Christophe Chamley analyzes the optimal tax on capital income in general equilibrium models with infinite lives. The paper examines how capital income taxes behave in the long run when individuals have infinite lives and utility functions that extend from the Koopmans form. It shows that the optimal tax rate on capital income tends to zero in the long run. The study considers heterogeneous populations and the equality between social and private discount rates in the long run. For a special case of additively separable utility functions, the paper determines tax rates along the dynamic path and conditions for the local stability of the steady state. The main result is that the optimal capital income tax rate is zero in the long run. The paper also discusses the implications of this result for capital income tax and bequest tax in economies with intergenerational transfers. The analysis includes a dynamic path example for a specific class of utility functions, showing that the tax rate transitions from a high level to zero over time. The paper concludes that the long-run optimal tax rate on capital income is zero, and that the social and private discount rates are equal in the long run. The study also highlights the importance of the second-best assumption and the stability of the steady state in dynamic models.Christophe Chamley analyzes the optimal tax on capital income in general equilibrium models with infinite lives. The paper examines how capital income taxes behave in the long run when individuals have infinite lives and utility functions that extend from the Koopmans form. It shows that the optimal tax rate on capital income tends to zero in the long run. The study considers heterogeneous populations and the equality between social and private discount rates in the long run. For a special case of additively separable utility functions, the paper determines tax rates along the dynamic path and conditions for the local stability of the steady state. The main result is that the optimal capital income tax rate is zero in the long run. The paper also discusses the implications of this result for capital income tax and bequest tax in economies with intergenerational transfers. The analysis includes a dynamic path example for a specific class of utility functions, showing that the tax rate transitions from a high level to zero over time. The paper concludes that the long-run optimal tax rate on capital income is zero, and that the social and private discount rates are equal in the long run. The study also highlights the importance of the second-best assumption and the stability of the steady state in dynamic models.