It's both corruption, and economics. A lot of places with famines are capable of being self-sufficient, in terms of food production, but it's just not profitable for farmers to grow it (And sell it domestically).

When a million people died in the Irish potato famine, it wasn't just because the United Kingdom prevented foreign aid from reaching Ireland. Ireland was the breadbasket of the empire - throughout that entire time, it was a net exporter of food.