Its sweet taste and low calorie count have made Greek yogurt a product that’s increasingly filling up the shopping carts of New Yorkers.

Experts say the high demand has hiked up the number of Greek yogurt manufacturers, causing a ripple effect that has buoyed the demand for milk from dairy farmers statewide.

In fact, Greek yogurt plants are hatching and growing at a rate that’s siphoned off much of the local milk supply at surrounding dairy farms — the pace of growth is too fast for farmers to keep up.

Though the north country is outside of the main network of Greek yogurt plants in Western and Central New York, manufacturers’ demand for milk has had a noticeable ripple effect here, too. Milk cooperatives here are now taking as much product as they can get, said Jay M. Matteson, agricultural coordinator for Jefferson County. It’s partly why about 20 dairy farms in Jefferson County are expanding their milking operations this year.

“The Greek yogurt demand in the state has certainly tightened up the milk supply across the state,” he said. “It’s keeping manufacturers’ demand for milk from our farms high so there’s a place for it to be shipped.”

Farmers in the north country, who battle low milk prices and low crop yields, are increasing the size of their dairy operations if they can, Mr. Matteson said. They’re expanding the size of their barns to make space for more cows in some cases, or keeping the young stock they’ve raised to sell to produce milk instead.

“Farmers know manufacturers need milk,” he said. “I know one farmer in particular (in Jefferson County) who purchased another farm that was out of operation because his children are interested in taking it over.”

But today’s milk prices are still down from last year in spite of the high demand in New York state, Mr. Matteson said. Prices were $17 to $18 per hundredweight last year but have now sunk to the $16 range.

Mr. Matteson said the oversupply of milk in the U.S. is why prices are still low in the state, even though demand here is higher than ever.

“That’s what’s frustrating for our farmers who are watching milk prices drop in New York state, where the milk supply is tight,” he said. “We’re not able to take advantage of the local demand.”

It’s tough for farmers to expand their operations when they’re not earning enough revenue by selling their milk. It’s a problem for most of the farmers here, who are barely getting by from year to year, said Arthur F. Baderman, agricultural outreach coordinator for Cornell Cooperative Extension of Jefferson County. While farmers hear the news that the Greek yogurt industry is booming, he said, they’re still cautious in making new investments.

“All improvement projects on farms to get more milk per animal add costs, but farmers need a higher price for their milk to afford them. Many farmers are still trying to get caught up from when the milk prices dropped in 2009. It takes several years,” he said, adding that milk prices tanked to between $11 and $12 per hundredweight that year.

The local milk supply in Jefferson, Lewis and St. Lawrence counties is now almost maxed out, Mr. Baderman said. He said Great Lakes Cheese in Adams, for example, can’t fill its milk quota from local suppliers to keep up with its rate of processing growth.

Today’s low milk supply in the north country is why most of the Greek yogurt plants are hatched in Western and Central New York instead, where they can fuel their operations with a greater supply, Mr. Baderman said. Yogurt plants need a lot to operate: three gallons of milk are need for every gallon of Greek yogurt.

“I doubt if there’ll be any Greek yogurt made around here unless one of the dairy plants expands to make it,” Mr. Baderman said. “There’s no incentive for any plant to make it here because most of the milk is in other parts of the state.”

Nonetheless, north country farmers already are reaping the benefits of the yogurt boom indirectly.

The majority of farmers here ship their milk to Dairylea Cooperative Inc., Syracuse, which has grown in a major way from the Greek yogurt boom, said Jennifer J. Huson, director of communications. The dairy farmers’ cooperative, which ships milk to giants such as Chobani Yogurt, garners milk from about 1,000 farms across the state, she said. Jefferson and St. Lawrence counties are its top producers.

Cooperatives such as Dairylea are expected to have ample future demand as more yogurt producers set up shop, Ms. Huson said. The escalating yogurt demand also has offset the waning demand for fluid milk products.

“A lot of that milk is being shifted to yogurt now because not as many people are purchasing fluid milk,” she said. “Farmers across the state are benefiting from the Greek yogurt boom.”

The state Legislature is trying to help dairy farmers produce enough milk to meet the rising demand with tax breaks and grants. Still, farmers will have to increase their total production by at least 15 percent to supply the growing demand, said Steve Ammerman, manager of public affairs for the New York Farm Bureau.

Farmers face a number of headwinds they could do without, Mr. Ammerman said. The Farm Bureau is trying to discontinue costly regulations implemented by the state Concentrated Animal Feeding Operations program that kick in at dairy farms with herds of 200 or more cows. The Environmental Protection Agency dairy program, by contrast, calls for regulations for herds with 300 or more cows.

Increasing “the threshold would make it easier to operate and expand operations,” he said.

Mr. Ammerman said about 800 of the state’s dairy farms have between 100 and 199 cows. If that group increased its herd size by only 10 percent, the state would produce an additional 160 million pounds of milk a year.

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