Wealth Inequality, or r-g, in the Economic Growth Model

We investigate a simple continuous-time overlapping generations model with a neoclassical production function and technological progress. We demonstrate that the degree of wealth inequality is positively related to the difference between the real interest rate r and the growth rate of income per capita g , and if g falls, the r-g gap widens and inequality worsens. We also argue that a wealth tax reduces the wealth inequality. All of these results are consistent with the famous predictions advanced by Thomas Piketty in Capital in the Twenty-First Century (2014). We next investigate consumption tax and find that it enhances capital accumulation and reduces r-g , and thus wealth inequality.