The first chapter, entitled "Life-time earnings inequality and income redistribution through social security in the U.S.", is devoted to social security, which is the public pension system in the U.S. In 2015, the Social Security Advisory Board proposed to the Congress to change the parameters of the pension benefit formula, which have been constant since 1977. This change implies a fall in statutory replacement rates for individuals with high lifetime earnings. I construct a model, which accounts for a significant portion of the proposed change. Counterfactual experiments suggest that increased uncertainty in the labor productivity process and the upward shift in the college premium explain most of the change in the parameters of the pension benefit formula. The second chapter, "Income inequality and political inequality in the U.S.", is devoted to the median voter theorem, which is one of the most celebrated results in the public choice theory. Existing structural models predict too high income redistribution for the U.S. economy if the tax rate is chosen by the median voter. One potential explanation is that the political process in the U.S. is biased towards richer agents. In this case, the decisive agent is richer than the standard median voter and therefore prefers lower redistribution consistent with the data. I introduce wealth-weighted majoritarian voting over progressive income taxation into a heterogeneous agent model with idiosyncratic risk. I show that the model can significantly better explain the dynamics of income redistribution in the U.S. since 1980s than a model with a standard median voter. In the third chapter of my dissertation, entitled "Voter mobilization and electoral competition", which is a joint work with Ilya Archakov, we analyze the impact of voter abstention on electoral competition in the U.S. We present a novel game theoretic approach to study the competition between two candidates for a seat in a legislature, when candidates can spend money both on advertising to gain a larger share of potential supporters and on voter mobilization to bring the supporters to the voting poll. We show that the results of our model are consistent with the campaign expenditure data by the Federal Election Commission for the 2010 and 2012 House of Representative election cycles.