This paper contributes to the limited literature on the welfare impacts of market concentration by developing a simple model that shows how exogenous variations in market power affect poverty. Increased market power leads to economy-wide welfare losses, because it raises the prices of goods and services for all agents in an economy and thus reduces the relative incomes of households, particularly among the poor. Declines in poverty in this context are only possible in the case wherein the poor have access to a share of oligopolistic rents. Although this scenario seems highly unlikely, this result has important implications for public policy, particularly for economies with less-than-perfect markets and social objectives of poverty eradication. This result suggest the possibility of taxing extranormal rents extracted by firms with market power and redistributing them through targeted lump-sum social transfers, thereby contributing to poverty reduction by mitigating welfare losses from the negative price effect.