It was perhaps not the best moment to be asking Reeves the question that brought me here: What would it take to get him to grow more? To till more land, buy more seed, run more irrigation lines, fight more pests, apply more fertilizer, endure more inspections, fix more old tractors, fill out more paperwork, miss more summer-leisure fun and generally wear himself further down in order to grow more produce so people could eat better.

The paradox of this last point was not lost on him. His own meals, especially during the summer months, were a wreck: coffee for breakfast, Mountain Dew for lunch, baked beans for dinner eaten straight from the can to save time for sleep — though he does get to snack on his crops. But Reeves is in many ways perfectly qualified to ponder the problems of increased production. The farm that he runs with his three brothers and one of their sons is an example of the kind of nonindustrial farm that’s necessary in a revamped vision of American food production and consumption. Last year, Reeves turned out 420,000 pounds of tomatoes, 65,000 pounds of strawberries and 2.4 million ears of sweet corn. And while they have a nice little farm stand just outside the small town of Baldwinsville, with a quaint patch of pick-your-own organic blueberries behind the sales shed, they mostly sell their crops to big grocers, including Tops, Price Chopper, Wegmans and, biggest of all, Walmart.

Reeves is particularly proud of being Walmart’s first farm supplier in the area, even if that adds significantly to his workload, from filling huge orders to enduring their painstaking food-safety audits. Only a fraction of his output is organic, but more would qualify with minor adjustments in his already-cautious use of pesticides and fertilizers. “I’m a personnel manager, bookkeeper, salesperson, computer guy, logistician and food-safety expert,” he said. “I didn’t sign up for that. I signed up for the sunshine, to grow crops and get my hands dirty. And that’s why I’m not as happy as I used to be. But I want this farm to be successful.”

What’s most telling about Reeves’s farm, though, when it comes to the question of produce supply and price structures, is that more than half of the land he owns, about 800 acres, is rented to farmers who grow soybeans and field corn, the type that’s used to make animal feed or corn syrup for soda and cookies or is turned into ethanol. The abundance of corn on Reeves’s land reflects its dominance nationwide. Ninety-seven million acres are planted with corn that goes toward syrup, cattle feed and ethanol, compared with the 240,000 acres planted for spinach, broccoli and cabbage.

Reeves said he could convert his corn land into produce if some basics were covered. He’d need more labor, already harder to secure, or even better, some of the expensive mechanization employed regularly for field corn: machines that could harvest broccoli, for instance, without damaging the heads. He’d also need more irrigation lines, because leafy vegetables can’t rely just on rainfall the way field corn can. But corn has become so dominant in American agriculture that it has spawned its own separate industry, with a host of incentives that sometimes tempt him to give up produce altogether. Field-corn farmers get turnkey service from agribusiness companies, including one-stop financing, supplies and technical aid. They spend about six weeks planting and six weeks harvesting, with much of the summer freed up to do other farm work. And when they do work the crop, they typically ride in tractors and combines, many with air-conditioning and stereos. “You can never overstate the desire of farmers to sit on their butts,” Reeves said. “We’re human, too.”

There are also huge financial supports for corn. A spokesman for the National Corn Growers Association told me that they conservatively estimate that two of the largest seed producers, Monsanto and DuPont Pioneer, together spend $2 billion a year on research and development for corn. This is the lab and genetics work that has driven yields upward by 1 percent each year. (Monsanto does spend some money on vegetable research — $181 million for 22 separate crops.) Government spending mirrors the private sector. Greens and leafy vegetables, for example, together get only $13 million from the government in research funding; corn receives $121 million.

Vast opportunities to increase production — and therefore lower the price — of produce are being lost. A few years ago, Reeves experimented with planting broccoli, most of which is still grown in California. Expanding produce production in the rest of the country would not only boost supplies but would also give consumers access to fresher, local fare. But he lost his entire crop when the heads suddenly bolted, bursting the green florets into yellowish petals. This is the kind of problem that could be addressed if there were more research money available to develop different strains; at the moment, the only money available for that is a tiny $3.2 million grant from the Department of Agriculture.