I present a model in which randomly matched pairs of people bargain over the division of output in each period. Output can be consumed or stored for later consumption.
People are identical except possibly in wealth (i.e., the stored output). The one-period utility is linear except for the starvation disutility (i.e., the additional drop in utility under no consumption).
The starvation disutility weakens the bargaining position of a poor person and strengthens that of a rich person in an otherwise symmetric bargaining, providing the incentive to accumulate wealth. Policies that deincentivize wealth accumulation (e.g., wealth tax, progressive income tax) can make both the rich and the poor become better off.