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Two critical questions about intergenerational outcomes are: one, whethersignificant barriers or traps exist between different social or economicstrata; and two, the extent to which intergenerational outcomes do (or can beused to) affect individual investment and consumption decisions. We develop amodel to explicitly relate these two questions, and prove the first such `ratrace' theorem, showing that a fundamental relationship exists between highlevels of individual investment and the existence of a wealth trap, which trapsotherwise identical agents at a lower level of wealth. Our simple model ofintergenerational wealth dynamics involves agents which balance currentconsumption with investment in a single descendant. Investments then determinedescendant wealth via a potentially nonlinear and discontinuous competitivenessfunction about which we do not make concavity assumptions. From this model wedemonstrate how to infer such a competitiveness function from investments,along with geometric criteria to determine individual decisions. Additionallywe investigate the stability of a wealth distribution, both to localperturbations and to the introduction of new agents with no wealth.

When a `rat race' implies an intergenerational wealth trap