How should monetary policy respond to large fluctuations in world food prices? We study this question in an open economy model in which imported food has a larger weight in domestic consumption than abroad and international risk sharing can be imperfect. A key novelty is that the real exchange rate and the terms of trade can move in opposite directions in response to world food price shocks. This exacerbates the policy trade-off between stabilizing output prices vis a vis the real exchange rate, to an extent that depends on risk sharing and the price elasticity of exports. Under perfect risk sharing, targeting the headline CPI welfare-dominates targeting the PPI if the variance of food price shocks is not too small and the export price elasticity is realistically high. In such a case, however, targeting forecast CPI is a superior choice. With incomplete risk sharing, PPI targeting is clearly a winner.