Inequality in Hierarchies

Abstract

The paper examines allocation of a resource in “hierarchies”, where individuals are exogenously ordered and those ranked higher in the ordering expropriate the resource earlier. Individuals get strictly increasing and strictly concave payoff from resource extracted, giving rise to endogenous resource distribution. A “donor” supplies costly resource after the agents sequentially commit to resource shares. I characterize equilibrium resource distributions for a large class of donor’s objectives (including utilitarian and egalitarian cases). When hierarchies are large, equilibrium resource shares follow a Geometric distribution over the ranks, irrespective of donor objective. Limiting extraction at the top or changing donor objective therefore may not significantly reduce inequality. Donor competition, on the other hand, reduces inequality and achieves efficiency in the limit.

Keywords: Weak Principal, Sequential access to resources, Geometric distribution, Jungle economy

JEL Classification: D30, D61, D63, Q15