Explorations in public economics: simple models of OLG and optimal tax

This book consist of two (parts) essays in OLG models and economics of taxation namely optimal taxation. Simple OLG model is explained (its algorithm) and optimal taxation models of Ramsey (1927) static model and Mirrlees (1971) dynamic model of optimal taxation. Also Diamond- Mirrleess efficiency theorem (1971) is explored and implemented to solve with a MATLAB code.An overlapping generations model is an applied DGE model for which the lifecycle models are applied. In the applied part benchmark models has been compared to, model with parameters that generate poverty traps and multiple equilibria.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.