This paper examines how wealth accumulation and risk sharing affect the evolution of inequality over time. We first assume risk sharing away and examine how inequality evolves over time when agents accumulate an asset. If asset accumulation is unbounded and the asset yields a positive return, inequality converges to single value over time. If the asset yields a zero or negative return (e.g., grain storage), there is no persistent inequality but inequality is nevertheless correlated over time. If wealth yields a positive return but is in finite supply (e.g., land), persistent inequality arises if one agent is more thrifty than the other. Multiple equilibria may obtain. Societies might prevent polarization by closing down markets in such assets. We then introduce risk sharing. With perfect risk sharing, welfare inequality is constant across time. For continued participation to mutual insurance to be voluntary, asset inequality must remain `close` to welfare inequality. With imperfect commitment, the end result is a hybrid situation half-way between the risk sharing model and the pure accumulation model. If risk aversion is high for poor agents but low for rich ones, patronage arises whereby the rich on average take away from the poor.
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