The article explores how monetary policy affects households with different levels of debt in an economy. When there are cost shocks, households with debt and those with savings respond differently, affecting their work and spending. The study shows that a flexible inflation targeting policy can be as effective as an optimal policy in improving social welfare, even in an economy with many debt-constrained households. Under these policies, the impact of cost shocks on consumption and work habits fades more slowly compared to a simple inflation targeting policy.