One of the most fundamental predictions of climate change models is that warming temperatures will disrupt the world’s food supply. Many countries will find their staple crops don’t grow as well, or at all, and the ones whose economies rely heavily on agriculture could suffer major losses in income and wealth.

For those particularly hard-hit companies, economic theory suggests a lifeline: If they can’t grow food anymore, perhaps they could trade for it instead, using their land for something else productive.

A newly published study in the Journal of Political Economy suggests that won’t be much help.

In the research, economists at MIT and Stanford built an economic model of global agriculture that predicts what grows where, what food costs on the global market and what crops are traded between countries, in a warming world. Then they developed a second, counterfactual model in which countries aren’t allowed to import and export food. The difference between those scenarios should suggest how much relief trade can bring for countries struggling with crop losses.

The answer was, not much. “We thought it would be more important,” Arnaud Costinot, an MIT economist who co-authored the study, said in an interview. “We were surprised that it made very little difference in this context for those crops.”

Costinot and his co-authors — Stanford economist Dave Donaldson and Cory Smith, a doctoral student in economics at MIT — found that what did make a big difference was individual countries’ ability to substitute new crops for the ones that don’t grow as well under climate change. If farmers couldn’t substitute, say, rice for wheat, then climate change could wipe out half of the world’s food production, the model found. Instead, because they very often can substitute, the model projects global crop yields will fall by about one-sixth.

The bigger problem suggested by the research is that not all countries are equally suited to switch crops, and the ones who are particularly ill-suited tend to be quite poor. Those include Ghana, Burma, Bangladesh and especially Malawi, which is projected to lose the equivalent of half of its gross domestic product. Trade simply didn’t do much to reduce those effects. “The margin that’s really important is within countries, farmers switching crops,” Costinot said.

What’s not surprising, to anyone who follows economic research on climate issues, is the idea that poor countries will suffer disproportionately as the climate changes. It’s striking to see how stark that suffering could be.