Bequests, Imperfections in Factor Markets, and Long-Run Inequality: A Theoretical Assessment of Piketty

The book Capital in the Twenty-First Century by Thomas Piketty (2014) has renewed the public and scholar debate about wealth and income inequality. Theoretical critiques have focused their attention on a regularity pointed out by the author, namely, the growth rate of the economy is lower than the interest rate, r > g. However, two other important insights are key to understand the persistence of inequality: bequests and differences between factor prices and the marginal productivity of factors. We present an OLG model that incorporates these two elements and explores under which circumstances inequality between two social groups, rich dynasties and poor dynasties, is a long-term equilibrium result with economic growth. The model considers two goods, one essential and the other non-essential. We find that inequality between rich and poor dynasties is a long-term equilibrium when (i) the marginal productivity of labor of the essential good is bounded from above and the marginal productivity of capital in the non-essential good sector is bounded from below by a positive value; and (ii) factor remunerations are not determined by the standard economic forces of marginal product.