American wheat farmers, whose incomes have been reduced to almost Depression-era levels, have apparently cut back on next year's crop to a surprising extent, the Agriculture Department said yesterday, and wheat prices could rise as a result.

The department's initial estimate of the 1978 winter wheat crop, which was planted this fall, shows that growers planted 14 per cent fewer acres than last year and that the 1978 crop could be 13 per cent smaller. Low prices, bad weather and the Carter administration's acreage idling program, designed to boost farm prices by reducing harvests, appear to account for the reductions.

"All in all, it would seem to indicate a production decrease a little larger than we had anticipated," said Agriculture's Howard Hjort. The department had estimated an 8 per cent reduction in the wheat crop in response to its land set-aside program. "There should be a strengthening in price," he said.

That news comes as untold numbers of American farmers are caught in the worst squeeze of high costs and low prices since the Great Depression.Many have taken to the streets with their tractors in a protest for higher prices, and their so-called farm strike, begun a week ago, continued yesterday with sporadic picketing and efforts to get food processors and warehouses to shut down temporarily.

But the crop estimate could also further disturb critics of the set-aside program. They had argued against it, saying that bad weather conditions in some parts of the world could rapidly deplete the now vast worldwide grain stocks and lead to food shortages like those of the early 1970s.

After three years of bountiful harvests, the United States now has enough wheat on hand to meet domestic needs for two years, according to the department. The result has been prices so low they don't cover the costs of growing the wheat.

Hjort and other department officials said the final size of the winter wheat crop will still depend on weather conditions, which could raise or lower the yield, and how many farmers actually join in the set-aside program and not harvest or plant 20 per cent of their land.

The winter wheat crop accounts for two-thirds to three-fourths of all wheat grown in the country, with the rest planted in the spring.

Yesterday's estimate, which coincides with rising U.S. grain sale abroad, was put at 1.32 billion bushels of winter wheat, compared with 1.52 billion bushels for the 1977 crop. If price increases follow, they would temper the amount of subsidy payments to farmers from the U.S. Treasury, which is now mailing out $1.2 billion in wheat subsidy checks.

The effect on consumer goods is less clear and would depend on the size of the increases; a loaf of bread contains 3 cents worth of wheat at today's prices. One federal government study found that when wheat prices rose sharply in the early 1970s, bakers raised their prices to offset their increased costs.

But when wheat prices dropped, the study found that the bakers kept their prices high for more profit.

The Agriculture Department said yesterday that winter wheat cutbacks were the most extensive east of the Mississippi where wheat is traditionally grown as a secondary cash crop. Lesser acreage reductions were noted in the Great Plains states.

Many major wheat producing states show acreage reductions far below the 20 per cent called for in the set-aside program. Thus, if large numbers of farmers in these states eventually decide not to harvest all of their crop, winter wheat production could be still lower.

On the other hand, if weather conditions improve, particularly in Texas, the actual final harvest could exceed the estimate. The department says that its survey of winter wheat, made as of Dec. 1, has historically proven to be correct within 10 per cent two out of three times.