“…Therefore, the model and their extensions [like Teixeira, Sugahara and Baranzini (2002); Baranzini, Bejuino and Teixeira (2003); Wei and Araujo (2009); Sugahara, Aragón, da Cunha, Perdigão (2016); and Góes and Teixeira (2022)] does not deal with the social security system, which interferes in the dynamic of the model, since the consumption of the retired persons is composed by the social security. In this vein, we decided to introduce the PAYG system in a balanced government budget, where the public revenue is used as income transfer from capitalists and younger workers to the retired workers' consumption.…”