The paper explores the mutual influence of inequality and monetary policy. The model introduces household heterogeneity in terms of access to the financial market and intertemporal preferences. The parameters are calibrated and estimated based on both Russia's microdata (including RLMS-HSE and HBS) and macro statistics. We have shown that the introduction of households with no access to the financial market has only a slight impact on the transmission of a monetary policy shock, while its secondary effects help amplify the action of most structural shocks. The behavior of wealthy hand-to-mouth households amplifies the response of macroeconomic variables to the monetary policy shock but has a slight impact on these variables' responses to most of the other structural shocks. We have identified non-structural inequality shocks at the bottom and the top of the Lorenz curve. As a result, we have found that the mutual influence of inequality and monetary policy is limited. The interest rate immediate response to changes in the Gini consumption index equals 0.1 for inequality shocks and 10 for a monetary policy shock. We have demonstrated that the shocks at the top of the Lorenz curve cause a more persistent response from the economy, whereas the shock at the bottom of the Lorenz curve. On first approximation, only one integral inequality indicator can be used to study the role of inequality in a business cycle. The relative consumption dynamics for specified household groups is not a conclusive indicator of either pro- or disinflationary policy, but it provides additional data to help identify structural shocks.