Piketty meets Pasinetti: On public investment and intelligent machinery
Wealth inequality is currently rising in rich countries. Expectations that ever more intelligent machines might replace people's jobs amplify the concerns about an increasingly unequal wealth distribution. We examine how capital tax-financed public investment affects the distribution of wealth when the substitutability between capital and labor changes. We consider a setting with a labor-augmenting public capital stock and distinct wealth cohorts: dynastic savers and life-cycle savers. We prove that for every elasticity of substitution greater than a threshold, there exists a capital tax rate at which the dynastic savers disappear in the long term. For every elasticity below that threshold, there exists a capital tax rate at which the life-cycle savers disappear. Below these capital tax rates, both types of households co-exist in equilibrium. Finally, we elaborate on how these results depend on the role of public investment in production.