.