From Immensity to Infinite Wealth? Extending RAYOBETH Theory to Returns, Concentration and Taxation

Whether wealth can compound without limit is a question shared by economics, finance, taxation and political science, yet the leading answers conflict. The inequality r > g predicts divergence that history often failed to deliver, standard random growth models cannot reproduce the speed at which top fortunes have risen, and studies of wealth taxes report large behavioral responses but small effects on concentration. This article extends RAYOBETH Theory, a conditional theory of generative systems, to fortunes. It shows that the r > g condition is the special case of constant returns to scale, and that what decides divergence is the scale elasticity of growth. When growth first falls and then rises with the size of a fortune, wealth has two regimes: a stable body in which fortunes regress toward an equilibrium, and an explosive tip above a critical fortune at which wealth outgrows the economy. A critical tax theorem shows that a flat wealth tax shifts these thresholds but changes the regime only if it reaches the growth advantage of the largest fortunes, and that the minimal schedule that prevents any fortune from outgrowing the economy is zero below the critical fortune. Applied to 31,606 person years of the Forbes billionaire lists from 2001 to 2024, instrumented tests reject Gibrat’s law in favor of a U shape: growth falls with size to a turning point near US$10 billion and rises above it, and fortunes above about US$43 billion (95% interval 32 to 68) outgrow world GDP. Billionaire wealth rose from 5.3% to 12.7% of world GDP between 2010 and 2024, the Pareto exponent of the tail fell from 1.38 to 1.18, and the largest fortunes outgrew the economy by about 2.1 points a year, close to the 2% minimum tax proposed for billionaires. Top 1% wealth shares, by contrast, decelerated in 49 of 59 countries where they had risen, and nine wealth tax repeals show no systematic effect on them, as the theory predicts.