This thesis includes an introduction chapter and four essays on the field of public and welfare economics. The first two essays are theoretical and the last two essays are empirical. The theoretical part of this thesis studies the optimal taxation in a setting where the social planner has different kinds of redistributive preferences and individuals differ in more than one background characteristic. The empirical part of the thesis examines income distribution and the consequences of public policies. The first empirical essay studies top income distribution over time and the second empirical essay evaluates the possibilities for elderly workers to reduce work hours through a part-time retirement scheme and how this possibility affects sickness and drug purchases. The objective of the public sector is to maximize social welfare by taking into account the efficiency of its policies and the equity perspectives. The main tool used is redistributing income through taxes and income transfers. The first essay of the thesis studies the optimal structure of income taxation in the Mirrleesian optimal taxation framework. The economy under study consists of individuals with different abilities to acquire income but they also have different preferences towards saving income for the future periods. The tax planner wants to redistribute income based on the ability to pay but the unobserved differences in saving preferences complicate the optimization problem. It is observed that in this kind of economy capital income taxation belongs to the optimal tax mix. In the second essay optimal tax mix is studied in an economy where individuals differ with respect to their abilities and initial endowment or inheritance received. The tax planner cannot observe either of the factors. The goal is to redistribute income from those who have better ability and higher initial wealth towards the less skilled and less endowed. Several countries have abolished inheritance taxation and for this reason the starting point in this essay is that the tax planner can only use the non-linear labour income tax and, if necessary, capital income tax. It is shown that non-linear capital income tax belongs to the optimal tax mix. The essay also discusses the role of income shifting in this type of economy. The effects of redistribution and other policies are seen as changes in the income distribution. The third essay in this thesis describes the Finnish income distribution and the evolution of incomes during the period of 1995- 2012. The essay especially examines the top of the income distribution from a gender perspective. While the income shares of the high-income individuals grew rapidly at the end of the 1990s, this mostly benefited men. The share of women in the top incomes did not improve before the financial crisis apart from the top 1 percent, where the share improved throughout the period. Income mobility and income composition are also studied. Men’s income ranks are more persistent than women’s. Women had a bigger share of capital and business income but towards the end of the period the share of wages grew for women. Beside the tax and transfer policy, the public sector can affect the well-being of citizens through different kinds of labour market and pension policies and programs. The fourth essay studies the part-time pension program and how it affected drug purchases and sickness. The part-time pension program reduced the hours worked but the combination of wages and pension reduced disposable income only by a little. The eligibility age for part-time pension programs was reduced in the year 1998, which enables the comparison of similar groups, where in one the reduction in work hours happened at a …