We develop a tractable small open-economy model to study the first-round effects of international food price shocks in developing countries. We define first-round effects as changes in headline inflation that, holding core inflation constant, help implement relative price adjustments. The model features three goods (food, a generic traded good and a non-traded good), varying degrees of tradability of the food basket, and alternative international asset market structures (complete and incomplete markets, and financial autarky). First-round effects depend crucially on the asset market structure and the different transmission mechanisms they trigger. Under complete markets, inter-temporal substitution prevails, making the inflationary impact of international food prices proportional to the food share in consumption, which in developing economies is typically large. Under financial autarky, the income channel is dominant, and first-round effects are instead proportional to the country's food balance-the difference between the country's food endowment and its consumption-which in developing countries is typically small. The latter result holds regardless of the degree of food tradability. Incomplete markets yield a combination of the two extremes. Our results cast some doubt on the view that international food price shocks are inherently inflationary in developing countries.