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We study how income inequality affects monetary policy through the inequality-household debt channel. We design a minimal macro Agent-Based model that replicates several stylized facts, including two novel ones: falling aggregate saving rate and decreasing bankruptcies during the household's debt boom phase. When inequality meets financial liberalization, a leaning against-the-wind strategy can preserve financial stability at the cost of high unemployment, whereas an accommodative strategy, i.e. lowering the policy rate, can dampen the fall of aggregate demand at the cost of larger leverage. We conclude that inequality may constrain the central bank, even when it is not explicitly targeted.