Averting Starvation: Obligation or Charity?

Just about everyone would acknowledge an obligation to save a life, where the person in danger is right in front of you, and where only a small sacrifice of time or money is needed from you. Suppose the person in danger is far away, and you could still save them. Suppose that you have the power to save many lives, by making just one small sacrifice at a time. In fact there are people who live far away, and who are in danger of dying from starvation or disease. If you have the power to save some of these lives, what obligation, if any, do you have to make a small sacrifice in order to do so?

Starved child