Food price volatility is a major threat for welfare, economic prosperity and political stability. The monetary authority is generally viewed in the literature as the only institution responsible for price stability, however this approach overlooks the importance of food price stabilization policies using fiscal instruments. We develop and estimate a Bayesian DSGE model that incorporates monetary and fiscal policy tailored to India, replicating food demand and food supply subsidies. We find that following a world food price shock, CPI and therefore interest rate volatility would be 21% higher in the absence of food subsidies. Putting this effect aside would lead to overestimating the effectiveness of inflation targeting by the central bank. Accordingly, we find that the subsidy policy has large heterogeneous distributional welfare effects: while farmers benefit from all subsidies, the inclusion of urban households into the demand subsidy program is required to offset supply subsidy welfare cost.