In order to investigate whether postponing retirement age contributes to fostering shared prosperity, we develop a dynamic general equilibrium model incorporating delayed retirement dynamics alongside survival probabilities and heterogeneous human capital distribution across generations. This framework provides a comprehensive assessment regarding how postponing retirement age policies affect both income inequality and economic growth dimensions. Theoretical analysis reveals disparities between low- and high-income group investments in their offspring's education as well as savings behavior. Specifically observed are heightened educational investments by lower income households compared to their affluent counterparts leading to relatively accelerated growth rates for lower income family offsprings' human capital; consequently narrowing intergenerational wealth gaps thus mitigating overall income inequalities. Furthermore,the influence exerted by postponed retirements upon economic expansion hinges largely upon its relative impacts on household educational investments vis-a-vis parental human capital accumulation.Finally, numerical simulations demonstrate that within plausible parameter ranges, pushing back retirements could indeed stimulate economic advancement.