Sometimes it seems that Americans and Europeans do little but argue with each other. Our latest entanglement involves French allegations that Tour de France champ Lance Armstrong drugged himself to victory in the world’s most famous bicycle race–a charge that Armstrong himself vigorously denies. “I’m sorry you don’t believe in miracles,” he has said.

Whatever the facts of Armstrong’s case–and it’s hard to think that his French accusers are motivated by something other than a deep-seated sense of wounded national pride–there’s no denying that the United States and the European Union have turned bickering into an art form. Indeed, you may have to believe in miracles to suppose that Americans and Europeans ever will see completely eye-to-eye on matters ranging from how to fight terrorism to whether snails are in fact an edible food.

Our disagreements are perhaps nowhere more evident than at global trade talks. We constantly hear about the World Trade Organization and all of its delicate negotiations–mainly because “negotiations” sounds a lot better than “squabbling,” which is in fact what trade representatives spend a great share of their time doing.

The squabbling has been worth it: Over the last half-century, we’ve lowered trade barriers across the planet–an accomplishment that has created jobs for workers, reduced prices for consumers, and enhanced prosperity for farmers and just about everybody.

Yet there’s much more squabbling to do, because the governments of the world continue to distort free trade with tariffs and subsidies. This is especially true for agriculture. Both the United States and the European Union will have to reform many of their farm policies if the WTO’s Doha round is to achieve success.

At the same time, American farmers should not assume that the key to export growth is improved access to European markets, as desirable as this would be. Even if the EU were to wipe out all of its trade barriers and export subsidies (the EU is currently responsible for about 90 percent of the world’s agricultural export subsidies), the demand for U.S. products would rise only slightly.

It’s a simple matter of demographics. Today, there are some 730 million Europeans. In 2050, according to one projection, this number will slip to about 650 million. Even if our children and grandchildren have better access to their markets, they may wind up selling less food simply because there are fewer mouths to feed.

That’s not true elsewhere. Global population is expected to increase from a little over 6 billion right now to about 9 billion in 2050. Every region will be more populous, except for Europe and southern Africa.

In addition, nearly half the world’s population, about 3 billion, now lives on $2 per day or less. As this segment of the global population grows and their incomes go up, the first things these people will want is more and better food.

Another important factor involves urbanization. Most of these new 3 billion people will live in cities as opposed to rural areas. They will find themselves in trade-based market economies, rather than rural subsistence economies that, to some extent, isolate themselves.

In other words, the developing world’s population boom, income increase and urbanization trend represent the future of American farm exports. As it happens, access to markets in the developing world is a key component of the ongoing WTO talks.

As U.S. trade negotiators again sit down with their counterparts this month to prepare for December’s big world trade meeting in Hong Kong, they should keep these facts squarely in mind. If they don’t, they’ll find themselves rehashing old debates with a declining Europe, rather than seizing new opportunities with a growing world.

American farmers, too, should understand what lies ahead: Enormous change, for one thing, because developing countries will demand that Washington reform our own trade-distorting policies before they allow anything like unfettered access to their markets.

Yet these changes also will bring boundless opportunities. All we have to do is confront the challenge properly. If we squabble smartly, we won’t even have to pray for a miracle.