When to Tax Labour?

We analyze optimal dynamic taxation when labor supply is indivisible, as in Hansen (1985) and Rogerson (1988). Markets are complete, and an employment lottery determines who works. The consumer can buy insurance to diversify this extrinsic income uncertainty. The optimal wage tax is zero in both the short and long run only when leisure is neutral. If leisure is normal (inferior), labor should be taxed (subsidized). We further derive a wide range of preferences, including HARA, which encompasses normal and non-normal leisure. For those preferences we characterize the dynamic paths of the wage tax.