Optimal taxation in theory

In this paper optimal income taxation theories are subject of investigation following the classic paper in public finance by Mirrlees (1971), than the models of Sadka (1976), Seade,(1977), Akerlof (1978),Stiglitz (1982), Diamond (1998), and Saez (2001) , Piketty-Saez-Stantcheva (2014), all related to the classic paper by Mirrlees (1971). The problem is to maximize integral over population of the social evaluation of individual utility, that depends on individual consumption and labor. This paper first posed the problem of asymmetric information since the basic idea of the paper is that a first-best redistribution scheme is based on innate ability, and the information about ability is known to the individual, the government observes instead earnings. Mirrlees (1971), provides analytical solutions for the second-best efficient tax system in presence of such an adverse selection. Untill late 1990s, Mirrlees results not closely connected to empirical tax studies and little impact on tax policy recommendations Since late 1990s, Diamond (1998), Saez (2001) have connected Mirrlees model to practical tax policy / empirical tax studies. Mankiw, Weinzierl, and Yagan (2009) provide MATLAB code for analyzing the Mirrlees model MTR and wages, they are using log-normal and Pareto distributions. Later we look up to theory for optimal commodity sales taxes Ramsey (1927),using Ramsey rule utilized in Feldstein (1978) also , Diamond-Mirrlees (1971a), Diamond-Mirrlees (1971b) propose alternative to Ramsey proposition