We build a New Keynesian business-cycle model with rich household heterogeneity. In the model, systematic monetary stabilization policy affects the distribution of income, income risks, and the demand for funds and supply of assets: the demand, because matching frictions render idiosyncratic labor-market risk endogenous; the supply, because markups, adjustment costs, and the tax system mean that the average profitability of firms is endogenous. Disagreement about systematic monetary stabilization policy is pronounced. The wealth-rich or retired tend to favor inflation targeting. The wealth-poor working class, instead, favors unemployment-centric policy. One- and two-agent alternatives can show unanimous disapproval of inflation-centric policy, instead. We highlight how the political support for inflation-centric policy depends on wage setting, the tax system, and the portfolio that households have.