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We study optimal policy design in a monetary model with heterogeneous preferences. In the model, financial markets are incomplete and households are heterogeneous with respect to their current consumption preferences and discount factors. The government controls the supply of money (liquid) and nominal bonds (illiquid), and households make optimal portfolio choices. We uncover that the two types of preference heterogeneity have distinct distributional consequences and different implications for the optimal monetary policy. While the heterogeneity in current consumption preferences pushes the economy towards a zero lower bound (ZLB) associated with nominal interest rates, the heterogeneity in discount factors moves the economy away from the ZLB. We characterize the optimal policy design and quantify the welfare losses associated with a binding ZLB - and thus also the potential welfare benefits of being able to implement negative interest rates. ; ISSN:0165-1889 ; ISSN:1879-1743