Heterogeneous conditions and power law robustness in intergenerational resource transfers

Organisms in nature and humans in socioeconomic systems alike face tradeoffs between selfish consumption of resources and investment in the welfare of their offspring. Previous work across the disciplines of biology and economics has sought to elucidate this process, develop a theoretical framework to solve for the optimal life history strategy, and deduce implications of these microscopic interactions for the distribution of resources at the macroscopic level. Such theory, however, has failed to account for heterogeneous conditions that various individuals and groupings of kin enjoy, like growth rate advantages for those with greater resource abundance. Furthermore, such emergent trends at the macroeconomic scale lack reconciliation with observations of power law distributions of wealth and income in vivo. We modify and extend an analytical framework here to allow for heterogeneity, and consider the long-term consequences for resource distributions with Pareto initial values. We find that power law phenomena are robust to such processes and, due to sensitivity to the form of the utility curve, higher-order uncertainty may not affect the optimal tradeoff. This stresses the impact of mechanistic choices when translating sociological findings to ecological and economic theory, and suggests future work must consider how social norms and other microscopic complexity can explain emergent patterns or disrupt trends of inequality at the macrolevel.