We propose an approach to mathematical modeling of human capital reproduction processes with endogenous fertility and heterogeneous agents. The rate of human capital accumulation is determined by a quality-quantity trade-off in agents’ decision on their children. An agent makes choice taking into account that his/her efforts for raising a child transform into human capital of a descendant according to some prescribed rule. The mechanism of human capital reproduction within the model is closely bound up with cultural transmission processes. In the expanded version of the mathematical model we take into consideration the type of the parent and his/her altruism, as well as his/her attitude to deviations of human capital of children and the intensity of intra-group ties.