How should we tax people's incomes? I address this question from three different angles. The first chapter describes the optimal income tax when people can hide earnings by working in a shadow economy. The second chapter examines the optimal taxation of employees when firms can insure their workers and help them avoid taxes. The final chapter shows that a basic income policy - an unconditional cash transfer to every citizen - can, under certain conditions, be justified on efficiency grounds. In 'Optimal Redistribution with a Shadow Economy', written jointly with Luis Rojas, we examine the constrained efficient allocations in the Mirrlees (1971) model with an informal sector. There are two labor markets: formal and informal. The planner observes only income from the formal market. We show that the shadow economy can be welfare improving through two channels. It can be used as a shelter against tax distortions, raising the efficiency of labor supply, and as a screening device, benefiting redistribution. We calibrate the model to Colombia, where 58% of workers are employed informally. The optimal share of shadow workers is close to 22% for the Rawlsian planner and less than 1% for the Utilitarian planner. Furthermore, we find that the optimal tax schedule is very different then the one implied by the Mirrlees (1971) model without the informal sector. New Dynamic Public Finance describes the optimal income tax in the economy without private insurance opportunities. In `Optimal Taxation with Permanent Employment Contracts' I extend this framework by introducing permanent employment contracts which facilitate insurance provision within firms. The optimal tax system becomes remarkably simple, as the government outsources most of the insurance provision to employers and focuses mainly on redistribution. When the government wants to redistribute to the poor, a dual labor market can be optimal. Less productive workers are hired on a fixed-term basis and are partially insured by the government, while the more productive ones enjoy the full insurance provided by the permanent employment. Such arrangement can be preferred, as it minimizes the tax avoidance of top earners. I provide empirical evidence consistent with the theory and characterize the constrained efficient allocations for Italy. When does paying a strictly positive compensation in every state of the world improves incentives to exert effort? In 'Minimal Compensation and Incentives for Effort' I show that in the typical model of moral hazard it happens only when the effort is a strict complement to consumption. If the cost of effort is monetary, a positive minimal compensation strengthens incentives only when the agent is prudent and always does so when the marginal utility of consumption is unbounded at zero consumption. I discuss potential applications of these results in personal income taxation. The minimal compensation can be interpreted as a basic income - an unconditional cash transfer to every citizen. Therefore, I provide an efficiency rationale for the basic income.