Piketty’s <i>r</i> > <i>g</i> Explained by Changes in the Average Productivity of Capital

Abstract

This article studies the ratio of the rates of profit and growth, in a growing economy, as a function of the average productivity of capital. It is shown that, if the savings rate and also the distribution of income between wage and profit are constant, the ratio mentioned remains constant or increases if the average productivity of capital respectively does not change or changes at a steady rate, whether it increases or decreases. If the change is repeated throughout a sufficiently large number of production cycles, the first rate grows above the second, even if in the initial situation the second rate is higher than the first. The result is the same if the savings rate and the rate of change of the average productivity of capital fluctuate within certain limits over a sufficiently large number of production cycles. In each case, the number of cycles required depends on the initial situation and the magnitude of the changes in both variables. These conclusions are compatible with the relevant historical data for economic variables involved. For this reason, they help to explain why, as a general rule, in a modern economy the rate of profit is higher than the growth rate.