It depends on whether the poor are selling or buying, of course.
High food prices benefit poor farmers who are net food sellers, and hurt poor food consumers in urban areas. Low food prices have the opposite effects. In each case, the net effect on poverty depends on the balance between these two effects. But you would hardly know it from reading what NGOs and international organizations have produced on the topic. (For my past instances of blowing off steam on the subject, see this and this.)
As Johan F.M. Swinnen notes in a new essay
these basic principles are well known, [yet] we do not find them reflected in most arguments put forward in the food policy debate. For example, there has been hardly any mentioning of the benefits of low food prices for urban consumers and net consuming rural households during the pre-2006 low price era, and there has been very little emphasis in more recent statements on the benefits for producers in poor countries from high food prices.
In 2005, Oxfam International wrote:
US and Europe[‘s s]urplus production is sold on world markets at artificially low prices, making it impossible for farmers in developing countries to compete. As a consequence, over 900 millions of farmers are losing their livelihoods.
Three years later, following a substantial rise in food prices, Oxfam International’s view was that:
Higher food prices have pushed millions of people in developing countries further into hunger and poverty. There are now 967 million malnourished people in the world….
It is unfair to single out Oxfam since organizations like the World Bank, OECD, and the FAO have not been much better. So here is the World Bank in 1990:
The combination of depressed world prices and developing country policies which tax agriculture relative to industry have discouraged farm output and hence lowered rural incomes. Because the majority of the world’s poorest households depend on agriculture and related activities for their livelihood, this … is especially alarming.
And the World Bank in 2008:
The increase in food prices represents a major crisis for the world’s poor.
(All these cites come from Swinnen’s article.)
In other words, the news on the food prices front is always bad for the world’s poor, regardless of whether prices are rising or falling.
Why do these institutions always accentuate the negative? Swinnen argues the reason has to do with international organizations’ incentives to capture media attention, capitalize on “sudden shocks,” and emphasize the negative in the “news” (to which people seem to pay more attention).
Whatever the reason, it makes for bad public policy.