# Do inheritances break Piketty's r>g model's conclusions?

In Capital in the Twenty-First Century Piketty suggests that if the return on capital is higher than the economic growth, then wealth inequality in society will rise.

Yet, this model seems to ignore that people leave their inheritance to more than one person on average and form marriges with people of not ideally equal wealth. I.e. if a billionare marries a millionare and have three children to whom they pass their wealth after 50 years, they'll pass $$\frac{1000m+1m}{3}(1+r)^{50}$$ to each of them, making the society more equal if r is small enough.

Does such effect of inheritances break the model's conclusions (and inequality may decrease when r is significantly higher than g) or the effect is negligible?

• "if r is small enough." That's the problem. I haven't read Capital in the 21th century by The economics of Inequalities and listened to many of his interviews, and one of the points Piketty focuses on is that $r$ is too large. Dec 8, 2022 at 3:50

It actually does not change conclusions from his model. Piketty's model is not about income inequality per se, it is about inequality between capital's and labor's share of income. Piketty's model does not even have heterogenous agents with different wealth or income in it. It has separate capital incomes and separate labor incomes, but the model does not even explicitly model these as two separate groups. What happens in the Piketty's model is that when $$r>g$$ the share of total GDP that goes to capitalists as a whole class increases. The model is not about inequality between individual capitalists. If the capitalist class would be very large they might be even poorer than workers per capita, Piketty's model does not analyze it at all. Piketty does argue that this should lead to more inequality in real world because he argues in real life capital tends to be concentrated but that is not direct conclusion of his model which only makes predictions about income shares (see overview of Piketty's model in Gusella 2020).
As such you proposed modification would not change the conclusions from Piketty's model since the inheritors of those millionaires (assuming they do have zero labor income) would be still members of capitalist class. If capitalist class gets 30% of GDP (lets say GDP is 100) then regardless whether there are 100 capitalists each getting 0.3 or 1 capitalist getting whole 30 they are still getting 30% of GDP in either case. Piketty's model just says that this share will be increasing always as long as $$r>g$$ so labor will be getting smaller and smaller share, but this is not the same income inequality amongst individuals but classes of people.