During the Global Food Price Crisis of 2007-2011, millions of people suffered from hunger because food had become expensive. To cope with this problem, the governments of several countries decided to establish public food reserves in order to stabilize domestic prices. In this paper we develop a model to evaluate the optimal grain storage policy for a poor grain-importing country. Households are heterogeneous in their income endowment, and those who cannot afford enough food suffer from hunger. The international price of grain follows a Markov process with two states (tranquil periods and food crises), and households are unable to self-insure against changes in this price. The objective of the reserve operation is to reduce hunger rates. The model captures the trade-off in implementing the policy: raising a stock to prevent hunger tomorrow requires resources that could be used to reduce hunger today. Parameters are calibrated to reflect food supply and demand in Haiti. Our results suggest that rather than storing food, a better approach for a poor country is to focus on fighting poverty directly, since the modest social protection provided by a storage policy could be also be obtained through relatively small improvements in income per capita and income distribution.