For highly social species, population dynamics depend on hierarchical demography that links local processes, group dynamics, and population growth. Here, we describe a stage-structured matrix model of hierarchical demography, which provides a framework for understanding social influences on population change. Our approach accounts for dispersal and affords insight into population dynamics at multiple scales. The method has close parallels to integral projection models but focuses on a discrete characteristic (group size). Using detailed long-term records for meerkats (Suricata suricatta), we apply our model to explore patterns of local density dependence and implications of group size for group and population growth. Taking into account dispersers, the model predicts a per capita growth rate for social groups that declines with group size. It predicts that larger social groups should produce a greater number of new breeding groups; thus, dominant breeding females (responsible for most reproduction) are likely to be more productive in larger groups. Considering the potential for future population growth, larger groups have the highest reproductive value, but per capita reproductive value is maximized for individuals in smaller groups. Across a plausible range of dispersal conditions, meerkats’ long-run population growth rate is maximized when individuals form groups of intermediate size.