Optimal capital income taxation in a two sector economy

We extend the celebrated Chamley-Judd result of zero capital income tax and show that the steady state optimal capital income tax is nonzero, in general. In particular, we find that the optimal plan involves zero capital income tax in investment sector and a nonzero capital income tax in consumption sector. In a two sector neoclassical economy, interdependence of labour and capital margins allows the government to choose an optimal policy that involves nonzero tax on capital income. The distortion created by capital income tax in consumption sector can be undone by setting different rates of labour income taxes. The optimal plan thus involves zero capital income tax in both sectors only if optimal labour income taxes are equal. This may not be the optimal policy if marginal disutility of work is different across sectors and/or the social marginal value of capital is different across sectors. The difference in social marginal value of capital can be undone by setting different labour income taxes across sectors. We also show that if the government faces a constraint of keeping same capital and labour income tax rates across sectors, optimal capital income tax is nonzero.