Piketty’s erroneous claim is due to the implicit assumption that savings are never consumed, nor spent on charitable purposes or used to exert power over others. It is only under this outlandish premise that wealth grows at the rate r. If people use their savings later on, as they do in the Diamond model as well as in reality, the growth of wealth is independent of the return on capital. This holds all the more in the presence of taxes.
Piketty’s allegation that the relationship r>g implies a rising wealth-income ratio is not only logically flawed, however, but also rebutted by his own data: On p. 354, the author reports that the return on capital has consistently exceeded the world growth rate over the last 2,000 years. According to his “central contradiction of capitalism”, this would have implied steadily increasing wealth-income ratios. Yet, over the last two centuries or so, the period for which data are available, wealth-income ratios have remained relatively stable in countries like the United States or Canada. In countries such as Britain, France, or Germany, which were heavily affected by the wars, wealth-income ratios declined at the start of World War I and recovered after the end of World War II. The book’s references to these wars and the implied destruction of capital abound. They are intended to rescue the claim that r>g implies an ever rising wealth-income ratio. The United States and Canada as obvious counter-examples remain unmentioned in this context.
For the pointer I thank David Levey.